Árboles de decisión, Machine Learning
JOSE BAEZA D.
29-05-2019
PROF. MJAV
Considere los datos “salary.csv”, que contiene información recabada en una empresa, sobre potenciales clientes y cuya descripción se muestra en la siguiente tabla.
Realice las siguientes actividades:
(1) Cargue el conjunto de datos en la sesión de trabajo de R.
(2) Simule 9.768 valores aleatorios 1 y 2 en proporciones 2/3 a 1/3 a través de la función sample(). Utilice aquellas tuplas de la base de datos asociadas al valor 1 para el conjunto de entrenamiento, y las restantes para el conjunto de validación. Utilice la semilla 1, mediante el comando set.seed(1).
(3) Construya un árbol de decisión para la variable clase, utilizando como criterio el índice de Gini. Realice el procedimiento completo, incluyendo la poda del árbol, usando los comandos rpart(), cptable() y prune() de la librería rpart. Use la opción cp = 0:012 en el proceso de poda.
(4) Utilizando la función naiveBayes() de la librería e1071 construya un clasificador de Bayes Ingenuo. Utilice la corrección de Laplace en caso de haber celdas vacías, laplace = 1.
(5) Utilizando los datos de validación, calcule: i. La sensibilidad del procedimiento de clasi…cación, de…nida como el porcentaje de personas para las que el modelo predice un sueldo anual mayor a US$50:000, dentro de todas aquellas que en realidad tienen un sueldo mayor a dicha cantidad. ii. La especi…cidad del procedimiento de clasi…cación, de…nida como el porcentaje de personas para las que el modelo predice un sueldo anual menor o igual a US$50:000, dentro de todas aquellas que en realidad tienen un sueldo menor o igual a dicha cantidad. iii. La precisión del procedimiento de clasi…cación, de…nida como el porcentaje de personas clasi…cadas correctamente. Interprete cada uno de los resultados obtenidos y compare los clasi…cadores. Utilice la función predict() para realizar las predicciones; puede utilizar la función mmetric(), de la librería rminer para veri…car sus resultados.
(1)
Carga de datos y limpieza
tabla<-read.csv2("salary.csv") # Lectura de .CSV desde la importación desde "Import Dataset"
tabla<-data.frame(tabla)
#La tabla inicial posee datos con caracteres "?" los cuales pueden generar errores al no ser reconocidos, por lo que se transformarán cada uno de estos en NA
tabla$trabajo[tabla$trabajo=="?"]<-NA
tabla$ocupacion[tabla$ocupacion=="?"]<-NA
tabla$pais[tabla$pais=="?"]<-NA
tabla(2)
Función Sample
sample(x,size, replace=FALSE,prob) muestra (x, tamaño, reemplazar = FALSO, prob = NULL)
Semilla
set.seed(1) Definir una semilla permite mantener el valor simulado fijo.
Probabilidad
Se generará dos valores aleatorios en proporciones distintas, con un largo total de 9768
La proporción se define como:
\(9768\approx[\frac{2}{3};\frac{1}{3}]\)
\(\frac{2}{3}=\frac{9768}{3}*2=6470\)
\(\frac{1}{3}=\frac{9768}{3}=3298\)
Luego se definiran los datos para entrenamiento=1 y validación=2
#Otra forma de definir la probabilidad de c(2/3, 1/3)
dos<-(9768/3)*2 # 2/3
un<-(9768/3) # 1/3
#Se generan los datos solicitados
set.seed(1);
aleatt<- sample(1:2, 9768, replace=TRUE, prob=c(dos, un))
table(aleatt)## aleatt
## 1 2
## 6470 3298#Creamos el set de entrenamiento y validación
entrenamiento<- tabla[aleatt==1,]
validacion<- tabla[aleatt==2,]
length(entrenamiento)## [1] 9 length(validacion)## [1] 9(3)
Árbol de decisión para la variable clase
Índice de GINI: En 1912, el ideólogo y estadístico italiano Corrado Gini desarrolló una metodología para medir el nivel de desigualdad en los países. Según la lógica del método, la desigualdad puede medirse en función de una escala que va del número 0 al número 1, siendo 0 el indicador de igualdad más alto y el 1 el de desigualdad máxima. https://www.statsdirect.com/help/default.htm#nonparametric_methods/gini.htm
A. Para cultivar y hacer crecer el árbol use:
usamos rpart(formula, data=, method=,control=)formula; outcome ~ predictor1+predictor2+predictor3+ect. resultado ~ predictor1 + predictor2 + predictor3 + ect.
data= especifica el marco de datos
method= “clase” para un árbol de clasificación “anova” para un árbol de regresión
control= Parámetros opcionales para controlar el crecimiento del árbol. Por ejemplo, control = rpart.control (minsplit = 30, cp = 0.001) requiere que el número mínimo de observaciones en un nodo sea 30 antes de intentar una división y que una división deba disminuir la falta general de ajuste por un factor de 0.001 ( factor de complejidad de costos) antes de ser intentado.
B. Examinar los resultados. Las siguientes funciones nos ayudan a examinar los resultados.
printcp ( ajuste ) mostrar tabla cp plotcp ( ajuste ) resultados de la validación cruzada de la trama rsq.rpart ( ajuste ) parcela aproximada R-cuadrado y error relativo para diferentes divisiones (2 parcelas). Las etiquetas solo son apropiadas para el método “anova”. impresión ( ajuste ) imprimir resultados resumen ( ajuste ) Resultados detallados incluyendo divisiones sustitutas parcela ( ajuste ) árbol de decisión de la trama texto ( ajuste ) etiqueta el diagrama del árbol de decisión publicar ( ajuste , archivo =) crear una gráfica de posdata del árbol de decisión
library(rpart)
library(rpart.plot)
#Uso de comando rpart()
modelo_arbol<-rpart(clase~., data = entrenamiento,parms = list(split = "gini"))
printcp (modelo_arbol)##
## Classification tree:
## rpart(formula = clase ~ ., data = entrenamiento, parms = list(split = "gini"))
##
## Variables actually used in tree construction:
## [1] educacion familiar ocupacion
##
## Root node error: 1514/6470 = 0.234
##
## n= 6470
##
## CP nsplit rel error xerror xstd
## 1 0.115258 0 1.00000 1.00000 0.022493
## 2 0.011889 2 0.76948 0.80053 0.020729
## 3 0.010000 3 0.75760 0.77279 0.020448summary(modelo_arbol)## Call:
## rpart(formula = clase ~ ., data = entrenamiento, parms = list(split = "gini"))
## n= 6470
##
## CP nsplit rel error xerror xstd
## 1 0.11525760 0 1.0000000 1.0000000 0.02249317
## 2 0.01188904 2 0.7694848 0.8005284 0.02072925
## 3 0.01000000 3 0.7575958 0.7727873 0.02044809
##
## Variable importance
## familiar estado.civil educacion sexo ocupacion
## 34 33 15 10 7
## trabajo
## 1
##
## Node number 1: 6470 observations, complexity param=0.1152576
## predicted class=<=50K expected loss=0.2340031 P(node) =1
## class counts: 4956 1514
## probabilities: 0.766 0.234
## left son=2 (3520 obs) right son=3 (2950 obs)
## Primary splits:
## familiar splits as RLLLLR, improve=440.70920, (0 missing)
## estado.civil splits as LRRLLLL, improve=427.93730, (0 missing)
## educacion splits as LLLLLLLLLRRLRLRL, improve=232.02290, (0 missing)
## ocupacion splits as -LRLRLLLLLRLRRL, improve=203.43240, (364 missing)
## sexo splits as LR, improve= 94.76942, (0 missing)
## Surrogate splits:
## estado.civil splits as LRRLLLL, agree=0.992, adj=0.983, (0 split)
## sexo splits as LR, agree=0.685, adj=0.309, (0 split)
## ocupacion splits as -LLRRRLLLLRRLLR, agree=0.586, adj=0.092, (0 split)
## educacion splits as LLLLLRRLLRRLRLRL, agree=0.570, adj=0.057, (0 split)
## trabajo splits as -LLLLRRLR, agree=0.552, adj=0.017, (0 split)
##
## Node number 2: 3520 observations
## predicted class=<=50K expected loss=0.06505682 P(node) =0.5440495
## class counts: 3291 229
## probabilities: 0.935 0.065
##
## Node number 3: 2950 observations, complexity param=0.1152576
## predicted class=<=50K expected loss=0.4355932 P(node) =0.4559505
## class counts: 1665 1285
## probabilities: 0.564 0.436
## left son=6 (1977 obs) right son=7 (973 obs)
## Primary splits:
## educacion splits as LLLLLLLRLRRLRLRL, improve=172.52180, (0 missing)
## ocupacion splits as -RRLRLLLLLRLRRL, improve=170.15930, (118 missing)
## trabajo splits as -RL-LRLLL, improve= 33.80523, (118 missing)
## pais splits as -RLLLRRRLRRRLLR--R-RRRRRLLLLLLLLR-RRL-RLR, improve= 16.71704, (52 missing)
## raza splits as LRLLR, improve= 5.19382, (0 missing)
## Surrogate splits:
## ocupacion splits as -LRLRLLLLLRLLLL, agree=0.737, adj=0.201, (0 split)
## raza splits as LRLLL, agree=0.675, adj=0.015, (0 split)
##
## Node number 6: 1977 observations
## predicted class=<=50K expected loss=0.3156297 P(node) =0.3055641
## class counts: 1353 624
## probabilities: 0.684 0.316
##
## Node number 7: 973 observations, complexity param=0.01188904
## predicted class=>50K expected loss=0.3206578 P(node) =0.1503864
## class counts: 312 661
## probabilities: 0.321 0.679
## left son=14 (132 obs) right son=15 (841 obs)
## Primary splits:
## ocupacion splits as -RRLRLLLL-RLRRR, improve=20.393600, (36 missing)
## educacion splits as -------L-LR-R-R-, improve=14.514860, (0 missing)
## pais splits as -LRLR--L-RRRR----R-RRRRLL-RL-RL-R-RR--RLR, improve= 9.232124, (23 missing)
## trabajo splits as -RR-RRLR-, improve= 4.923184, (36 missing)
## raza splits as LLLRR, improve= 2.776767, (0 missing)
##
## Node number 14: 132 observations
## predicted class=<=50K expected loss=0.4318182 P(node) =0.02040185
## class counts: 75 57
## probabilities: 0.568 0.432
##
## Node number 15: 841 observations
## predicted class=>50K expected loss=0.2818074 P(node) =0.1299845
## class counts: 237 604
## probabilities: 0.282 0.718prp(modelo_arbol, type = 2, extra = 6, split.font = 3, box.col = c("110011","110101"))
Uso de comando prune() podaremos el árbol al tamaño deseado comando: prune(fit,cp=xxx)
cp=0.012 Signifíca que una división deba disminuir la falta general de ajuste por un factor de 0.012 ( factor de complejidad de costos) antes de ser intentado.
modelo_arbol_prune <- prune(modelo_arbol, cp = 0.012)
printcp (modelo_arbol_prune)##
## Classification tree:
## rpart(formula = clase ~ ., data = entrenamiento, parms = list(split = "gini"))
##
## Variables actually used in tree construction:
## [1] educacion familiar
##
## Root node error: 1514/6470 = 0.234
##
## n= 6470
##
## CP nsplit rel error xerror xstd
## 1 0.11526 0 1.00000 1.00000 0.022493
## 2 0.01200 2 0.76948 0.80053 0.020729summary(modelo_arbol_prune)## Call:
## rpart(formula = clase ~ ., data = entrenamiento, parms = list(split = "gini"))
## n= 6470
##
## CP nsplit rel error xerror xstd
## 1 0.1152576 0 1.0000000 1.0000000 0.02249317
## 2 0.0120000 2 0.7694848 0.8005284 0.02072925
##
## Variable importance
## familiar estado.civil educacion sexo ocupacion
## 34 33 15 11 6
## trabajo
## 1
##
## Node number 1: 6470 observations, complexity param=0.1152576
## predicted class=<=50K expected loss=0.2340031 P(node) =1
## class counts: 4956 1514
## probabilities: 0.766 0.234
## left son=2 (3520 obs) right son=3 (2950 obs)
## Primary splits:
## familiar splits as RLLLLR, improve=440.70920, (0 missing)
## estado.civil splits as LRRLLLL, improve=427.93730, (0 missing)
## educacion splits as LLLLLLLLLRRLRLRL, improve=232.02290, (0 missing)
## ocupacion splits as -LRLRLLLLLRLRRL, improve=203.43240, (364 missing)
## sexo splits as LR, improve= 94.76942, (0 missing)
## Surrogate splits:
## estado.civil splits as LRRLLLL, agree=0.992, adj=0.983, (0 split)
## sexo splits as LR, agree=0.685, adj=0.309, (0 split)
## ocupacion splits as -LLRRRLLLLRRLLR, agree=0.586, adj=0.092, (0 split)
## educacion splits as LLLLLRRLLRRLRLRL, agree=0.570, adj=0.057, (0 split)
## trabajo splits as -LLLLRRLR, agree=0.552, adj=0.017, (0 split)
##
## Node number 2: 3520 observations
## predicted class=<=50K expected loss=0.06505682 P(node) =0.5440495
## class counts: 3291 229
## probabilities: 0.935 0.065
##
## Node number 3: 2950 observations, complexity param=0.1152576
## predicted class=<=50K expected loss=0.4355932 P(node) =0.4559505
## class counts: 1665 1285
## probabilities: 0.564 0.436
## left son=6 (1977 obs) right son=7 (973 obs)
## Primary splits:
## educacion splits as LLLLLLLRLRRLRLRL, improve=172.52180, (0 missing)
## ocupacion splits as -RRLRLLLLLRLRRL, improve=170.15930, (118 missing)
## trabajo splits as -RL-LRLLL, improve= 33.80523, (118 missing)
## pais splits as -RLLLRRRLRRRLLR--R-RRRRRLLLLLLLLR-RRL-RLR, improve= 16.71704, (52 missing)
## raza splits as LRLLR, improve= 5.19382, (0 missing)
## Surrogate splits:
## ocupacion splits as -LRLRLLLLLRLLLL, agree=0.737, adj=0.201, (0 split)
## raza splits as LRLLL, agree=0.675, adj=0.015, (0 split)
##
## Node number 6: 1977 observations
## predicted class=<=50K expected loss=0.3156297 P(node) =0.3055641
## class counts: 1353 624
## probabilities: 0.684 0.316
##
## Node number 7: 973 observations
## predicted class=>50K expected loss=0.3206578 P(node) =0.1503864
## class counts: 312 661
## probabilities: 0.321 0.679prp(modelo_arbol_prune, type = 2, extra = 6, split.font = 3, box.col = c("110111","100101"))
(4)
Función naiveBayes() de la librería e1071 Clasificador de Bayes Ingenuo
Probabilistic Learning – Classification Using Naïve Bayes naïve Overview The Idea The naïve Bayes classifier is founded on Bayesian probability, which originated from Reverend Thomas Bayes. Bayesian probability incorporates the concept of conditional probability, the probabilty of event A given that event B has occurred [denoted as \(P(A|B)\)]. In the context of our attrition data, we are seeking the probability of an employee belonging to attrition class \(C_{k}\) (where \(C_{yes} = \text{positive class}\) and \(C_{no} = \text{negative class}\)) given that its predictor values are \(x_{1}, x_{2}, \ldots , x_{p}\). This can be written as \(P(C_{k}|x_{1}, x_{2}, \ldots , x_{p})\).
The Bayesian formula for calculating this probability is \[P(C_{k}|X) = \frac{P(C_{k})P(X|C_{k})}{P(X)}\] where:
- \(P(C_{k}|X)\) is the prior probability of the outcome. Essentially, based on the historical data, what is the probability of the class variable.
- \(P(X)\) is the probability of the predictor variables (same as \(P(C_{k}|x_{1}, x_{2}, \ldots , x_{p})\)). Essentially, based on the historical data, what is the probability of each observed combination of predictor variables. When new data comes in, this becomes our evidence.
- \(P(X|C_{k})\) is the conditional probability or likelihood. Essentially, for each class of the response variable, what is the probability of observing the predictor values.
- \(P(C_{k}|X)\) is called our posterior probability. By combining our observed information, we are updating our a priori information on probabilities to compute a posterior probability that an observation has class \(C_{k}\).
We can re-write Eq. (1) in plain english as: \[\text{posterior} = \frac{\text{prior} \times \text{likelihood}}{\text{evidence}}\]
Although the first equation has simplistic beauty on its surface, it becomes complex and intractable as the number of predictor variables grow. In fact, to compute the posterior probability for a response variable with \(m\) classes and a data set with \(p\) predictors, it would require \(m^p\) probabilities computed. So for example, if we have \(2\) classes and \(31\) variables, we need to calculate \(2^{31} = 2.147.483.648\) probabilities.
library(e1071)
#En los datos de la tabla se observan valores NA por lo que se integra la correción de laplace=1
NB_entrenamiento <- naiveBayes(clase ~ .,data=entrenamiento, laplace = 1)
NB_entrenamiento##
## Naive Bayes Classifier for Discrete Predictors
##
## Call:
## naiveBayes.default(x = X, y = Y, laplace = laplace)
##
## A-priori probabilities:
## Y
## <=50K >50K
## 0.7659969 0.2340031
##
## Conditional probabilities:
## trabajo
## Y ? Federal-gov Local-gov Never-worked Private
## <=50K 0.0002156567 0.0243692042 0.0679318525 0.0004313133 0.7599741212
## >50K 0.0006720430 0.0463709677 0.0725806452 0.0006720430 0.6478494624
## trabajo
## Y Self-emp-inc Self-emp-not-inc State-gov Without-pay
## <=50K 0.0222126375 0.0791459996 0.0450722450 0.0006469700
## >50K 0.0907258065 0.0893817204 0.0504032258 0.0013440860
##
## educacion
## Y 10th 11th 12th 1st-4th 5th-6th
## <=50K 0.0398230088 0.0436444087 0.0150844730 0.0070394208 0.0124698311
## >50K 0.0065359477 0.0065359477 0.0045751634 0.0013071895 0.0006535948
## educacion
## Y 7th-8th 9th Assoc-acdm Assoc-voc Bachelors
## <=50K 0.0235317780 0.0164923572 0.0297666935 0.0458567981 0.1279163315
## >50K 0.0045751634 0.0045751634 0.0405228758 0.0450980392 0.2771241830
## educacion
## Y Doctorate HS-grad Masters Preschool Prof-school
## <=50K 0.0046259051 0.3471440064 0.0355993564 0.0018101368 0.0052292840
## >50K 0.0326797386 0.2058823529 0.1339869281 0.0006535948 0.0496732026
## educacion
## Y Some-college
## <=50K 0.2439662108
## >50K 0.1856209150
##
## estado.civil
## Y Divorced Married-AF-spouse Married-civ-spouse
## <=50K 0.1561555511 0.0008059641 0.3445496675
## >50K 0.0552268245 0.0019723866 0.8468113083
## estado.civil
## Y Married-spouse-absent Never-married Separated Widowed
## <=50K 0.0157163006 0.4102357445 0.0378803143 0.0346564578
## >50K 0.0052596976 0.0756081525 0.0052596976 0.0098619329
##
## ocupacion
## Y ? Adm-clerical Armed-Forces Craft-repair
## <=50K 0.0002154244 0.1361482120 0.0006462732 0.1350710900
## >50K 0.0006693440 0.0662650602 0.0013386881 0.1178045515
## ocupacion
## Y Exec-managerial Farming-fishing Handlers-cleaners
## <=50K 0.0887548470 0.0381301163 0.0629039207
## >50K 0.2576974565 0.0133868809 0.0127175368
## ocupacion
## Y Machine-op-inspct Other-service Priv-house-serv Prof-specialty
## <=50K 0.0766910814 0.1423955192 0.0051701853 0.0982335200
## >50K 0.0388219545 0.0187416332 0.0006693440 0.2342704150
## ocupacion
## Y Protective-serv Sales Tech-support Transport-moving
## <=50K 0.0196036191 0.1109435588 0.0288668677 0.0562257648
## >50K 0.0207496653 0.1385542169 0.0381526104 0.0401606426
##
## familiar
## Y Husband Not-in-family Other-relative Own-child Unmarried
## <=50K 0.303506651 0.301088271 0.036880290 0.202539299 0.123538896
## >50K 0.742763158 0.109868421 0.003947368 0.009210526 0.030263158
## familiar
## Y Wife
## <=50K 0.032446594
## >50K 0.103947368
##
## raza
## Y Amer-Indian-Eskimo Asian-Pac-Islander Black Other
## <=50K 0.012295908 0.027816972 0.109252167 0.011086475
## >50K 0.005266623 0.028308097 0.048716261 0.005924951
## raza
## Y White
## <=50K 0.839548478
## >50K 0.911784068
##
## sexo
## Y Female Male
## <=50K 0.3799919 0.6200081
## >50K 0.1563325 0.8436675
##
## pais
## Y ? Cambodia Canada China Columbia
## <=50K 0.0002032520 0.0004065041 0.0034552846 0.0030487805 0.0030487805
## >50K 0.0006535948 0.0019607843 0.0032679739 0.0019607843 0.0019607843
## pais
## Y Cuba Dominican-Republic Ecuador El-Salvador
## <=50K 0.0022357724 0.0026422764 0.0012195122 0.0034552846
## >50K 0.0039215686 0.0019607843 0.0013071895 0.0006535948
## pais
## Y England France Germany Greece Guatemala
## <=50K 0.0020325203 0.0008130081 0.0034552846 0.0012195122 0.0018292683
## >50K 0.0052287582 0.0013071895 0.0039215686 0.0013071895 0.0006535948
## pais
## Y Haiti Holand-Netherlands Honduras Hong
## <=50K 0.0026422764 0.0004065041 0.0004065041 0.0004065041
## >50K 0.0019607843 0.0006535948 0.0006535948 0.0013071895
## pais
## Y Hungary India Iran Ireland Italy
## <=50K 0.0008130081 0.0030487805 0.0006097561 0.0008130081 0.0010162602
## >50K 0.0006535948 0.0052287582 0.0013071895 0.0039215686 0.0052287582
## pais
## Y Jamaica Japan Laos Mexico Nicaragua
## <=50K 0.0020325203 0.0014227642 0.0006097561 0.0241869919 0.0014227642
## >50K 0.0026143791 0.0026143791 0.0006535948 0.0065359477 0.0013071895
## pais
## Y Peru Philippines Poland Portugal Puerto-Rico
## <=50K 0.0014227642 0.0063008130 0.0032520325 0.0014227642 0.0032520325
## >50K 0.0006535948 0.0026143791 0.0032679739 0.0013071895 0.0019607843
## pais
## Y Scotland South Taiwan Thailand
## <=50K 0.0002032520 0.0026422764 0.0008130081 0.0012195122
## >50K 0.0006535948 0.0013071895 0.0045751634 0.0006535948
## pais
## Y Trinadad&Tobago United-States Vietnam Yugoslavia
## <=50K 0.0002032520 0.9079268293 0.0022357724 0.0002032520
## >50K 0.0006535948 0.9156862745 0.0006535948 0.0013071895(5)
Utilizando los datos de validación, calcule:
i. La sensibilidad del procedimiento de clasificación, definida como el porcentaje de personas para las que el modelo predice un sueldo anual mayor a US$50.000, dentro de todas aquellas que en realidad tienen un sueldo mayor a dicha cantidad.
Ejecuta La Validación Cruzada En V Con Pliegue
Los datos se dividen en V subconjuntos no superpuestos de tamaño aproximadamente igual. Luego, bagging se aplica sobre (V-1) los subconjuntos. Finalmente, se hacen predicciones para los subconjuntos omitidos y el proceso se repite para cada uno de los V subconjuntos.
Los resultados arrojan la siguiente información:
Observed ClassPredicted Class <=50K >50K <=50K 4668 852 >50K 288 662
**El modelo predice un sueldo anual mayor a US$50.000, dentro de todas aquellas que en realidad tienen un sueldo mayor a dicha cantidad correspondiente a 662.**library(adabag)## Loading required package: caret## Loading required package: lattice## Loading required package: ggplot2## Loading required package: foreach## Loading required package: doParallel## Loading required package: iterators## Loading required package: parallellibrary(rpart)
library(lattice)
library(ggplot2)
library(foreach)
library(doParallel)
library(iterators)
library(parallel)
bagging.cv_entrenamiento <- bagging.cv(clase~.,v=10,data=entrenamiento,mfinal=100,control=rpart.control(maxdepth=5))
bagging.cv_entrenamiento## $class
## [1] "<=50K" ">50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" ">50K"
## [9] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [17] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [25] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [33] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K"
## [41] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [49] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [57] ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [65] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [73] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [81] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [89] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [97] ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [105] "<=50K" "<=50K" ">50K" "<=50K" ">50K" ">50K" ">50K" "<=50K"
## [113] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [121] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [129] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K"
## [137] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [145] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [153] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [161] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [169] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [177] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [185] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K"
## [193] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [201] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [209] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [217] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [225] "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [233] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [241] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K"
## [249] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K"
## [257] ">50K" ">50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [265] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K"
## [273] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [281] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [289] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [297] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [305] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [313] ">50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K"
## [321] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [329] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K"
## [337] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [345] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [353] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [361] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [369] "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [377] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [385] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [393] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [401] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [409] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [417] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [425] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [433] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [441] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [449] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [457] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [465] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [473] ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [481] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [489] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K"
## [497] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [505] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [513] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [521] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [529] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [537] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [545] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [553] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [561] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [569] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K"
## [577] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [585] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [593] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [601] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K"
## [609] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [617] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [625] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [633] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [641] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [649] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [657] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [665] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [673] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [681] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [689] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [697] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [705] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [713] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [721] "<=50K" "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" ">50K"
## [729] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [737] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [745] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [753] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [761] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [769] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [777] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [785] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [793] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [801] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [809] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [817] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [825] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [833] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [841] ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [849] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [857] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [865] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [873] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [881] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [889] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [897] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [905] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [913] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [921] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [929] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [937] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [945] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [953] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [961] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [969] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [977] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [985] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [993] ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1001] ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1009] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1017] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1025] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1033] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1041] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1049] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1057] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1065] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1073] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" ">50K"
## [1081] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1089] ">50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1097] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1105] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1113] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1121] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1129] "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1137] "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K"
## [1145] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1153] ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1161] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1169] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1177] ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1185] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1193] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1201] ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1209] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1217] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1225] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1233] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1241] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1249] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1257] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1265] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1273] "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1281] ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1289] "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1297] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K"
## [1305] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1313] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1321] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1329] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1337] "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1345] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1353] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1361] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1369] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1377] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1385] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1393] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1401] "<=50K" ">50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1409] "<=50K" "<=50K" ">50K" ">50K" "<=50K" ">50K" ">50K" "<=50K"
## [1417] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1425] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K"
## [1433] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1441] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1449] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1457] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1465] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1473] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1481] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1489] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1497] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1505] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1513] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K"
## [1521] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1529] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1537] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1545] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1553] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1561] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1569] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1577] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1585] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1593] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1601] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1609] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1617] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1625] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1633] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1641] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1649] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1657] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1665] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1673] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1681] ">50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1689] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1697] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1705] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1713] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1721] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1729] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1737] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1745] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [1753] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1761] "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1769] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1777] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1785] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1793] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1801] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1809] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1817] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1825] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1833] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1841] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [1849] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1857] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K"
## [1865] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1873] "<=50K" "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" ">50K"
## [1881] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1889] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1897] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1905] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1913] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1921] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1929] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1937] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [1945] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1953] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [1961] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1969] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [1977] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" ">50K"
## [1985] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [1993] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2001] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2009] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" ">50K" ">50K"
## [2017] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2025] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2033] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2041] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2049] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2057] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2065] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2073] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2081] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2089] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [2097] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [2105] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [2113] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2121] ">50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2129] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2137] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2145] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [2153] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2161] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2169] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2177] ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2185] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2193] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [2201] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2209] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K"
## [2217] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [2225] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2233] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2241] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2249] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2257] "<=50K" "<=50K" ">50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [2265] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2273] ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2281] "<=50K" "<=50K" "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K"
## [2289] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2297] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2305] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [2313] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2321] "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2329] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K"
## [2337] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2345] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2353] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2361] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [2369] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2377] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2385] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2393] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K"
## [2401] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2409] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2417] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K"
## [2425] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [2433] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2441] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2449] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2457] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K"
## [2465] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2473] "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K"
## [2481] "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2489] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2497] "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2505] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [2513] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2521] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2529] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2537] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2545] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" ">50K"
## [2553] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [2561] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2569] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [2577] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2585] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2593] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [2601] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" ">50K" "<=50K"
## [2609] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2617] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2625] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [2633] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" ">50K" ">50K"
## [2641] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2649] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2657] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2665] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2673] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2681] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2689] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2697] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2705] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2713] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [2721] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2729] ">50K" "<=50K" ">50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [2737] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K"
## [2745] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2753] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2761] "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2769] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2777] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2785] "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2793] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2801] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2809] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2817] ">50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" ">50K" ">50K"
## [2825] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2833] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2841] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2849] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2857] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2865] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2873] ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2881] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [2889] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2897] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2905] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [2913] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2921] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [2929] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2937] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [2945] "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2953] ">50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [2961] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K"
## [2969] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [2977] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [2985] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K"
## [2993] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3001] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K"
## [3009] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3017] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3025] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K"
## [3033] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [3041] "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [3049] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3057] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K"
## [3065] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [3073] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3081] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3089] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3097] "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [3105] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [3113] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K"
## [3121] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3129] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3137] "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [3145] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [3153] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3161] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3169] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [3177] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K"
## [3185] ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3193] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3201] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3209] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3217] ">50K" "<=50K" "<=50K" ">50K" ">50K" ">50K" ">50K" "<=50K"
## [3225] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [3233] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" ">50K" ">50K"
## [3241] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3249] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3257] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [3265] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3273] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3281] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3289] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3297] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3305] ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K"
## [3313] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3321] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [3329] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3337] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3345] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3353] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3361] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3369] "<=50K" ">50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K"
## [3377] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3385] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3393] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3401] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [3409] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3417] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3425] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3433] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3441] ">50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [3449] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3457] "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3465] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3473] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3481] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3489] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" ">50K" "<=50K"
## [3497] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [3505] ">50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [3513] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K"
## [3521] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3529] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [3537] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3545] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3553] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [3561] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3569] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [3577] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3585] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3593] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3601] ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3609] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3617] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3625] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [3633] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [3641] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K"
## [3649] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3657] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3665] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3673] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3681] "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K"
## [3689] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3697] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3705] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3713] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3721] "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [3729] ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3737] "<=50K" "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [3745] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [3753] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3761] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [3769] "<=50K" "<=50K" "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K"
## [3777] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3785] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3793] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3801] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [3809] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3817] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [3825] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3833] "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3841] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [3849] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3857] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [3865] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K"
## [3873] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3881] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [3889] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3897] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3905] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3913] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3921] ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3929] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3937] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" ">50K"
## [3945] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3953] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3961] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3969] ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3977] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3985] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [3993] "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4001] "<=50K" ">50K" ">50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K"
## [4009] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4017] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4025] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4033] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [4041] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4049] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4057] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4065] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4073] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4081] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [4089] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4097] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4105] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K"
## [4113] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4121] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4129] ">50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4137] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [4145] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4153] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4161] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4169] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [4177] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K"
## [4185] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4193] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4201] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4209] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4217] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [4225] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [4233] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4241] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4249] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4257] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4265] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" ">50K" "<=50K"
## [4273] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4281] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K"
## [4289] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4297] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [4305] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4313] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4321] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [4329] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4337] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4345] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4353] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4361] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4369] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4377] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4385] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4393] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [4401] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4409] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4417] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [4425] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4433] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [4441] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4449] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4457] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4465] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K"
## [4473] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4481] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4489] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4497] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4505] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4513] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [4521] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [4529] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4537] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4545] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4553] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4561] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4569] "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4577] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4585] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4593] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4601] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [4609] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4617] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [4625] ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4633] "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [4641] "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4649] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4657] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4665] "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4673] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4681] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4689] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4697] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [4705] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4713] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4721] "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4729] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4737] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4745] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K"
## [4753] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4761] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4769] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4777] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4785] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4793] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4801] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4809] "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4817] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4825] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4833] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4841] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4849] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4857] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4865] ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4873] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4881] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [4889] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K"
## [4897] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4905] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4913] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4921] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [4929] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4937] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K"
## [4945] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4953] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4961] "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [4969] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [4977] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [4985] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [4993] "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [5001] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5009] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5017] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5025] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" ">50K" "<=50K"
## [5033] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5041] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5049] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5057] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5065] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5073] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5081] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5089] "<=50K" "<=50K" ">50K" "<=50K" ">50K" ">50K" ">50K" "<=50K"
## [5097] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5105] "<=50K" ">50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [5113] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [5121] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5129] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5137] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5145] "<=50K" ">50K" "<=50K" ">50K" ">50K" "<=50K" ">50K" "<=50K"
## [5153] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" ">50K"
## [5161] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5169] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5177] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5185] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5193] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5201] ">50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5209] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5217] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5225] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [5233] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [5241] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5249] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5257] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5265] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5273] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5281] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [5289] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5297] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K"
## [5305] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5313] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5321] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5329] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5337] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5345] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [5353] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5361] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5369] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5377] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5385] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5393] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5401] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5409] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5417] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5425] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5433] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5441] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5449] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5457] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5465] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5473] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [5481] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5489] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5497] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5505] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5513] "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5521] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5529] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [5537] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5545] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5553] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5561] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5569] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5577] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5585] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5593] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5601] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5609] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5617] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5625] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5633] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5641] ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5649] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5657] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K"
## [5665] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5673] "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" ">50K" ">50K"
## [5681] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5689] "<=50K" ">50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" ">50K"
## [5697] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5705] "<=50K" ">50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [5713] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5721] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [5729] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K"
## [5737] ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [5745] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5753] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [5761] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [5769] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5777] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5785] ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5793] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5801] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5809] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5817] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [5825] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5833] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [5841] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5849] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [5857] "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5865] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5873] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5881] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5889] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5897] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5905] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [5913] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5921] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5929] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5937] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5945] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [5953] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5961] "<=50K" "<=50K" ">50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K"
## [5969] ">50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5977] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K"
## [5985] "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [5993] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [6001] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [6009] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6017] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6025] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6033] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6041] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [6049] "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [6057] ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6065] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6073] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6081] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [6089] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [6097] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [6105] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K"
## [6113] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6121] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [6129] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6137] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6145] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6153] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [6161] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6169] "<=50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K" ">50K" "<=50K"
## [6177] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [6185] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6193] "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6201] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6209] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [6217] "<=50K" "<=50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [6225] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6233] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6241] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6249] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [6257] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [6265] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6273] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K"
## [6281] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6289] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6297] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [6305] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [6313] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6321] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K"
## [6329] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K"
## [6337] "<=50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K"
## [6345] "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6353] ">50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K"
## [6361] "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [6369] "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" ">50K"
## [6377] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [6385] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6393] "<=50K" ">50K" "<=50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K"
## [6401] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6409] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K"
## [6417] ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6425] "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K" "<=50K" "<=50K"
## [6433] "<=50K" ">50K" ">50K" ">50K" "<=50K" "<=50K" "<=50K" ">50K"
## [6441] "<=50K" ">50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" ">50K"
## [6449] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" ">50K" ">50K"
## [6457] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" "<=50K" "<=50K" "<=50K"
## [6465] "<=50K" "<=50K" "<=50K" "<=50K" ">50K" ">50K"
##
## $confusion
## Observed Class
## Predicted Class <=50K >50K
## <=50K 4655 848
## >50K 301 666
##
## $error
## [1] 0.1775889predictor_arbol <- predict(modelo_arbol_prune,validacion[,-9])
predictor_arbol2 <- predict(modelo_arbol,validacion[,-9])
predictor_arbol ## <=50K >50K
## 4 0.6843703 0.31562974
## 6 0.9349432 0.06505682
## 7 0.6843703 0.31562974
## 13 0.9349432 0.06505682
## 15 0.9349432 0.06505682
## 17 0.6843703 0.31562974
## 18 0.9349432 0.06505682
## 20 0.3206578 0.67934224
## 21 0.6843703 0.31562974
## 29 0.9349432 0.06505682
## 35 0.9349432 0.06505682
## 36 0.9349432 0.06505682
## 37 0.9349432 0.06505682
## 39 0.3206578 0.67934224
## 41 0.6843703 0.31562974
## 43 0.6843703 0.31562974
## 46 0.3206578 0.67934224
## 49 0.6843703 0.31562974
## 50 0.9349432 0.06505682
## 52 0.9349432 0.06505682
## 61 0.9349432 0.06505682
## 68 0.9349432 0.06505682
## 70 0.9349432 0.06505682
## 72 0.9349432 0.06505682
## 76 0.9349432 0.06505682
## 77 0.9349432 0.06505682
## 79 0.3206578 0.67934224
## 80 0.9349432 0.06505682
## 82 0.9349432 0.06505682
## 85 0.9349432 0.06505682
## 87 0.3206578 0.67934224
## 94 0.6843703 0.31562974
## 95 0.9349432 0.06505682
## 96 0.9349432 0.06505682
## 99 0.9349432 0.06505682
## 104 0.9349432 0.06505682
## 109 0.9349432 0.06505682
## 111 0.9349432 0.06505682
## 112 0.6843703 0.31562974
## 117 0.9349432 0.06505682
## 121 0.3206578 0.67934224
## 125 0.6843703 0.31562974
## 135 0.9349432 0.06505682
## 139 0.9349432 0.06505682
## 141 0.6843703 0.31562974
## 145 0.3206578 0.67934224
## 148 0.6843703 0.31562974
## 150 0.3206578 0.67934224
## 162 0.6843703 0.31562974
## 164 0.3206578 0.67934224
## 165 0.6843703 0.31562974
## 169 0.9349432 0.06505682
## 172 0.9349432 0.06505682
## 173 0.3206578 0.67934224
## 176 0.6843703 0.31562974
## 178 0.9349432 0.06505682
## 180 0.3206578 0.67934224
## 183 0.9349432 0.06505682
## 185 0.6843703 0.31562974
## 187 0.6843703 0.31562974
## 188 0.9349432 0.06505682
## 189 0.3206578 0.67934224
## 191 0.9349432 0.06505682
## 194 0.6843703 0.31562974
## 198 0.6843703 0.31562974
## 200 0.9349432 0.06505682
## 210 0.9349432 0.06505682
## 211 0.9349432 0.06505682
## 213 0.9349432 0.06505682
## 214 0.6843703 0.31562974
## 215 0.6843703 0.31562974
## 218 0.9349432 0.06505682
## 219 0.6843703 0.31562974
## 225 0.9349432 0.06505682
## 230 0.3206578 0.67934224
## 236 0.9349432 0.06505682
## 237 0.6843703 0.31562974
## 243 0.9349432 0.06505682
## 250 0.9349432 0.06505682
## 251 0.6843703 0.31562974
## 252 0.3206578 0.67934224
## 260 0.9349432 0.06505682
## 264 0.6843703 0.31562974
## 265 0.9349432 0.06505682
## 268 0.9349432 0.06505682
## 280 0.9349432 0.06505682
## 283 0.6843703 0.31562974
## 293 0.9349432 0.06505682
## 296 0.9349432 0.06505682
## 300 0.9349432 0.06505682
## 301 0.6843703 0.31562974
## 306 0.6843703 0.31562974
## 308 0.6843703 0.31562974
## 313 0.9349432 0.06505682
## 314 0.9349432 0.06505682
## 319 0.9349432 0.06505682
## 324 0.9349432 0.06505682
## 325 0.9349432 0.06505682
## 326 0.9349432 0.06505682
## 327 0.3206578 0.67934224
## 328 0.9349432 0.06505682
## 330 0.9349432 0.06505682
## 331 0.3206578 0.67934224
## 334 0.3206578 0.67934224
## 340 0.9349432 0.06505682
## 341 0.9349432 0.06505682
## 345 0.9349432 0.06505682
## 350 0.6843703 0.31562974
## 353 0.6843703 0.31562974
## 355 0.9349432 0.06505682
## 357 0.9349432 0.06505682
## 359 0.9349432 0.06505682
## 363 0.6843703 0.31562974
## 366 0.6843703 0.31562974
## 368 0.6843703 0.31562974
## 369 0.3206578 0.67934224
## 373 0.9349432 0.06505682
## 378 0.9349432 0.06505682
## 384 0.9349432 0.06505682
## 387 0.9349432 0.06505682
## 388 0.9349432 0.06505682
## 390 0.9349432 0.06505682
## 393 0.3206578 0.67934224
## 403 0.9349432 0.06505682
## 404 0.3206578 0.67934224
## 405 0.6843703 0.31562974
## 406 0.9349432 0.06505682
## 408 0.9349432 0.06505682
## 410 0.9349432 0.06505682
## 411 0.9349432 0.06505682
## 413 0.6843703 0.31562974
## 414 0.6843703 0.31562974
## 415 0.9349432 0.06505682
## 419 0.3206578 0.67934224
## 420 0.9349432 0.06505682
## 428 0.6843703 0.31562974
## 429 0.9349432 0.06505682
## 430 0.9349432 0.06505682
## 431 0.9349432 0.06505682
## 436 0.3206578 0.67934224
## 437 0.9349432 0.06505682
## 440 0.6843703 0.31562974
## 448 0.6843703 0.31562974
## 451 0.9349432 0.06505682
## 458 0.6843703 0.31562974
## 466 0.9349432 0.06505682
## 467 0.9349432 0.06505682
## 470 0.3206578 0.67934224
## 472 0.3206578 0.67934224
## 473 0.9349432 0.06505682
## 477 0.9349432 0.06505682
## 480 0.9349432 0.06505682
## 481 0.6843703 0.31562974
## 483 0.6843703 0.31562974
## 484 0.9349432 0.06505682
## 489 0.6843703 0.31562974
## 492 0.9349432 0.06505682
## 499 0.9349432 0.06505682
## 502 0.6843703 0.31562974
## 506 0.9349432 0.06505682
## 508 0.6843703 0.31562974
## 509 0.9349432 0.06505682
## 511 0.9349432 0.06505682
## 514 0.9349432 0.06505682
## 515 0.9349432 0.06505682
## 521 0.3206578 0.67934224
## 522 0.9349432 0.06505682
## 526 0.6843703 0.31562974
## 527 0.3206578 0.67934224
## 528 0.6843703 0.31562974
## 529 0.9349432 0.06505682
## 530 0.9349432 0.06505682
## 542 0.9349432 0.06505682
## 547 0.9349432 0.06505682
## 550 0.9349432 0.06505682
## 551 0.9349432 0.06505682
## 554 0.9349432 0.06505682
## 555 0.6843703 0.31562974
## 559 0.9349432 0.06505682
## 560 0.9349432 0.06505682
## 564 0.9349432 0.06505682
## 565 0.6843703 0.31562974
## 566 0.9349432 0.06505682
## 570 0.6843703 0.31562974
## 575 0.6843703 0.31562974
## 577 0.9349432 0.06505682
## 579 0.9349432 0.06505682
## 580 0.9349432 0.06505682
## 582 0.6843703 0.31562974
## 589 0.6843703 0.31562974
## 590 0.3206578 0.67934224
## 593 0.9349432 0.06505682
## 595 0.6843703 0.31562974
## 601 0.9349432 0.06505682
## 602 0.9349432 0.06505682
## 604 0.6843703 0.31562974
## 605 0.9349432 0.06505682
## 606 0.9349432 0.06505682
## 609 0.9349432 0.06505682
## 611 0.6843703 0.31562974
## 615 0.9349432 0.06505682
## 621 0.9349432 0.06505682
## 630 0.6843703 0.31562974
## 631 0.9349432 0.06505682
## 634 0.9349432 0.06505682
## 639 0.6843703 0.31562974
## 640 0.9349432 0.06505682
## 641 0.6843703 0.31562974
## 643 0.9349432 0.06505682
## 645 0.3206578 0.67934224
## 648 0.9349432 0.06505682
## 649 0.9349432 0.06505682
## 650 0.9349432 0.06505682
## 651 0.9349432 0.06505682
## 652 0.9349432 0.06505682
## 659 0.9349432 0.06505682
## 660 0.9349432 0.06505682
## 662 0.6843703 0.31562974
## 667 0.6843703 0.31562974
## 670 0.6843703 0.31562974
## 671 0.6843703 0.31562974
## 673 0.9349432 0.06505682
## 681 0.6843703 0.31562974
## 682 0.9349432 0.06505682
## 690 0.9349432 0.06505682
## 693 0.9349432 0.06505682
## 697 0.6843703 0.31562974
## 699 0.9349432 0.06505682
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## 9768 0.9349432 0.06505682 predictor_arbol2## <=50K >50K
## 4 0.6843703 0.31562974
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## 9240 0.9349432 0.06505682
## 9243 0.9349432 0.06505682
## 9246 0.9349432 0.06505682
## 9247 0.9349432 0.06505682
## 9249 0.6843703 0.31562974
## 9251 0.6843703 0.31562974
## 9253 0.6843703 0.31562974
## 9256 0.9349432 0.06505682
## 9257 0.9349432 0.06505682
## 9264 0.2818074 0.71819263
## 9268 0.9349432 0.06505682
## 9270 0.6843703 0.31562974
## 9271 0.6843703 0.31562974
## 9273 0.9349432 0.06505682
## 9276 0.2818074 0.71819263
## 9278 0.9349432 0.06505682
## 9279 0.6843703 0.31562974
## 9284 0.2818074 0.71819263
## 9287 0.9349432 0.06505682
## 9289 0.9349432 0.06505682
## 9292 0.9349432 0.06505682
## 9300 0.9349432 0.06505682
## 9303 0.9349432 0.06505682
## 9305 0.6843703 0.31562974
## 9307 0.9349432 0.06505682
## 9316 0.9349432 0.06505682
## 9321 0.9349432 0.06505682
## 9330 0.2818074 0.71819263
## 9333 0.6843703 0.31562974
## 9336 0.9349432 0.06505682
## 9338 0.9349432 0.06505682
## 9341 0.6843703 0.31562974
## 9342 0.9349432 0.06505682
## 9345 0.9349432 0.06505682
## 9347 0.9349432 0.06505682
## 9352 0.6843703 0.31562974
## 9353 0.9349432 0.06505682
## 9355 0.2818074 0.71819263
## 9358 0.9349432 0.06505682
## 9359 0.6843703 0.31562974
## 9365 0.6843703 0.31562974
## 9370 0.9349432 0.06505682
## 9372 0.6843703 0.31562974
## 9374 0.9349432 0.06505682
## 9377 0.2818074 0.71819263
## 9381 0.9349432 0.06505682
## 9383 0.9349432 0.06505682
## 9384 0.9349432 0.06505682
## 9385 0.2818074 0.71819263
## 9386 0.9349432 0.06505682
## 9387 0.9349432 0.06505682
## 9390 0.9349432 0.06505682
## 9392 0.9349432 0.06505682
## 9393 0.9349432 0.06505682
## 9394 0.9349432 0.06505682
## 9396 0.9349432 0.06505682
## 9399 0.5681818 0.43181818
## 9402 0.9349432 0.06505682
## 9403 0.9349432 0.06505682
## 9405 0.5681818 0.43181818
## 9407 0.6843703 0.31562974
## 9408 0.9349432 0.06505682
## 9410 0.6843703 0.31562974
## 9412 0.6843703 0.31562974
## 9413 0.9349432 0.06505682
## 9414 0.9349432 0.06505682
## 9416 0.9349432 0.06505682
## 9418 0.6843703 0.31562974
## 9422 0.9349432 0.06505682
## 9426 0.9349432 0.06505682
## 9427 0.6843703 0.31562974
## 9431 0.6843703 0.31562974
## 9432 0.9349432 0.06505682
## 9436 0.9349432 0.06505682
## 9440 0.6843703 0.31562974
## 9441 0.2818074 0.71819263
## 9443 0.9349432 0.06505682
## 9447 0.6843703 0.31562974
## 9452 0.9349432 0.06505682
## 9457 0.9349432 0.06505682
## 9461 0.9349432 0.06505682
## 9462 0.9349432 0.06505682
## 9469 0.9349432 0.06505682
## 9471 0.9349432 0.06505682
## 9472 0.9349432 0.06505682
## 9473 0.6843703 0.31562974
## 9476 0.2818074 0.71819263
## 9477 0.9349432 0.06505682
## 9479 0.9349432 0.06505682
## 9480 0.6843703 0.31562974
## 9482 0.9349432 0.06505682
## 9483 0.6843703 0.31562974
## 9484 0.2818074 0.71819263
## 9489 0.9349432 0.06505682
## 9491 0.9349432 0.06505682
## 9493 0.9349432 0.06505682
## 9496 0.6843703 0.31562974
## 9501 0.9349432 0.06505682
## 9502 0.5681818 0.43181818
## 9507 0.9349432 0.06505682
## 9508 0.9349432 0.06505682
## 9515 0.9349432 0.06505682
## 9517 0.9349432 0.06505682
## 9523 0.9349432 0.06505682
## 9525 0.9349432 0.06505682
## 9530 0.2818074 0.71819263
## 9535 0.9349432 0.06505682
## 9545 0.9349432 0.06505682
## 9555 0.9349432 0.06505682
## 9556 0.9349432 0.06505682
## 9558 0.9349432 0.06505682
## 9563 0.6843703 0.31562974
## 9570 0.9349432 0.06505682
## 9571 0.9349432 0.06505682
## 9575 0.6843703 0.31562974
## 9578 0.9349432 0.06505682
## 9581 0.9349432 0.06505682
## 9583 0.2818074 0.71819263
## 9594 0.9349432 0.06505682
## 9596 0.2818074 0.71819263
## 9598 0.6843703 0.31562974
## 9602 0.9349432 0.06505682
## 9603 0.9349432 0.06505682
## 9604 0.9349432 0.06505682
## 9607 0.2818074 0.71819263
## 9613 0.6843703 0.31562974
## 9615 0.6843703 0.31562974
## 9617 0.9349432 0.06505682
## 9621 0.5681818 0.43181818
## 9623 0.9349432 0.06505682
## 9624 0.9349432 0.06505682
## 9627 0.9349432 0.06505682
## 9633 0.2818074 0.71819263
## 9634 0.2818074 0.71819263
## 9637 0.6843703 0.31562974
## 9640 0.2818074 0.71819263
## 9642 0.9349432 0.06505682
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## 9652 0.9349432 0.06505682
## 9653 0.6843703 0.31562974
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## 9661 0.6843703 0.31562974
## 9662 0.9349432 0.06505682
## 9663 0.5681818 0.43181818
## 9668 0.9349432 0.06505682
## 9680 0.6843703 0.31562974
## 9681 0.9349432 0.06505682
## 9687 0.6843703 0.31562974
## 9688 0.9349432 0.06505682
## 9691 0.6843703 0.31562974
## 9697 0.6843703 0.31562974
## 9698 0.9349432 0.06505682
## 9699 0.9349432 0.06505682
## 9704 0.9349432 0.06505682
## 9712 0.6843703 0.31562974
## 9713 0.9349432 0.06505682
## 9715 0.6843703 0.31562974
## 9722 0.6843703 0.31562974
## 9723 0.9349432 0.06505682
## 9728 0.9349432 0.06505682
## 9730 0.9349432 0.06505682
## 9731 0.9349432 0.06505682
## 9733 0.9349432 0.06505682
## 9734 0.2818074 0.71819263
## 9736 0.6843703 0.31562974
## 9737 0.2818074 0.71819263
## 9743 0.6843703 0.31562974
## 9747 0.6843703 0.31562974
## 9751 0.9349432 0.06505682
## 9753 0.6843703 0.31562974
## 9755 0.9349432 0.06505682
## 9756 0.6843703 0.31562974
## 9758 0.9349432 0.06505682
## 9760 0.9349432 0.06505682
## 9768 0.9349432 0.06505682ii. La especificidad del procedimiento de clasi…cación, de…nida como el porcentaje de personas para las que el modelo predice un sueldo anual menor o igual a US$50.000, dentro de todas aquellas que en realidad tienen un sueldo menor o igual a dicha cantidad.
iii. La precisión del procedimiento de clasificación, definida como el porcentaje de personas clasificadas correctamente. Interprete cada uno de los resultados obtenidos y compare los clasificadores. Utilice la función predict() para realizar las predicciones; puede utilizar la función mmetric(), de la librería rminer para verificar sus resultados.
library(rminer)
# Determinación de la precisiÓn
mmetric(validacion[,9],predictor_arbol,"ACC") ## [1] 82.50455# Determinación de la sensibilidad
mmetric(validacion[,9],predictor_arbol,"TPR") ## [1] 94.20056 46.87117 # Determinación de la especificidad
mmetric(validacion[,9],predictor_arbol,"TNR")## [1] 46.87117 94.20056ROC_predictor_arbol <- mmetric(validacion[,9],predictor_arbol,"ROC")
AUC_predictor_arbol<- mmetric(validacion[,9],predictor_arbol,"AUC")
AUC_predictor_arbol## [1] 0.8086156plot(ROC_predictor_arbol$ROC$ROC[,1],ROC_predictor_arbol$ROC$ROC[,2],ylim = 0:1,xlim=0:1, "p", col="GREEN", xlab = "FPR or (1 - especificidad)", ylab="TPR o sensibilidad")
par(new=TRUE)