#importar datos y librerias
library(pacman)
p_load("base64enc", "htmltools", "mime", "xfun", "prettydoc", "readr", "knitr", "DT", "tidyverse", "scales", "gridExtra", "modeest", "fdth")
pozos_3_ <- readxl::read_excel("pozos (3).xlsx")
View(pozos_3_)Preguntas teoricas
##¿Qué es la estadística y que aplicaciones tiene en ingeniería (según su ingeniería)? * se describe como el lenguaje universal de la ciencia, la estadistica usa numeros para resumir información y su interpretación. resumen: es la ciencia de recolectar, describir e interpretar datos.
- en matematicas la estadistica es la aplicación de modelos probabilisticos.
##Enliste y defina los tipos de variables usados en estadística, de 2 ejemplos de cada uno. Defina distribución de frecuencia y explique que es la distribución normal. * tipos de variables: -variables cualitativas: no se pueden medir numéricamente. -variables cuantitativas: tienen valor numerico.
- distribucion de frecuencia: es la representación estructurada, en forma de tabla o gráfica, de toda la información que se ha recogido sobre la varibale que se estudia.
Usando datos de Ph y Temperatura de pozos de agua subterrania
##Ordenar datos de mayor a menor.
#ordenando datos de menor a mayor de la mediante un data.frame
datosPh <- pozos_3_$PH
datosTemp <- pozos_3_$TEMP
datosPh <- sort(datosPh, decreasing = FALSE)
datosTemp <- sort(datosTemp, decreasing = FALSE)
dfGeneral <-data.frame(datosPh, datosTemp)
#data frame ordenado de menor a mayor
dfGeneral## datosPh datosTemp
## 1 6.1 25.6
## 2 6.3 25.8
## 3 6.4 26.2
## 4 6.4 26.3
## 5 6.4 26.3
## 6 6.4 26.4
## 7 6.4 26.4
## 8 6.4 26.8
## 9 6.4 26.8
## 10 6.5 26.9
## 11 6.5 27.0
## 12 6.5 27.0
## 13 6.5 27.1
## 14 6.5 27.2
## 15 6.5 27.2
## 16 6.5 27.3
## 17 6.5 27.3
## 18 6.5 27.3
## 19 6.5 27.3
## 20 6.5 27.4
## 21 6.5 27.4
## 22 6.5 27.4
## 23 6.5 27.4
## 24 6.5 27.4
## 25 6.5 27.5
## 26 6.5 27.5
## 27 6.6 27.5
## 28 6.6 27.5
## 29 6.6 27.5
## 30 6.6 27.5
## 31 6.6 27.5
## 32 6.6 27.5
## 33 6.6 27.5
## 34 6.6 27.5
## 35 6.6 27.5
## 36 6.6 27.5
## 37 6.6 27.6
## 38 6.6 27.7
## 39 6.6 27.7
## 40 6.6 27.7
## 41 6.6 27.7
## 42 6.6 27.8
## 43 6.6 27.8
## 44 6.6 27.8
## 45 6.6 27.8
## 46 6.6 27.8
## 47 6.6 27.8
## 48 6.6 27.8
## 49 6.6 27.8
## 50 6.7 27.8
## 51 6.7 27.8
## 52 6.7 27.8
## 53 6.7 27.9
## 54 6.7 27.9
## 55 6.7 27.9
## 56 6.7 27.9
## 57 6.7 27.9
## 58 6.7 27.9
## 59 6.8 27.9
## 60 6.8 27.9
## 61 6.8 27.9
## 62 6.8 27.9
## 63 6.8 27.9
## 64 6.8 27.9
## 65 6.8 27.9
## 66 6.8 27.9
## 67 6.8 28.0
## 68 6.8 28.0
## 69 6.8 28.0
## 70 6.8 28.0
## 71 6.8 28.0
## 72 6.8 28.0
## 73 6.8 28.0
## 74 6.8 28.0
## 75 6.8 28.0
## 76 6.8 28.0
## 77 6.8 28.0
## 78 6.8 28.0
## 79 6.8 28.0
## 80 6.8 28.0
## 81 6.8 28.0
## 82 6.8 28.0
## 83 6.8 28.0
## 84 6.8 28.0
## 85 6.8 28.1
## 86 6.8 28.1
## 87 6.8 28.1
## 88 6.8 28.2
## 89 6.8 28.2
## 90 6.8 28.2
## 91 6.8 28.2
## 92 6.8 28.2
## 93 6.8 28.2
## 94 6.8 28.2
## 95 6.8 28.2
## 96 6.8 28.2
## 97 6.8 28.2
## 98 6.8 28.2
## 99 6.8 28.2
## 100 6.8 28.3
## 101 6.8 28.3
## 102 6.8 28.3
## 103 6.8 28.3
## 104 6.8 28.3
## 105 6.8 28.3
## 106 6.8 28.3
## 107 6.8 28.4
## 108 6.8 28.4
## 109 6.8 28.4
## 110 6.8 28.4
## 111 6.8 28.4
## 112 6.8 28.4
## 113 6.8 28.4
## 114 6.8 28.5
## 115 6.8 28.5
## 116 6.8 28.5
## 117 6.9 28.5
## 118 6.9 28.5
## 119 6.9 28.5
## 120 6.9 28.5
## 121 6.9 28.5
## 122 6.9 28.5
## 123 6.9 28.6
## 124 6.9 28.6
## 125 6.9 28.6
## 126 6.9 28.6
## 127 6.9 28.6
## 128 6.9 28.6
## 129 6.9 28.6
## 130 6.9 28.6
## 131 6.9 28.6
## 132 6.9 28.6
## 133 6.9 28.6
## 134 6.9 28.6
## 135 6.9 28.6
## 136 6.9 28.6
## 137 6.9 28.6
## 138 6.9 28.6
## 139 6.9 28.6
## 140 6.9 28.6
## 141 6.9 28.6
## 142 6.9 28.7
## 143 6.9 28.7
## 144 6.9 28.7
## 145 6.9 28.7
## 146 6.9 28.7
## 147 6.9 28.7
## 148 6.9 28.7
## 149 6.9 28.7
## 150 6.9 28.7
## 151 6.9 28.7
## 152 6.9 28.7
## 153 6.9 28.7
## 154 6.9 28.7
## 155 6.9 28.8
## 156 6.9 28.8
## 157 6.9 28.8
## 158 6.9 28.8
## 159 6.9 28.8
## 160 6.9 28.8
## 161 7.0 28.8
## 162 7.0 28.8
## 163 7.0 28.8
## 164 7.0 28.8
## 165 7.0 28.8
## 166 7.0 28.8
## 167 7.0 28.9
## 168 7.0 28.9
## 169 7.0 28.9
## 170 7.0 28.9
## 171 7.0 28.9
## 172 7.0 28.9
## 173 7.0 28.9
## 174 7.0 28.9
## 175 7.0 28.9
## 176 7.0 28.9
## 177 7.0 28.9
## 178 7.0 28.9
## 179 7.0 28.9
## 180 7.0 28.9
## 181 7.0 28.9
## 182 7.0 28.9
## 183 7.0 28.9
## 184 7.0 28.9
## 185 7.0 29.0
## 186 7.0 29.0
## 187 7.0 29.0
## 188 7.0 29.0
## 189 7.0 29.0
## 190 7.0 29.0
## 191 7.0 29.0
## 192 7.0 29.0
## 193 7.0 29.0
## 194 7.0 29.0
## 195 7.0 29.0
## 196 7.0 29.0
## 197 7.0 29.0
## 198 7.0 29.0
## 199 7.0 29.1
## 200 7.0 29.1
## 201 7.0 29.1
## 202 7.0 29.1
## 203 7.0 29.1
## 204 7.0 29.1
## 205 7.0 29.1
## 206 7.0 29.1
## 207 7.0 29.1
## 208 7.0 29.1
## 209 7.0 29.1
## 210 7.0 29.2
## 211 7.0 29.2
## 212 7.0 29.2
## 213 7.0 29.2
## 214 7.0 29.2
## 215 7.0 29.2
## 216 7.0 29.2
## 217 7.0 29.2
## 218 7.0 29.2
## 219 7.0 29.2
## 220 7.0 29.2
## 221 7.0 29.2
## 222 7.0 29.2
## 223 7.0 29.2
## 224 7.0 29.3
## 225 7.0 29.3
## 226 7.0 29.3
## 227 7.0 29.3
## 228 7.0 29.4
## 229 7.0 29.4
## 230 7.0 29.4
## 231 7.0 29.4
## 232 7.0 29.4
## 233 7.0 29.4
## 234 7.0 29.4
## 235 7.0 29.4
## 236 7.0 29.4
## 237 7.0 29.4
## 238 7.0 29.4
## 239 7.1 29.5
## 240 7.1 29.5
## 241 7.1 29.5
## 242 7.1 29.5
## 243 7.1 29.5
## 244 7.1 29.5
## 245 7.1 29.5
## 246 7.1 29.5
## 247 7.1 29.5
## 248 7.1 29.6
## 249 7.1 29.6
## 250 7.1 29.6
## 251 7.1 29.7
## 252 7.1 29.7
## 253 7.1 29.8
## 254 7.1 29.8
## 255 7.1 29.8
## 256 7.1 29.8
## 257 7.1 29.8
## 258 7.1 29.8
## 259 7.1 29.9
## 260 7.1 29.9
## 261 7.1 29.9
## 262 7.1 29.9
## 263 7.1 30.0
## 264 7.1 30.0
## 265 7.1 30.0
## 266 7.1 30.0
## 267 7.1 30.0
## 268 7.1 30.0
## 269 7.2 30.1
## 270 7.2 30.1
## 271 7.2 30.1
## 272 7.2 30.1
## 273 7.2 30.2
## 274 7.2 30.2
## 275 7.2 30.2
## 276 7.2 30.3
## 277 7.2 30.3
## 278 7.2 30.3
## 279 7.2 30.3
## 280 7.2 30.4
## 281 7.3 30.5
## 282 7.3 30.6
## 283 7.3 30.8
## 284 7.3 30.9
## 285 7.3 31.1
## 286 7.3 31.1
## 287 7.4 31.1
## 288 7.4 31.2
## 289 7.4 31.4
## 290 7.4 31.5
## 291 7.4 31.7
## 292 7.4 31.9
## 293 7.5 32.1- para la columna PH el valor menor es \(6.1\) y el mayor es \(7.5\), el rango es \(7.5-6.1=1.4\)
- para la columna Temperatura el valor menor es \(25.6\) y el mayor es \(32.1\), el rango es \(32.1-25.6=6.5\)
##obteniendo el numero de intervalos usando la fórmula de Sturges y el ancho de clase los obtendremos utilizando la formula de sturges y histogramas. * PH, distribucion de frecuencias absolutas
## [1] 6.1 7.5## [1] 6.5 7.0 7.5#distribución de los valores
ph.cut <- cut(dfGeneral$datosPh, breaksPh, right = FALSE)
ph.freq <- table(ph.cut)
#cbind(ph.cut) comentado por retrasar el codigo
ph.cumfreq <- c(0, cumsum(ph.freq))
#grafica de poligonos
plot(breaksPh, ph.cumfreq,
main = "porcentaje PH",
xlab = "nivel de PH",
ylab = "PH acumulado")
lines(breaksPh, ph.cumfreq)
- Temperatura, distribucion de frecuencias absolutas
## [1] 25.6 32.1## [1] 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0 30.5 31.0 31.5 32.0 32.5#distribucion de valores
temp.cut <- cut(dfGeneral$datosTemp, breaksTemp, right = FALSE)
temp.freq <- table(temp.cut)
#cbind(temp.cut) comentado por retrasar el codigo
temp.cumfreq <- c(0, cumsum(temp.freq))
#grafica de poligonos
plot(breaksTemp, temp.cumfreq,
main = "porcentaje de temperaturas",
xlab = "nivel de temperatura",
ylab = "temperaturas acumuladas")
lines(breaksTemp, temp.cumfreq)
##Tabla de frecuencias. * datos de PH
#primero encontrar la media, moda y mediana de los datos de PH
mediaph <- mean(dfGeneral$datosPh, na.rm = TRUE)
mediaph #media## [1] 6.890444## [1] 6.9## [1] 7- datos de Temperatura
## [1] 28.69795## [1] 28.7## [1] 28.6- calculo de frecuencias, PH
##
## 6.1 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5
## 1 1 7 17 23 9 58 44 78 30 12 6 6 1#frecuancia relativa proporcional
prop.table(tablaph) #cada celda se divide sobre la cantidad de ph y el total de los mismos.##
## 6.1 6.3 6.4 6.5 6.6 6.7
## 0.003412969 0.003412969 0.023890785 0.058020478 0.078498294 0.030716724
## 6.8 6.9 7 7.1 7.2 7.3
## 0.197952218 0.150170648 0.266211604 0.102389078 0.040955631 0.020477816
## 7.4 7.5
## 0.020477816 0.003412969#frecuencia relativa porcentual
round((prop.table(tablaph)*100), 2) #aqui se redondea a dos decimales##
## 6.1 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4
## 0.34 0.34 2.39 5.80 7.85 3.07 19.80 15.02 26.62 10.24 4.10 2.05 2.05
## 7.5
## 0.34## 6.1 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5
## 1 2 9 26 49 58 116 160 238 268 280 286 292 293#frecuencia relativas acumuladas
tablaPhReAcu<-round(cumsum(prop.table(tablaph)*100), 2)
tablaPhReAcu## 6.1 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7 7.1 7.2
## 0.34 0.68 3.07 8.87 16.72 19.80 39.59 54.61 81.23 91.47 95.56
## 7.3 7.4 7.5
## 97.61 99.66 100.00#histograma
hist(dfGeneral$datosPh,
main = "Histograma de frecuencias de PH",
xlab = "PH",
ylab = "Frecuencia",
col = "gray",
border = "black",
ylim = c(0, 293),
xlim = c(6.1, 7.5))
- calculo de frecuencias, Temperatura
##
## 25.6 25.8 26.2 26.3 26.4 26.8 26.9 27 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8
## 1 1 1 2 2 2 1 2 1 2 4 5 12 1 4 11
## 27.9 28 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 29 29.1 29.2 29.3 29.4
## 14 18 3 12 7 7 9 19 13 12 18 14 11 14 4 11
## 29.5 29.6 29.7 29.8 29.9 30 30.1 30.2 30.3 30.4 30.5 30.6 30.8 30.9 31.1 31.2
## 9 3 2 6 4 6 4 3 4 1 1 1 1 1 3 1
## 31.4 31.5 31.7 31.9 32.1
## 1 1 1 1 1##
## 25.6 25.8 26.2 26.3 26.4 26.8
## 0.003412969 0.003412969 0.003412969 0.006825939 0.006825939 0.006825939
## 26.9 27 27.1 27.2 27.3 27.4
## 0.003412969 0.006825939 0.003412969 0.006825939 0.013651877 0.017064846
## 27.5 27.6 27.7 27.8 27.9 28
## 0.040955631 0.003412969 0.013651877 0.037542662 0.047781570 0.061433447
## 28.1 28.2 28.3 28.4 28.5 28.6
## 0.010238908 0.040955631 0.023890785 0.023890785 0.030716724 0.064846416
## 28.7 28.8 28.9 29 29.1 29.2
## 0.044368601 0.040955631 0.061433447 0.047781570 0.037542662 0.047781570
## 29.3 29.4 29.5 29.6 29.7 29.8
## 0.013651877 0.037542662 0.030716724 0.010238908 0.006825939 0.020477816
## 29.9 30 30.1 30.2 30.3 30.4
## 0.013651877 0.020477816 0.013651877 0.010238908 0.013651877 0.003412969
## 30.5 30.6 30.8 30.9 31.1 31.2
## 0.003412969 0.003412969 0.003412969 0.003412969 0.010238908 0.003412969
## 31.4 31.5 31.7 31.9 32.1
## 0.003412969 0.003412969 0.003412969 0.003412969 0.003412969##
## 25.6 25.8 26.2 26.3 26.4 26.8 26.9 27 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8
## 0.34 0.34 0.34 0.68 0.68 0.68 0.34 0.68 0.34 0.68 1.37 1.71 4.10 0.34 1.37 3.75
## 27.9 28 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 29 29.1 29.2 29.3 29.4
## 4.78 6.14 1.02 4.10 2.39 2.39 3.07 6.48 4.44 4.10 6.14 4.78 3.75 4.78 1.37 3.75
## 29.5 29.6 29.7 29.8 29.9 30 30.1 30.2 30.3 30.4 30.5 30.6 30.8 30.9 31.1 31.2
## 3.07 1.02 0.68 2.05 1.37 2.05 1.37 1.02 1.37 0.34 0.34 0.34 0.34 0.34 1.02 0.34
## 31.4 31.5 31.7 31.9 32.1
## 0.34 0.34 0.34 0.34 0.34## 25.6 25.8 26.2 26.3 26.4 26.8 26.9 27 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8
## 1 2 3 5 7 9 10 12 13 15 19 24 36 37 41 52
## 27.9 28 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 29 29.1 29.2 29.3 29.4
## 66 84 87 99 106 113 122 141 154 166 184 198 209 223 227 238
## 29.5 29.6 29.7 29.8 29.9 30 30.1 30.2 30.3 30.4 30.5 30.6 30.8 30.9 31.1 31.2
## 247 250 252 258 262 268 272 275 279 280 281 282 283 284 287 288
## 31.4 31.5 31.7 31.9 32.1
## 289 290 291 292 293##
## 25.6 25.8 26.2 26.3 26.4 26.8 26.9 27 27.1 27.2 27.3 27.4 27.5 27.6 27.7 27.8
## 0.34 0.34 0.34 0.68 0.68 0.68 0.34 0.68 0.34 0.68 1.37 1.71 4.10 0.34 1.37 3.75
## 27.9 28 28.1 28.2 28.3 28.4 28.5 28.6 28.7 28.8 28.9 29 29.1 29.2 29.3 29.4
## 4.78 6.14 1.02 4.10 2.39 2.39 3.07 6.48 4.44 4.10 6.14 4.78 3.75 4.78 1.37 3.75
## 29.5 29.6 29.7 29.8 29.9 30 30.1 30.2 30.3 30.4 30.5 30.6 30.8 30.9 31.1 31.2
## 3.07 1.02 0.68 2.05 1.37 2.05 1.37 1.02 1.37 0.34 0.34 0.34 0.34 0.34 1.02 0.34
## 31.4 31.5 31.7 31.9 32.1
## 0.34 0.34 0.34 0.34 0.34#histograma
hist(dfGeneral$datosTemp,
main = "histograma de frecuencia de Temperatura",
xlab = "temperatura",
ylab = "frecuencia",
col = "black",
border = "white",
ylim = c(0,293),
xlim = c(25.6,32.1))
#Obteniendo la varianza y la desviación estándar. ## Valores de PH * varianza y desviación estándar
## [1] 0.04908645## [1] 0.2215546
