Week 3
Govind Prakash
12/02/2021
Class 7 (18th Jan)
Setting working directory
getwd()## [1] "X:/1.Study/4th year semester 2/Biostat/Assignment 1"setwd("X:/1.Study/4th year semester 2/Biostat/Assignment 1")Importing Life expectancy dataset
LifeExpectancyInYears<- read.csv("life_expectancy_years.csv", header = T, check.names = F )Subletting specific countries’ Life expectancies
as.vector(na.omit(as.numeric(unlist(LifeExpectancyInYears[LifeExpectancyInYears$country=="Sweden",]))))-> swedenlife## Warning in
## na.omit(as.numeric(unlist(LifeExpectancyInYears[LifeExpectancyInYears$country
## == : NAs introduced by coercionas.vector(na.omit(as.numeric(unlist(LifeExpectancyInYears[LifeExpectancyInYears$country=="India",]))))-> indialife## Warning in
## na.omit(as.numeric(unlist(LifeExpectancyInYears[LifeExpectancyInYears$country
## == : NAs introduced by coercionas.vector(na.omit(as.numeric(unlist(LifeExpectancyInYears[LifeExpectancyInYears$country=="Bangladesh",]))))-> banglalife## Warning in
## na.omit(as.numeric(unlist(LifeExpectancyInYears[LifeExpectancyInYears$country
## == : NAs introduced by coercionas.vector(na.omit(as.numeric(unlist(LifeExpectancyInYears[LifeExpectancyInYears$country=="Switzeland",]))))-> SwitzerlandlifeComparing life expactancy between countries
Box Plot
boxplot(swedenlife, indialife, banglalife, names = c("sweden", "india", "bangladesh"), ylab= "life expectancy", xlab= "Countries")
Creating data frame
data.frame(Lifeexpec= c(swedenlife, indialife, banglalife),
Country=c(rep("sweden", length(swedenlife)),
rep("India", length(indialife)),
rep("Bangladesh", length(banglalife))))-> countryboxBoxplot using dataframe
~ tilde denotes the arguments inside boxplot functions are not characters but are values
boxplot(countrybox$Lifeexpec~countrybox$Country)
single sample t-test
using a mean of 10, it generates random normal distribution
single_sample = rnorm(10, mean = 10)to tets weather mean=10, NULL HYPTHESIS= true mean is equal to 10
t.test(single_sample, mu=10) ##
## One Sample t-test
##
## data: single_sample
## t = -0.032904, df = 9, p-value = 0.9745
## alternative hypothesis: true mean is not equal to 10
## 95 percent confidence interval:
## 9.372204 10.609795
## sample estimates:
## mean of x
## 9.990999Here instead of w we are seeing t, df (degrees of freedom), also here P value is 0.2169, so we can’t reject our null hypothesis
taking mean of 100
single_sample= rnorm(100, mean = 100)now we are checking weather the mean is 10 or not, NULL HYPOTHESIS= true mean is equal to 10
t.test(single_sample, mu= 10)##
## One Sample t-test
##
## data: single_sample
## t = 950, df = 99, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 10
## 95 percent confidence interval:
## 99.94884 100.32537
## sample estimates:
## mean of x
## 100.1371Here p value is way less than 0.05 so we can reject the Null hypothesis, means mean isn’t equal to 10 NOTE: while doing T test we have to assume our data is normally distributed * T test is a type of parametric test- means it needs to meet certain assumptions , one of these assumptions is * it needs to be Normally distributed
we can check weather average life expactancy of india is near ~35 years or not
t.test(indialife, mu= 35)##
## One Sample t-test
##
## data: indialife
## t = 8.4823, df = 300, p-value = 1.022e-15
## alternative hypothesis: true mean is not equal to 35
## 95 percent confidence interval:
## 43.46090 48.57272
## sample estimates:
## mean of x
## 46.01681t = 8.4823, df = 300, p-value = 1.022e-15, p value is so low so our hypothesis was wrong
Now lets assume the average life expactancy is 45 years
t.test(indialife, mu= 45)##
## One Sample t-test
##
## data: indialife
## t = 0.78289, df = 300, p-value = 0.4343
## alternative hypothesis: true mean is not equal to 45
## 95 percent confidence interval:
## 43.46090 48.57272
## sample estimates:
## mean of x
## 46.01681P>> 0.05 so we cant reject the assumption
- India life expectancy isn’t normally distributes as it has increased only, but for any parametric test like t test so we can’t use this test
- First check your data for normality then only use any type of tests
Paired T-test
Outline = F is to get rid of the outliers (values those are completely outside the range)
x= rnorm(10)
y= rnorm(10)
boxplot(x, y, names = c("X", "Y"))
boxplot(x, y, names = c("X", "Y"), outline = F)
- By looking at plots we can say the means look same, so we can check weather their mean are same or not
- So here NULL HYPOTHESIS = means are same
t.test(x, y)##
## Welch Two Sample t-test
##
## data: x and y
## t = -0.87754, df = 17.842, p-value = 0.3919
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1.1270259 0.4632136
## sample estimates:
## mean of x mean of y
## -0.1028464 0.2290597p >> 0.05 it means our assumption was right means are same
Paired
t.test(x, y, paired = T)##
## Paired t-test
##
## data: x and y
## t = -0.76506, df = 9, p-value = 0.4638
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -1.3132943 0.6494819
## sample estimates:
## mean of the differences
## -0.3319062- The values of P is different from the above (Welch T test), as it uses a different formula
- paired test is much more conservative than Welch t test
- It takes care of confounding factors (means the factors that are effecting the data but aren’t visible), for example, the world wars
- Paired Data set USes: For example comparing samples from a diseased person and a normal person (control)
- Paired T test is similar to Welch t test but it is more designed to compare pair data set means similar datas
Creating test normal functions
x=rnorm(10)
y=rnorm(40)Unpaired T- test
It works even x and y have different no of values
t.test(x, y)##
## Welch Two Sample t-test
##
## data: x and y
## t = -0.12533, df = 11.52, p-value = 0.9024
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.8460380 0.7543989
## sample estimates:
## mean of x mean of y
## 0.01088495 0.05670448But it doesnt work as it needs x and y have same number of values (length)
t.test(x, y, paired = T) ## Error in complete.cases(x, y): not all arguments have the same lengthQ: Can we use T-test on life expectancy data? Ans: No, because Life expectancy data is not normalized so it cant be used in any parametric test
Though the following will give some results, but it should not be used as the data is not normal
t.test(swedenlife, indialife) ##
## Welch Two Sample t-test
##
## data: swedenlife and indialife
## t = 12.011, df = 578.84, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 16.90768 23.51850
## sample estimates:
## mean of x mean of y
## 66.22990 46.01681Degree of freedom is more
t.test(swedenlife, indialife, var.equal = T)##
## Two Sample t-test
##
## data: swedenlife and indialife
## t = 12.011, df = 600, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 16.90793 23.51825
## sample estimates:
## mean of x mean of y
## 66.22990 46.01681Degree of freedom is reduced when varience isn’t equal
t.test(swedenlife, indialife, var.equal = F)##
## Welch Two Sample t-test
##
## data: swedenlife and indialife
## t = 12.011, df = 578.84, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 16.90768 23.51850
## sample estimates:
## mean of x mean of y
## 66.22990 46.01681- The above tests are two tailed test as the values can be either greater or lesser as we haven’t specified anything we have only told the difference is
var(swedenlife)## [1] 344.7674variance= 344.7674 for Sweden life expectancy
var(indialife)## [1] 507.7486variance= 507.7486 for India life expectancy
So to check these variance are similar or different we’ll do some tests * based on weather variance is equal or not we’ll give arguments in t.test(swedenlife, indialife, var.equal = T or F) * F test is done to check weather the variance is similar or not
NOTE: As we want to change our null hypothesis as difference of mean (First value - second value) is less, so we we’ll set our alternate hypothesis to greater so automatically our Null hypothesis will become less, as Alternate hypotheis is opposite to null hypothesis. For following we are supposing (NULL hypothesis) that mean of Sweden is less than India
t.test(swedenlife, indialife, var.equal = T, alternative = "greater")##
## Two Sample t-test
##
## data: swedenlife and indialife
## t = 12.011, df = 600, p-value < 2.2e-16
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
## 17.44062 Inf
## sample estimates:
## mean of x mean of y
## 66.22990 46.01681As the p value is very less, so hypothesis mean of Sweden is less than India was wrong , means mean of sweden must be greater than india, lets check this hypothesis too.
Now our NULL hypothesis is Mean of india India is lesser so the difference of first and second must be greater than zero, so the opposite of our null hypotheis means the alternate hypotheis must be set to less
t.test(swedenlife, indialife, var.equal = T, alternative = "less")##
## Two Sample t-test
##
## data: swedenlife and indialife
## t = 12.011, df = 600, p-value = 1
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
## -Inf 22.98556
## sample estimates:
## mean of x mean of y
## 66.22990 46.01681For this p value is greater than alpha 0.05, P= 1 here, so our hypothesis was correct
- NOTE: difference is taken between 1st Sweden and 2nd India
- The above tests are one tailed test as the values were defined either greater or lesser
set exact = F to ensure it doesn’t calculate exact P values, it will give approximate or threshold of P value
t.test(swedenlife, indialife, paired = T, exact= F)##
## Paired t-test
##
## data: swedenlife and indialife
## t = 39.538, df = 300, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 19.20703 21.21915
## sample estimates:
## mean of the differences
## 20.21309Wilcoxon test
- The non parametric alternative of T-test
- Performs one and two-sample Wilcoxon tests on vectors of data
- The latter is also known as ‘Mann-Whitney’ test
wilcox.test(swedenlife, indialife, paired = T)##
## Wilcoxon signed rank test with continuity correction
##
## data: swedenlife and indialife
## V = 45451, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0now we know sweden is more developed so our alternative hypothesis is sweden has less life expectancy so the alternate= “greater”
wilcox.test(swedenlife, indialife, paired = T, alternative = "less") ##
## Wilcoxon signed rank test with continuity correction
##
## data: swedenlife and indialife
## V = 45451, p-value = 1
## alternative hypothesis: true location shift is less than 0p value is significant so the hypothesis is correct
Plotting Bangladesh and India Life expectancy
par(mfrow= c(1,2))
hist(banglalife)
hist(indialife)
Just by looking at data we cant say its normally distributed or not
boxplot(banglalife, indialife, names = c("banglalife", "indialife"))
By box plot we can assume the meanlife of bangla desh is greater then, so lets test
wilcox.test(banglalife, indialife, paired = T)##
## Wilcoxon signed rank test with continuity correction
##
## data: banglalife and indialife
## V = 34228, p-value = 8.592e-15
## alternative hypothesis: true location shift is not equal to 0Q: what if data from some years are missing? Ans: It becomes unpaired
wilcox.test(banglalife, indialife, paired = F)##
## Wilcoxon rank sum test with continuity correction
##
## data: banglalife and indialife
## W = 49105, p-value = 0.07421
## alternative hypothesis: true location shift is not equal to 0The P value is less then 0.05 so it isn’t that significant * So if data isn’t paired P value isn’t very significant * So we must do a paired test
wilcox.test(banglalife, indialife, paired = T, alternative = "greater") ##
## Wilcoxon signed rank test with continuity correction
##
## data: banglalife and indialife
## V = 34228, p-value = 4.296e-15
## alternative hypothesis: true location shift is greater than 0Its true because, Hypothesis= Bangladesh has greater life expectancy
wilcox.test(indialife, banglalife, paired = T, alternative = "greater") ##
## Wilcoxon signed rank test with continuity correction
##
## data: indialife and banglalife
## V = 10922, p-value = 1
## alternative hypothesis: true location shift is greater than 0Its false as, Hypothesis= India has greater life expectancy
Order does matter in one tailed test, but it doesn’t matter in two tailed test
summary(banglalife)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 12.60 25.50 40.50 47.66 75.30 87.60summary(indialife)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.16 25.40 35.20 46.02 70.80 81.80- T tests can only do tests with 2 variables,
- For more than two variables we should try ANOVA or
- Some non parametric tests like cruxcallwalis test or pair wise wilcoxon test
Installing Data packages and using them directly
install.packages("gapminder", repos = "http://cran.us.r-project.org") #installing gapminder dataset## Installing package into 'C:/Users/govin/OneDrive/Documents/R/win-library/4.0'
## (as 'lib' is unspecified)## package 'gapminder' successfully unpacked and MD5 sums checked
##
## The downloaded binary packages are in
## C:\Users\govin\AppData\Local\Temp\Rtmpw90n0U\downloaded_packageslibrary(gapminder) #loading gapminderChecking properties of Gapminder dataset
str(gapminder_unfiltered)## tibble [3,313 x 6] (S3: tbl_df/tbl/data.frame)
## $ country : Factor w/ 187 levels "Afghanistan",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ continent: Factor w/ 6 levels "Africa","Americas",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ year : int [1:3313] 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 ...
## $ lifeExp : num [1:3313] 28.8 30.3 32 34 36.1 ...
## $ pop : int [1:3313] 8425333 9240934 10267083 11537966 13079460 14880372 12881816 13867957 16317921 22227415 ...
## $ gdpPercap: num [1:3313] 779 821 853 836 740 ...str(gapminder) #both gapminder and gapminder_unfiltered are stored in the form of tibble## tibble [1,704 x 6] (S3: tbl_df/tbl/data.frame)
## $ country : Factor w/ 142 levels "Afghanistan",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ continent: Factor w/ 5 levels "Africa","Americas",..: 3 3 3 3 3 3 3 3 3 3 ...
## $ year : int [1:1704] 1952 1957 1962 1967 1972 1977 1982 1987 1992 1997 ...
## $ lifeExp : num [1:1704] 28.8 30.3 32 34 36.1 ...
## $ pop : int [1:1704] 8425333 9240934 10267083 11537966 13079460 14880372 12881816 13867957 16317921 22227415 ...
## $ gdpPercap: num [1:1704] 779 821 853 836 740 ...summary(gapminder_unfiltered) # for each of the column tells summary## country continent year lifeExp
## Czech Republic: 58 Africa : 637 Min. :1950 Min. :23.60
## Denmark : 58 Americas: 470 1st Qu.:1967 1st Qu.:58.33
## Finland : 58 Asia : 578 Median :1982 Median :69.61
## Iceland : 58 Europe :1302 Mean :1980 Mean :65.24
## Japan : 58 FSU : 139 3rd Qu.:1996 3rd Qu.:73.66
## Netherlands : 58 Oceania : 187 Max. :2007 Max. :82.67
## (Other) :2965
## pop gdpPercap
## Min. :5.941e+04 Min. : 241.2
## 1st Qu.:2.680e+06 1st Qu.: 2505.3
## Median :7.560e+06 Median : 7825.8
## Mean :3.177e+07 Mean : 11313.8
## 3rd Qu.:1.961e+07 3rd Qu.: 17355.8
## Max. :1.319e+09 Max. :113523.1
## Installing Hmisc Package
install.packages("Hmisc", repos = "http://cran.us.r-project.org") #Miscelenious functions very helpful## Installing package into 'C:/Users/govin/OneDrive/Documents/R/win-library/4.0'
## (as 'lib' is unspecified)## package 'Hmisc' successfully unpacked and MD5 sums checked
##
## The downloaded binary packages are in
## C:\Users\govin\AppData\Local\Temp\Rtmpw90n0U\downloaded_packageslibrary(Hmisc)## Loading required package: lattice## Loading required package: survival## Loading required package: Formula## Loading required package: ggplot2##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:base':
##
## format.pval, unitsView(gapminder)Attaching values
LifeExpectancyInYears$country # will show the vector ## [1] "Afghanistan" "Albania"
## [3] "Algeria" "Andorra"
## [5] "Angola" "Antigua and Barbuda"
## [7] "Argentina" "Armenia"
## [9] "Australia" "Austria"
## [11] "Azerbaijan" "Bahamas"
## [13] "Bahrain" "Bangladesh"
## [15] "Barbados" "Belarus"
## [17] "Belgium" "Belize"
## [19] "Benin" "Bhutan"
## [21] "Bolivia" "Bosnia and Herzegovina"
## [23] "Botswana" "Brazil"
## [25] "Brunei" "Bulgaria"
## [27] "Burkina Faso" "Burundi"
## [29] "Cambodia" "Cameroon"
## [31] "Canada" "Cape Verde"
## [33] "Central African Republic" "Chad"
## [35] "Chile" "China"
## [37] "Colombia" "Comoros"
## [39] "Congo, Dem. Rep." "Congo, Rep."
## [41] "Costa Rica" "Cote d'Ivoire"
## [43] "Croatia" "Cuba"
## [45] "Cyprus" "Czech Republic"
## [47] "Denmark" "Djibouti"
## [49] "Dominica" "Dominican Republic"
## [51] "Ecuador" "Egypt"
## [53] "El Salvador" "Equatorial Guinea"
## [55] "Eritrea" "Estonia"
## [57] "Eswatini" "Ethiopia"
## [59] "Fiji" "Finland"
## [61] "France" "Gabon"
## [63] "Gambia" "Georgia"
## [65] "Germany" "Ghana"
## [67] "Greece" "Grenada"
## [69] "Guatemala" "Guinea"
## [71] "Guinea-Bissau" "Guyana"
## [73] "Haiti" "Honduras"
## [75] "Hungary" "Iceland"
## [77] "India" "Indonesia"
## [79] "Iran" "Iraq"
## [81] "Ireland" "Israel"
## [83] "Italy" "Jamaica"
## [85] "Japan" "Jordan"
## [87] "Kazakhstan" "Kenya"
## [89] "Kiribati" "Kuwait"
## [91] "Kyrgyz Republic" "Lao"
## [93] "Latvia" "Lebanon"
## [95] "Lesotho" "Liberia"
## [97] "Libya" "Lithuania"
## [99] "Luxembourg" "Madagascar"
## [101] "Malawi" "Malaysia"
## [103] "Maldives" "Mali"
## [105] "Malta" "Marshall Islands"
## [107] "Mauritania" "Mauritius"
## [109] "Mexico" "Micronesia, Fed. Sts."
## [111] "Moldova" "Mongolia"
## [113] "Montenegro" "Morocco"
## [115] "Mozambique" "Myanmar"
## [117] "Namibia" "Nepal"
## [119] "Netherlands" "New Zealand"
## [121] "Nicaragua" "Niger"
## [123] "Nigeria" "North Korea"
## [125] "North Macedonia" "Norway"
## [127] "Oman" "Pakistan"
## [129] "Palestine" "Panama"
## [131] "Papua New Guinea" "Paraguay"
## [133] "Peru" "Philippines"
## [135] "Poland" "Portugal"
## [137] "Qatar" "Romania"
## [139] "Russia" "Rwanda"
## [141] "Samoa" "Sao Tome and Principe"
## [143] "Saudi Arabia" "Senegal"
## [145] "Serbia" "Seychelles"
## [147] "Sierra Leone" "Singapore"
## [149] "Slovak Republic" "Slovenia"
## [151] "Solomon Islands" "Somalia"
## [153] "South Africa" "South Korea"
## [155] "South Sudan" "Spain"
## [157] "Sri Lanka" "St. Lucia"
## [159] "St. Vincent and the Grenadines" "Sudan"
## [161] "Suriname" "Sweden"
## [163] "Switzerland" "Syria"
## [165] "Tajikistan" "Tanzania"
## [167] "Thailand" "Timor-Leste"
## [169] "Togo" "Tonga"
## [171] "Trinidad and Tobago" "Tunisia"
## [173] "Turkey" "Turkmenistan"
## [175] "Uganda" "Ukraine"
## [177] "United Arab Emirates" "United Kingdom"
## [179] "United States" "Uruguay"
## [181] "Uzbekistan" "Vanuatu"
## [183] "Venezuela" "Vietnam"
## [185] "Yemen" "Zambia"
## [187] "Zimbabwe"country # just typing country will not show the vector## Error in eval(expr, envir, enclos): object 'country' not foundattach(LifeExpectancyInYears)now just by typing country well get country values
To detach
detach(LifeExpectancyInYears)detach just reverses the attach function
Exploratory data analysis (EDA)
describe(gapminder_unfiltered) #part of Hmisc package, it has taken the dataset and summarised it## gapminder_unfiltered
##
## 6 Variables 3313 Observations
## --------------------------------------------------------------------------------
## country
## n missing distinct
## 3313 0 187
##
## lowest : Afghanistan Albania Algeria Angola Argentina
## highest: Vietnam West Bank and Gaza Yemen, Rep. Zambia Zimbabwe
## --------------------------------------------------------------------------------
## continent
## n missing distinct
## 3313 0 6
##
## lowest : Africa Americas Asia Europe FSU
## highest: Americas Asia Europe FSU Oceania
##
## Value Africa Americas Asia Europe FSU Oceania
## Frequency 637 470 578 1302 139 187
## Proportion 0.192 0.142 0.174 0.393 0.042 0.056
## --------------------------------------------------------------------------------
## year
## n missing distinct Info Mean Gmd .05 .10
## 3313 0 58 0.998 1980 19.52 1952 1957
## .25 .50 .75 .90 .95
## 1967 1982 1996 2002 2007
##
## lowest : 1950 1951 1952 1953 1954, highest: 2003 2004 2005 2006 2007
## --------------------------------------------------------------------------------
## lifeExp
## n missing distinct Info Mean Gmd .05 .10
## 3313 0 2571 1 65.24 12.73 41.22 45.37
## .25 .50 .75 .90 .95
## 58.33 69.61 73.66 77.12 78.68
##
## lowest : 23.599 28.801 30.000 30.015 30.331, highest: 82.208 82.270 82.360 82.603 82.670
## --------------------------------------------------------------------------------
## pop
## n missing distinct Info Mean Gmd .05 .10
## 3313 0 3312 1 31773251 50168977 235605 436150
## .25 .50 .75 .90 .95
## 2680018 7559776 19610538 56737055 121365965
##
## lowest : 59412 59461 60011 60427 61325
## highest: 1110396331 1164970000 1230075000 1280400000 1318683096
## --------------------------------------------------------------------------------
## gdpPercap
## n missing distinct Info Mean Gmd .05 .10
## 3313 0 3313 1 11314 11542 665.7 887.9
## .25 .50 .75 .90 .95
## 2505.3 7825.8 17355.7 26592.7 31534.9
##
## lowest : 241.1659 277.5519 298.8462 299.8503 312.1884
## highest: 82010.9780 95458.1118 108382.3529 109347.8670 113523.1329
## --------------------------------------------------------------------------------dim(gapminder_unfiltered) #dimentions of the object, row and column of the tibble## [1] 3313 6nrow(gapminder_unfiltered) # shows number of rows ## [1] 3313ncol(gapminder_unfiltered) # shows number of columns## [1] 6colnames(gapminder_unfiltered) # shows column names## [1] "country" "continent" "year" "lifeExp" "pop" "gdpPercap"rownames(gapminder_unfiltered) # shows row names## [1] "1" "2" "3" "4" "5" "6" "7" "8" "9" "10"
## [11] "11" "12" "13" "14" "15" "16" "17" "18" "19" "20"
## [21] "21" "22" "23" "24" "25" "26" "27" "28" "29" "30"
## [31] "31" "32" "33" "34" "35" "36" "37" "38" "39" "40"
## [41] "41" "42" "43" "44" "45" "46" "47" "48" "49" "50"
## [51] "51" "52" "53" "54" "55" "56" "57" "58" "59" "60"
## [61] "61" "62" "63" "64" "65" "66" "67" "68" "69" "70"
## [71] "71" "72" "73" "74" "75" "76" "77" "78" "79" "80"
## [81] "81" "82" "83" "84" "85" "86" "87" "88" "89" "90"
## [91] "91" "92" "93" "94" "95" "96" "97" "98" "99" "100"
## [101] "101" "102" "103" "104" "105" "106" "107" "108" "109" "110"
## [111] "111" "112" "113" "114" "115" "116" "117" "118" "119" "120"
## [121] "121" "122" "123" "124" "125" "126" "127" "128" "129" "130"
## [131] "131" "132" "133" "134" "135" "136" "137" "138" "139" "140"
## [141] "141" "142" "143" "144" "145" "146" "147" "148" "149" "150"
## [151] "151" "152" "153" "154" "155" "156" "157" "158" "159" "160"
## [161] "161" "162" "163" "164" "165" "166" "167" "168" "169" "170"
## [171] "171" "172" "173" "174" "175" "176" "177" "178" "179" "180"
## [181] "181" "182" "183" "184" "185" "186" "187" "188" "189" "190"
## [191] "191" "192" "193" "194" "195" "196" "197" "198" "199" "200"
## [201] "201" "202" "203" "204" "205" "206" "207" "208" "209" "210"
## [211] "211" "212" "213" "214" "215" "216" "217" "218" "219" "220"
## [221] "221" "222" "223" "224" "225" "226" "227" "228" "229" "230"
## [231] "231" "232" "233" "234" "235" "236" "237" "238" "239" "240"
## [241] "241" "242" "243" "244" "245" "246" "247" "248" "249" "250"
## [251] "251" "252" "253" "254" "255" "256" "257" "258" "259" "260"
## [261] "261" "262" "263" "264" "265" "266" "267" "268" "269" "270"
## [271] "271" "272" "273" "274" "275" "276" "277" "278" "279" "280"
## [281] "281" "282" "283" "284" "285" "286" "287" "288" "289" "290"
## [291] "291" "292" "293" "294" "295" "296" "297" "298" "299" "300"
## [301] "301" "302" "303" "304" "305" "306" "307" "308" "309" "310"
## [311] "311" "312" "313" "314" "315" "316" "317" "318" "319" "320"
## [321] "321" "322" "323" "324" "325" "326" "327" "328" "329" "330"
## [331] "331" "332" "333" "334" "335" "336" "337" "338" "339" "340"
## [341] "341" "342" "343" "344" "345" "346" "347" "348" "349" "350"
## [351] "351" "352" "353" "354" "355" "356" "357" "358" "359" "360"
## [361] "361" "362" "363" "364" "365" "366" "367" "368" "369" "370"
## [371] "371" "372" "373" "374" "375" "376" "377" "378" "379" "380"
## [381] "381" "382" "383" "384" "385" "386" "387" "388" "389" "390"
## [391] "391" "392" "393" "394" "395" "396" "397" "398" "399" "400"
## [401] "401" "402" "403" "404" "405" "406" "407" "408" "409" "410"
## [411] "411" "412" "413" "414" "415" "416" "417" "418" "419" "420"
## [421] "421" "422" "423" "424" "425" "426" "427" "428" "429" "430"
## [431] "431" "432" "433" "434" "435" "436" "437" "438" "439" "440"
## [441] "441" "442" "443" "444" "445" "446" "447" "448" "449" "450"
## [451] "451" "452" "453" "454" "455" "456" "457" "458" "459" "460"
## [461] "461" "462" "463" "464" "465" "466" "467" "468" "469" "470"
## [471] "471" "472" "473" "474" "475" "476" "477" "478" "479" "480"
## [481] "481" "482" "483" "484" "485" "486" "487" "488" "489" "490"
## [491] "491" "492" "493" "494" "495" "496" "497" "498" "499" "500"
## [501] "501" "502" "503" "504" "505" "506" "507" "508" "509" "510"
## [511] "511" "512" "513" "514" "515" "516" "517" "518" "519" "520"
## [521] "521" "522" "523" "524" "525" "526" "527" "528" "529" "530"
## [531] "531" "532" "533" "534" "535" "536" "537" "538" "539" "540"
## [541] "541" "542" "543" "544" "545" "546" "547" "548" "549" "550"
## [551] "551" "552" "553" "554" "555" "556" "557" "558" "559" "560"
## [561] "561" "562" "563" "564" "565" "566" "567" "568" "569" "570"
## [571] "571" "572" "573" "574" "575" "576" "577" "578" "579" "580"
## [581] "581" "582" "583" "584" "585" "586" "587" "588" "589" "590"
## [591] "591" "592" "593" "594" "595" "596" "597" "598" "599" "600"
## [601] "601" "602" "603" "604" "605" "606" "607" "608" "609" "610"
## [611] "611" "612" "613" "614" "615" "616" "617" "618" "619" "620"
## [621] "621" "622" "623" "624" "625" "626" "627" "628" "629" "630"
## [631] "631" "632" "633" "634" "635" "636" "637" "638" "639" "640"
## [641] "641" "642" "643" "644" "645" "646" "647" "648" "649" "650"
## [651] "651" "652" "653" "654" "655" "656" "657" "658" "659" "660"
## [661] "661" "662" "663" "664" "665" "666" "667" "668" "669" "670"
## [671] "671" "672" "673" "674" "675" "676" "677" "678" "679" "680"
## [681] "681" "682" "683" "684" "685" "686" "687" "688" "689" "690"
## [691] "691" "692" "693" "694" "695" "696" "697" "698" "699" "700"
## [701] "701" "702" "703" "704" "705" "706" "707" "708" "709" "710"
## [711] "711" "712" "713" "714" "715" "716" "717" "718" "719" "720"
## [721] "721" "722" "723" "724" "725" "726" "727" "728" "729" "730"
## [731] "731" "732" "733" "734" "735" "736" "737" "738" "739" "740"
## [741] "741" "742" "743" "744" "745" "746" "747" "748" "749" "750"
## [751] "751" "752" "753" "754" "755" "756" "757" "758" "759" "760"
## [761] "761" "762" "763" "764" "765" "766" "767" "768" "769" "770"
## [771] "771" "772" "773" "774" "775" "776" "777" "778" "779" "780"
## [781] "781" "782" "783" "784" "785" "786" "787" "788" "789" "790"
## [791] "791" "792" "793" "794" "795" "796" "797" "798" "799" "800"
## [801] "801" "802" "803" "804" "805" "806" "807" "808" "809" "810"
## [811] "811" "812" "813" "814" "815" "816" "817" "818" "819" "820"
## [821] "821" "822" "823" "824" "825" "826" "827" "828" "829" "830"
## [831] "831" "832" "833" "834" "835" "836" "837" "838" "839" "840"
## [841] "841" "842" "843" "844" "845" "846" "847" "848" "849" "850"
## [851] "851" "852" "853" "854" "855" "856" "857" "858" "859" "860"
## [861] "861" "862" "863" "864" "865" "866" "867" "868" "869" "870"
## [871] "871" "872" "873" "874" "875" "876" "877" "878" "879" "880"
## [881] "881" "882" "883" "884" "885" "886" "887" "888" "889" "890"
## [891] "891" "892" "893" "894" "895" "896" "897" "898" "899" "900"
## [901] "901" "902" "903" "904" "905" "906" "907" "908" "909" "910"
## [911] "911" "912" "913" "914" "915" "916" "917" "918" "919" "920"
## [921] "921" "922" "923" "924" "925" "926" "927" "928" "929" "930"
## [931] "931" "932" "933" "934" "935" "936" "937" "938" "939" "940"
## [941] "941" "942" "943" "944" "945" "946" "947" "948" "949" "950"
## [951] "951" "952" "953" "954" "955" "956" "957" "958" "959" "960"
## [961] "961" "962" "963" "964" "965" "966" "967" "968" "969" "970"
## [971] "971" "972" "973" "974" "975" "976" "977" "978" "979" "980"
## [981] "981" "982" "983" "984" "985" "986" "987" "988" "989" "990"
## [991] "991" "992" "993" "994" "995" "996" "997" "998" "999" "1000"
## [1001] "1001" "1002" "1003" "1004" "1005" "1006" "1007" "1008" "1009" "1010"
## [1011] "1011" "1012" "1013" "1014" "1015" "1016" "1017" "1018" "1019" "1020"
## [1021] "1021" "1022" "1023" "1024" "1025" "1026" "1027" "1028" "1029" "1030"
## [1031] "1031" "1032" "1033" "1034" "1035" "1036" "1037" "1038" "1039" "1040"
## [1041] "1041" "1042" "1043" "1044" "1045" "1046" "1047" "1048" "1049" "1050"
## [1051] "1051" "1052" "1053" "1054" "1055" "1056" "1057" "1058" "1059" "1060"
## [1061] "1061" "1062" "1063" "1064" "1065" "1066" "1067" "1068" "1069" "1070"
## [1071] "1071" "1072" "1073" "1074" "1075" "1076" "1077" "1078" "1079" "1080"
## [1081] "1081" "1082" "1083" "1084" "1085" "1086" "1087" "1088" "1089" "1090"
## [1091] "1091" "1092" "1093" "1094" "1095" "1096" "1097" "1098" "1099" "1100"
## [1101] "1101" "1102" "1103" "1104" "1105" "1106" "1107" "1108" "1109" "1110"
## [1111] "1111" "1112" "1113" "1114" "1115" "1116" "1117" "1118" "1119" "1120"
## [1121] "1121" "1122" "1123" "1124" "1125" "1126" "1127" "1128" "1129" "1130"
## [1131] "1131" "1132" "1133" "1134" "1135" "1136" "1137" "1138" "1139" "1140"
## [1141] "1141" "1142" "1143" "1144" "1145" "1146" "1147" "1148" "1149" "1150"
## [1151] "1151" "1152" "1153" "1154" "1155" "1156" "1157" "1158" "1159" "1160"
## [1161] "1161" "1162" "1163" "1164" "1165" "1166" "1167" "1168" "1169" "1170"
## [1171] "1171" "1172" "1173" "1174" "1175" "1176" "1177" "1178" "1179" "1180"
## [1181] "1181" "1182" "1183" "1184" "1185" "1186" "1187" "1188" "1189" "1190"
## [1191] "1191" "1192" "1193" "1194" "1195" "1196" "1197" "1198" "1199" "1200"
## [1201] "1201" "1202" "1203" "1204" "1205" "1206" "1207" "1208" "1209" "1210"
## [1211] "1211" "1212" "1213" "1214" "1215" "1216" "1217" "1218" "1219" "1220"
## [1221] "1221" "1222" "1223" "1224" "1225" "1226" "1227" "1228" "1229" "1230"
## [1231] "1231" "1232" "1233" "1234" "1235" "1236" "1237" "1238" "1239" "1240"
## [1241] "1241" "1242" "1243" "1244" "1245" "1246" "1247" "1248" "1249" "1250"
## [1251] "1251" "1252" "1253" "1254" "1255" "1256" "1257" "1258" "1259" "1260"
## [1261] "1261" "1262" "1263" "1264" "1265" "1266" "1267" "1268" "1269" "1270"
## [1271] "1271" "1272" "1273" "1274" "1275" "1276" "1277" "1278" "1279" "1280"
## [1281] "1281" "1282" "1283" "1284" "1285" "1286" "1287" "1288" "1289" "1290"
## [1291] "1291" "1292" "1293" "1294" "1295" "1296" "1297" "1298" "1299" "1300"
## [1301] "1301" "1302" "1303" "1304" "1305" "1306" "1307" "1308" "1309" "1310"
## [1311] "1311" "1312" "1313" "1314" "1315" "1316" "1317" "1318" "1319" "1320"
## [1321] "1321" "1322" "1323" "1324" "1325" "1326" "1327" "1328" "1329" "1330"
## [1331] "1331" "1332" "1333" "1334" "1335" "1336" "1337" "1338" "1339" "1340"
## [1341] "1341" "1342" "1343" "1344" "1345" "1346" "1347" "1348" "1349" "1350"
## [1351] "1351" "1352" "1353" "1354" "1355" "1356" "1357" "1358" "1359" "1360"
## [1361] "1361" "1362" "1363" "1364" "1365" "1366" "1367" "1368" "1369" "1370"
## [1371] "1371" "1372" "1373" "1374" "1375" "1376" "1377" "1378" "1379" "1380"
## [1381] "1381" "1382" "1383" "1384" "1385" "1386" "1387" "1388" "1389" "1390"
## [1391] "1391" "1392" "1393" "1394" "1395" "1396" "1397" "1398" "1399" "1400"
## [1401] "1401" "1402" "1403" "1404" "1405" "1406" "1407" "1408" "1409" "1410"
## [1411] "1411" "1412" "1413" "1414" "1415" "1416" "1417" "1418" "1419" "1420"
## [1421] "1421" "1422" "1423" "1424" "1425" "1426" "1427" "1428" "1429" "1430"
## [1431] "1431" "1432" "1433" "1434" "1435" "1436" "1437" "1438" "1439" "1440"
## [1441] "1441" "1442" "1443" "1444" "1445" "1446" "1447" "1448" "1449" "1450"
## [1451] "1451" "1452" "1453" "1454" "1455" "1456" "1457" "1458" "1459" "1460"
## [1461] "1461" "1462" "1463" "1464" "1465" "1466" "1467" "1468" "1469" "1470"
## [1471] "1471" "1472" "1473" "1474" "1475" "1476" "1477" "1478" "1479" "1480"
## [1481] "1481" "1482" "1483" "1484" "1485" "1486" "1487" "1488" "1489" "1490"
## [1491] "1491" "1492" "1493" "1494" "1495" "1496" "1497" "1498" "1499" "1500"
## [1501] "1501" "1502" "1503" "1504" "1505" "1506" "1507" "1508" "1509" "1510"
## [1511] "1511" "1512" "1513" "1514" "1515" "1516" "1517" "1518" "1519" "1520"
## [1521] "1521" "1522" "1523" "1524" "1525" "1526" "1527" "1528" "1529" "1530"
## [1531] "1531" "1532" "1533" "1534" "1535" "1536" "1537" "1538" "1539" "1540"
## [1541] "1541" "1542" "1543" "1544" "1545" "1546" "1547" "1548" "1549" "1550"
## [1551] "1551" "1552" "1553" "1554" "1555" "1556" "1557" "1558" "1559" "1560"
## [1561] "1561" "1562" "1563" "1564" "1565" "1566" "1567" "1568" "1569" "1570"
## [1571] "1571" "1572" "1573" "1574" "1575" "1576" "1577" "1578" "1579" "1580"
## [1581] "1581" "1582" "1583" "1584" "1585" "1586" "1587" "1588" "1589" "1590"
## [1591] "1591" "1592" "1593" "1594" "1595" "1596" "1597" "1598" "1599" "1600"
## [1601] "1601" "1602" "1603" "1604" "1605" "1606" "1607" "1608" "1609" "1610"
## [1611] "1611" "1612" "1613" "1614" "1615" "1616" "1617" "1618" "1619" "1620"
## [1621] "1621" "1622" "1623" "1624" "1625" "1626" "1627" "1628" "1629" "1630"
## [1631] "1631" "1632" "1633" "1634" "1635" "1636" "1637" "1638" "1639" "1640"
## [1641] "1641" "1642" "1643" "1644" "1645" "1646" "1647" "1648" "1649" "1650"
## [1651] "1651" "1652" "1653" "1654" "1655" "1656" "1657" "1658" "1659" "1660"
## [1661] "1661" "1662" "1663" "1664" "1665" "1666" "1667" "1668" "1669" "1670"
## [1671] "1671" "1672" "1673" "1674" "1675" "1676" "1677" "1678" "1679" "1680"
## [1681] "1681" "1682" "1683" "1684" "1685" "1686" "1687" "1688" "1689" "1690"
## [1691] "1691" "1692" "1693" "1694" "1695" "1696" "1697" "1698" "1699" "1700"
## [1701] "1701" "1702" "1703" "1704" "1705" "1706" "1707" "1708" "1709" "1710"
## [1711] "1711" "1712" "1713" "1714" "1715" "1716" "1717" "1718" "1719" "1720"
## [1721] "1721" "1722" "1723" "1724" "1725" "1726" "1727" "1728" "1729" "1730"
## [1731] "1731" "1732" "1733" "1734" "1735" "1736" "1737" "1738" "1739" "1740"
## [1741] "1741" "1742" "1743" "1744" "1745" "1746" "1747" "1748" "1749" "1750"
## [1751] "1751" "1752" "1753" "1754" "1755" "1756" "1757" "1758" "1759" "1760"
## [1761] "1761" "1762" "1763" "1764" "1765" "1766" "1767" "1768" "1769" "1770"
## [1771] "1771" "1772" "1773" "1774" "1775" "1776" "1777" "1778" "1779" "1780"
## [1781] "1781" "1782" "1783" "1784" "1785" "1786" "1787" "1788" "1789" "1790"
## [1791] "1791" "1792" "1793" "1794" "1795" "1796" "1797" "1798" "1799" "1800"
## [1801] "1801" "1802" "1803" "1804" "1805" "1806" "1807" "1808" "1809" "1810"
## [1811] "1811" "1812" "1813" "1814" "1815" "1816" "1817" "1818" "1819" "1820"
## [1821] "1821" "1822" "1823" "1824" "1825" "1826" "1827" "1828" "1829" "1830"
## [1831] "1831" "1832" "1833" "1834" "1835" "1836" "1837" "1838" "1839" "1840"
## [1841] "1841" "1842" "1843" "1844" "1845" "1846" "1847" "1848" "1849" "1850"
## [1851] "1851" "1852" "1853" "1854" "1855" "1856" "1857" "1858" "1859" "1860"
## [1861] "1861" "1862" "1863" "1864" "1865" "1866" "1867" "1868" "1869" "1870"
## [1871] "1871" "1872" "1873" "1874" "1875" "1876" "1877" "1878" "1879" "1880"
## [1881] "1881" "1882" "1883" "1884" "1885" "1886" "1887" "1888" "1889" "1890"
## [1891] "1891" "1892" "1893" "1894" "1895" "1896" "1897" "1898" "1899" "1900"
## [1901] "1901" "1902" "1903" "1904" "1905" "1906" "1907" "1908" "1909" "1910"
## [1911] "1911" "1912" "1913" "1914" "1915" "1916" "1917" "1918" "1919" "1920"
## [1921] "1921" "1922" "1923" "1924" "1925" "1926" "1927" "1928" "1929" "1930"
## [1931] "1931" "1932" "1933" "1934" "1935" "1936" "1937" "1938" "1939" "1940"
## [1941] "1941" "1942" "1943" "1944" "1945" "1946" "1947" "1948" "1949" "1950"
## [1951] "1951" "1952" "1953" "1954" "1955" "1956" "1957" "1958" "1959" "1960"
## [1961] "1961" "1962" "1963" "1964" "1965" "1966" "1967" "1968" "1969" "1970"
## [1971] "1971" "1972" "1973" "1974" "1975" "1976" "1977" "1978" "1979" "1980"
## [1981] "1981" "1982" "1983" "1984" "1985" "1986" "1987" "1988" "1989" "1990"
## [1991] "1991" "1992" "1993" "1994" "1995" "1996" "1997" "1998" "1999" "2000"
## [2001] "2001" "2002" "2003" "2004" "2005" "2006" "2007" "2008" "2009" "2010"
## [2011] "2011" "2012" "2013" "2014" "2015" "2016" "2017" "2018" "2019" "2020"
## [2021] "2021" "2022" "2023" "2024" "2025" "2026" "2027" "2028" "2029" "2030"
## [2031] "2031" "2032" "2033" "2034" "2035" "2036" "2037" "2038" "2039" "2040"
## [2041] "2041" "2042" "2043" "2044" "2045" "2046" "2047" "2048" "2049" "2050"
## [2051] "2051" "2052" "2053" "2054" "2055" "2056" "2057" "2058" "2059" "2060"
## [2061] "2061" "2062" "2063" "2064" "2065" "2066" "2067" "2068" "2069" "2070"
## [2071] "2071" "2072" "2073" "2074" "2075" "2076" "2077" "2078" "2079" "2080"
## [2081] "2081" "2082" "2083" "2084" "2085" "2086" "2087" "2088" "2089" "2090"
## [2091] "2091" "2092" "2093" "2094" "2095" "2096" "2097" "2098" "2099" "2100"
## [2101] "2101" "2102" "2103" "2104" "2105" "2106" "2107" "2108" "2109" "2110"
## [2111] "2111" "2112" "2113" "2114" "2115" "2116" "2117" "2118" "2119" "2120"
## [2121] "2121" "2122" "2123" "2124" "2125" "2126" "2127" "2128" "2129" "2130"
## [2131] "2131" "2132" "2133" "2134" "2135" "2136" "2137" "2138" "2139" "2140"
## [2141] "2141" "2142" "2143" "2144" "2145" "2146" "2147" "2148" "2149" "2150"
## [2151] "2151" "2152" "2153" "2154" "2155" "2156" "2157" "2158" "2159" "2160"
## [2161] "2161" "2162" "2163" "2164" "2165" "2166" "2167" "2168" "2169" "2170"
## [2171] "2171" "2172" "2173" "2174" "2175" "2176" "2177" "2178" "2179" "2180"
## [2181] "2181" "2182" "2183" "2184" "2185" "2186" "2187" "2188" "2189" "2190"
## [2191] "2191" "2192" "2193" "2194" "2195" "2196" "2197" "2198" "2199" "2200"
## [2201] "2201" "2202" "2203" "2204" "2205" "2206" "2207" "2208" "2209" "2210"
## [2211] "2211" "2212" "2213" "2214" "2215" "2216" "2217" "2218" "2219" "2220"
## [2221] "2221" "2222" "2223" "2224" "2225" "2226" "2227" "2228" "2229" "2230"
## [2231] "2231" "2232" "2233" "2234" "2235" "2236" "2237" "2238" "2239" "2240"
## [2241] "2241" "2242" "2243" "2244" "2245" "2246" "2247" "2248" "2249" "2250"
## [2251] "2251" "2252" "2253" "2254" "2255" "2256" "2257" "2258" "2259" "2260"
## [2261] "2261" "2262" "2263" "2264" "2265" "2266" "2267" "2268" "2269" "2270"
## [2271] "2271" "2272" "2273" "2274" "2275" "2276" "2277" "2278" "2279" "2280"
## [2281] "2281" "2282" "2283" "2284" "2285" "2286" "2287" "2288" "2289" "2290"
## [2291] "2291" "2292" "2293" "2294" "2295" "2296" "2297" "2298" "2299" "2300"
## [2301] "2301" "2302" "2303" "2304" "2305" "2306" "2307" "2308" "2309" "2310"
## [2311] "2311" "2312" "2313" "2314" "2315" "2316" "2317" "2318" "2319" "2320"
## [2321] "2321" "2322" "2323" "2324" "2325" "2326" "2327" "2328" "2329" "2330"
## [2331] "2331" "2332" "2333" "2334" "2335" "2336" "2337" "2338" "2339" "2340"
## [2341] "2341" "2342" "2343" "2344" "2345" "2346" "2347" "2348" "2349" "2350"
## [2351] "2351" "2352" "2353" "2354" "2355" "2356" "2357" "2358" "2359" "2360"
## [2361] "2361" "2362" "2363" "2364" "2365" "2366" "2367" "2368" "2369" "2370"
## [2371] "2371" "2372" "2373" "2374" "2375" "2376" "2377" "2378" "2379" "2380"
## [2381] "2381" "2382" "2383" "2384" "2385" "2386" "2387" "2388" "2389" "2390"
## [2391] "2391" "2392" "2393" "2394" "2395" "2396" "2397" "2398" "2399" "2400"
## [2401] "2401" "2402" "2403" "2404" "2405" "2406" "2407" "2408" "2409" "2410"
## [2411] "2411" "2412" "2413" "2414" "2415" "2416" "2417" "2418" "2419" "2420"
## [2421] "2421" "2422" "2423" "2424" "2425" "2426" "2427" "2428" "2429" "2430"
## [2431] "2431" "2432" "2433" "2434" "2435" "2436" "2437" "2438" "2439" "2440"
## [2441] "2441" "2442" "2443" "2444" "2445" "2446" "2447" "2448" "2449" "2450"
## [2451] "2451" "2452" "2453" "2454" "2455" "2456" "2457" "2458" "2459" "2460"
## [2461] "2461" "2462" "2463" "2464" "2465" "2466" "2467" "2468" "2469" "2470"
## [2471] "2471" "2472" "2473" "2474" "2475" "2476" "2477" "2478" "2479" "2480"
## [2481] "2481" "2482" "2483" "2484" "2485" "2486" "2487" "2488" "2489" "2490"
## [2491] "2491" "2492" "2493" "2494" "2495" "2496" "2497" "2498" "2499" "2500"
## [2501] "2501" "2502" "2503" "2504" "2505" "2506" "2507" "2508" "2509" "2510"
## [2511] "2511" "2512" "2513" "2514" "2515" "2516" "2517" "2518" "2519" "2520"
## [2521] "2521" "2522" "2523" "2524" "2525" "2526" "2527" "2528" "2529" "2530"
## [2531] "2531" "2532" "2533" "2534" "2535" "2536" "2537" "2538" "2539" "2540"
## [2541] "2541" "2542" "2543" "2544" "2545" "2546" "2547" "2548" "2549" "2550"
## [2551] "2551" "2552" "2553" "2554" "2555" "2556" "2557" "2558" "2559" "2560"
## [2561] "2561" "2562" "2563" "2564" "2565" "2566" "2567" "2568" "2569" "2570"
## [2571] "2571" "2572" "2573" "2574" "2575" "2576" "2577" "2578" "2579" "2580"
## [2581] "2581" "2582" "2583" "2584" "2585" "2586" "2587" "2588" "2589" "2590"
## [2591] "2591" "2592" "2593" "2594" "2595" "2596" "2597" "2598" "2599" "2600"
## [2601] "2601" "2602" "2603" "2604" "2605" "2606" "2607" "2608" "2609" "2610"
## [2611] "2611" "2612" "2613" "2614" "2615" "2616" "2617" "2618" "2619" "2620"
## [2621] "2621" "2622" "2623" "2624" "2625" "2626" "2627" "2628" "2629" "2630"
## [2631] "2631" "2632" "2633" "2634" "2635" "2636" "2637" "2638" "2639" "2640"
## [2641] "2641" "2642" "2643" "2644" "2645" "2646" "2647" "2648" "2649" "2650"
## [2651] "2651" "2652" "2653" "2654" "2655" "2656" "2657" "2658" "2659" "2660"
## [2661] "2661" "2662" "2663" "2664" "2665" "2666" "2667" "2668" "2669" "2670"
## [2671] "2671" "2672" "2673" "2674" "2675" "2676" "2677" "2678" "2679" "2680"
## [2681] "2681" "2682" "2683" "2684" "2685" "2686" "2687" "2688" "2689" "2690"
## [2691] "2691" "2692" "2693" "2694" "2695" "2696" "2697" "2698" "2699" "2700"
## [2701] "2701" "2702" "2703" "2704" "2705" "2706" "2707" "2708" "2709" "2710"
## [2711] "2711" "2712" "2713" "2714" "2715" "2716" "2717" "2718" "2719" "2720"
## [2721] "2721" "2722" "2723" "2724" "2725" "2726" "2727" "2728" "2729" "2730"
## [2731] "2731" "2732" "2733" "2734" "2735" "2736" "2737" "2738" "2739" "2740"
## [2741] "2741" "2742" "2743" "2744" "2745" "2746" "2747" "2748" "2749" "2750"
## [2751] "2751" "2752" "2753" "2754" "2755" "2756" "2757" "2758" "2759" "2760"
## [2761] "2761" "2762" "2763" "2764" "2765" "2766" "2767" "2768" "2769" "2770"
## [2771] "2771" "2772" "2773" "2774" "2775" "2776" "2777" "2778" "2779" "2780"
## [2781] "2781" "2782" "2783" "2784" "2785" "2786" "2787" "2788" "2789" "2790"
## [2791] "2791" "2792" "2793" "2794" "2795" "2796" "2797" "2798" "2799" "2800"
## [2801] "2801" "2802" "2803" "2804" "2805" "2806" "2807" "2808" "2809" "2810"
## [2811] "2811" "2812" "2813" "2814" "2815" "2816" "2817" "2818" "2819" "2820"
## [2821] "2821" "2822" "2823" "2824" "2825" "2826" "2827" "2828" "2829" "2830"
## [2831] "2831" "2832" "2833" "2834" "2835" "2836" "2837" "2838" "2839" "2840"
## [2841] "2841" "2842" "2843" "2844" "2845" "2846" "2847" "2848" "2849" "2850"
## [2851] "2851" "2852" "2853" "2854" "2855" "2856" "2857" "2858" "2859" "2860"
## [2861] "2861" "2862" "2863" "2864" "2865" "2866" "2867" "2868" "2869" "2870"
## [2871] "2871" "2872" "2873" "2874" "2875" "2876" "2877" "2878" "2879" "2880"
## [2881] "2881" "2882" "2883" "2884" "2885" "2886" "2887" "2888" "2889" "2890"
## [2891] "2891" "2892" "2893" "2894" "2895" "2896" "2897" "2898" "2899" "2900"
## [2901] "2901" "2902" "2903" "2904" "2905" "2906" "2907" "2908" "2909" "2910"
## [2911] "2911" "2912" "2913" "2914" "2915" "2916" "2917" "2918" "2919" "2920"
## [2921] "2921" "2922" "2923" "2924" "2925" "2926" "2927" "2928" "2929" "2930"
## [2931] "2931" "2932" "2933" "2934" "2935" "2936" "2937" "2938" "2939" "2940"
## [2941] "2941" "2942" "2943" "2944" "2945" "2946" "2947" "2948" "2949" "2950"
## [2951] "2951" "2952" "2953" "2954" "2955" "2956" "2957" "2958" "2959" "2960"
## [2961] "2961" "2962" "2963" "2964" "2965" "2966" "2967" "2968" "2969" "2970"
## [2971] "2971" "2972" "2973" "2974" "2975" "2976" "2977" "2978" "2979" "2980"
## [2981] "2981" "2982" "2983" "2984" "2985" "2986" "2987" "2988" "2989" "2990"
## [2991] "2991" "2992" "2993" "2994" "2995" "2996" "2997" "2998" "2999" "3000"
## [3001] "3001" "3002" "3003" "3004" "3005" "3006" "3007" "3008" "3009" "3010"
## [3011] "3011" "3012" "3013" "3014" "3015" "3016" "3017" "3018" "3019" "3020"
## [3021] "3021" "3022" "3023" "3024" "3025" "3026" "3027" "3028" "3029" "3030"
## [3031] "3031" "3032" "3033" "3034" "3035" "3036" "3037" "3038" "3039" "3040"
## [3041] "3041" "3042" "3043" "3044" "3045" "3046" "3047" "3048" "3049" "3050"
## [3051] "3051" "3052" "3053" "3054" "3055" "3056" "3057" "3058" "3059" "3060"
## [3061] "3061" "3062" "3063" "3064" "3065" "3066" "3067" "3068" "3069" "3070"
## [3071] "3071" "3072" "3073" "3074" "3075" "3076" "3077" "3078" "3079" "3080"
## [3081] "3081" "3082" "3083" "3084" "3085" "3086" "3087" "3088" "3089" "3090"
## [3091] "3091" "3092" "3093" "3094" "3095" "3096" "3097" "3098" "3099" "3100"
## [3101] "3101" "3102" "3103" "3104" "3105" "3106" "3107" "3108" "3109" "3110"
## [3111] "3111" "3112" "3113" "3114" "3115" "3116" "3117" "3118" "3119" "3120"
## [3121] "3121" "3122" "3123" "3124" "3125" "3126" "3127" "3128" "3129" "3130"
## [3131] "3131" "3132" "3133" "3134" "3135" "3136" "3137" "3138" "3139" "3140"
## [3141] "3141" "3142" "3143" "3144" "3145" "3146" "3147" "3148" "3149" "3150"
## [3151] "3151" "3152" "3153" "3154" "3155" "3156" "3157" "3158" "3159" "3160"
## [3161] "3161" "3162" "3163" "3164" "3165" "3166" "3167" "3168" "3169" "3170"
## [3171] "3171" "3172" "3173" "3174" "3175" "3176" "3177" "3178" "3179" "3180"
## [3181] "3181" "3182" "3183" "3184" "3185" "3186" "3187" "3188" "3189" "3190"
## [3191] "3191" "3192" "3193" "3194" "3195" "3196" "3197" "3198" "3199" "3200"
## [3201] "3201" "3202" "3203" "3204" "3205" "3206" "3207" "3208" "3209" "3210"
## [3211] "3211" "3212" "3213" "3214" "3215" "3216" "3217" "3218" "3219" "3220"
## [3221] "3221" "3222" "3223" "3224" "3225" "3226" "3227" "3228" "3229" "3230"
## [3231] "3231" "3232" "3233" "3234" "3235" "3236" "3237" "3238" "3239" "3240"
## [3241] "3241" "3242" "3243" "3244" "3245" "3246" "3247" "3248" "3249" "3250"
## [3251] "3251" "3252" "3253" "3254" "3255" "3256" "3257" "3258" "3259" "3260"
## [3261] "3261" "3262" "3263" "3264" "3265" "3266" "3267" "3268" "3269" "3270"
## [3271] "3271" "3272" "3273" "3274" "3275" "3276" "3277" "3278" "3279" "3280"
## [3281] "3281" "3282" "3283" "3284" "3285" "3286" "3287" "3288" "3289" "3290"
## [3291] "3291" "3292" "3293" "3294" "3295" "3296" "3297" "3298" "3299" "3300"
## [3301] "3301" "3302" "3303" "3304" "3305" "3306" "3307" "3308" "3309" "3310"
## [3311] "3311" "3312" "3313"summary(gapminder_unfiltered) # summarised the data sets## country continent year lifeExp
## Czech Republic: 58 Africa : 637 Min. :1950 Min. :23.60
## Denmark : 58 Americas: 470 1st Qu.:1967 1st Qu.:58.33
## Finland : 58 Asia : 578 Median :1982 Median :69.61
## Iceland : 58 Europe :1302 Mean :1980 Mean :65.24
## Japan : 58 FSU : 139 3rd Qu.:1996 3rd Qu.:73.66
## Netherlands : 58 Oceania : 187 Max. :2007 Max. :82.67
## (Other) :2965
## pop gdpPercap
## Min. :5.941e+04 Min. : 241.2
## 1st Qu.:2.680e+06 1st Qu.: 2505.3
## Median :7.560e+06 Median : 7825.8
## Mean :3.177e+07 Mean : 11313.8
## 3rd Qu.:1.961e+07 3rd Qu.: 17355.8
## Max. :1.319e+09 Max. :113523.1
## Q: How is summary different from describe?? Ans: Summary is more consice and it comes with base package, in general summary is more than enough
Subsetting the data
gm.subset <- gapminder[gapminder$year %in% c(2002, 2007),]Perform a function for each country
Calulate mean GDP per capita per country
aggregate(gm.subset$gdpPercap, by= list(gm.subset$country), FUN = mean)## Group.1 x
## 1 Afghanistan 850.6572
## 2 Albania 5270.6206
## 3 Algeria 5755.7039
## 4 Angola 3785.2593
## 5 Argentina 10788.5102
## 6 Australia 32561.5611
## 7 Austria 34272.0502
## 8 Bahrain 26599.8038
## 9 Bangladesh 1263.8221
## 10 Belgium 32089.2444
## 11 Benin 1407.0814
## 12 Bolivia 3617.6999
## 13 Bosnia and Herzegovina 6732.6370
## 14 Botswana 11786.7284
## 15 Brazil 8598.5068
## 16 Bulgaria 9188.7853
## 17 Burkina Faso 1127.3391
## 18 Burundi 438.2371
## 19 Cambodia 1305.0024
## 20 Cameroon 1988.0533
## 21 Canada 34824.1000
## 22 Central African Republic 722.3536
## 23 Chad 1430.1228
## 24 Chile 11975.2113
## 25 China 4039.1979
## 26 Colombia 6380.9202
## 27 Comoros 1030.9797
## 28 Congo, Dem. Rep. 259.3589
## 29 Congo, Rep. 3558.3099
## 30 Costa Rica 8684.2543
## 31 Cote d'Ivoire 1596.7755
## 32 Croatia 13123.8058
## 33 Cuba 7644.3748
## 34 Czech Republic 20214.7594
## 35 Denmark 33722.4594
## 36 Djibouti 1995.3712
## 37 Dominican Republic 5294.5915
## 38 Ecuador 6323.1534
## 39 Egypt 5167.8927
## 40 El Salvador 5539.9611
## 41 Equatorial Guinea 9928.7928
## 42 Eritrea 703.3598
## 43 Ethiopia 610.4296
## 44 Finland 30705.8375
## 45 France 29698.0245
## 46 Gabon 12864.0992
## 47 Gambia 706.6677
## 48 Germany 31103.0882
## 49 Ghana 1219.7967
## 50 Greece 25026.3333
## 51 Guatemala 5022.1987
## 52 Guinea 944.1189
## 53 Guinea-Bissau 577.4682
## 54 Haiti 1236.0010
## 55 Honduras 3324.0298
## 56 Hong Kong, China 34966.9969
## 57 Hungary 16426.4400
## 58 Iceland 33671.9956
## 59 India 2099.4899
## 60 Indonesia 3207.2822
## 61 Iran 10423.2382
## 62 Iraq 4430.8896
## 63 Ireland 37376.5229
## 64 Israel 23714.4361
## 65 Italy 28268.9089
## 66 Jamaica 7157.8276
## 67 Japan 30130.3300
## 68 Jordan 4182.1892
## 69 Kenya 1375.3820
## 70 Korea, Dem. Rep. 1619.9118
## 71 Korea, Rep. 21291.0640
## 72 Kuwait 41208.5477
## 73 Lebanon 9887.4988
## 74 Lesotho 1422.2580
## 75 Liberia 472.9949
## 76 Libya 10796.0884
## 77 Madagascar 969.7036
## 78 Malawi 712.3865
## 79 Malaysia 11329.3169
## 80 Mali 996.9957
## 81 Mauritania 1691.0855
## 82 Mauritius 9989.4035
## 83 Mexico 11360.0077
## 84 Mongolia 2618.2558
## 85 Montenegro 7905.5452
## 86 Morocco 3539.3354
## 87 Mozambique 728.6518
## 88 Myanmar 777.5000
## 89 Namibia 4441.6926
## 90 Nepal 1074.2830
## 91 Netherlands 35261.3455
## 92 New Zealand 24187.4052
## 93 Nicaragua 2611.9349
## 94 Niger 610.3757
## 95 Nigeria 1814.6318
## 96 Norway 47020.5827
## 97 Oman 21045.5149
## 98 Pakistan 2349.3300
## 99 Panama 8582.6088
## 100 Paraguay 3978.2564
## 101 Peru 6658.9628
## 102 Philippines 2920.7010
## 103 Poland 13696.0819
## 104 Portugal 20240.2778
## 105 Puerto Rico 19092.1576
## 106 Reunion 6993.1439
## 107 Romania 9346.9178
## 108 Rwanda 824.3711
## 109 Sao Tome and Principe 1475.7637
## 110 Saudi Arabia 20334.6866
## 111 Senegal 1616.0537
## 112 Serbia 8511.3050
## 113 Sierra Leone 781.0152
## 114 Singapore 41583.1425
## 115 Slovak Republic 16158.5464
## 116 Slovenia 23214.1385
## 117 Somalia 904.1114
## 118 South Africa 8490.3021
## 119 Spain 26828.2677
## 120 Sri Lanka 3492.7371
## 121 Sudan 2297.8967
## 122 Swaziland 4320.7988
## 123 Sweden 31600.6896
## 124 Switzerland 35993.6884
## 125 Syria 4137.7367
## 126 Taiwan 25976.8501
## 127 Tanzania 1003.2782
## 128 Thailand 6685.7919
## 129 Togo 884.5953
## 130 Trinidad and Tobago 14734.5547
## 131 Tunisia 6407.9093
## 132 Turkey 7483.1811
## 133 Uganda 992.0506
## 134 United Kingdom 31341.1302
## 135 United States 41024.3763
## 136 Uruguay 9169.2325
## 137 Venezuela 10010.4268
## 138 Vietnam 2103.0165
## 139 West Bank and Gaza 3770.4187
## 140 Yemen, Rep. 2257.7954
## 141 Zambia 1171.4128
## 142 Zimbabwe 570.8740Now this is giving us mean gdp per capita for each country
There are three arguments in this function * 1st is the Vector (gm.subset\(gdpPercap) on which we want to apply the function * 2nd the criteria ( list(gm.subset\)country)) on which we want to apply * 3rd is the Funtion (FUN = mean)
Similarly For mean GDP per capita for per continent
aggregate(gm.subset$gdpPercap, by= list(gm.subset$continent), FUN = mean) ## Group.1 x
## 1 Africa 2844.209
## 2 Americas 10145.354
## 3 Asia 11323.559
## 4 Europe 23383.107
## 5 Oceania 28374.483Now this is giving us mean gdp per capita for each continent
Similarly For mean GDP per capita for both continent and country
aggregate(gm.subset$gdpPercap, by= list(gm.subset$country, gm.subset$continent), FUN = mean)## Group.1 Group.2 x
## 1 Algeria Africa 5755.7039
## 2 Angola Africa 3785.2593
## 3 Benin Africa 1407.0814
## 4 Botswana Africa 11786.7284
## 5 Burkina Faso Africa 1127.3391
## 6 Burundi Africa 438.2371
## 7 Cameroon Africa 1988.0533
## 8 Central African Republic Africa 722.3536
## 9 Chad Africa 1430.1228
## 10 Comoros Africa 1030.9797
## 11 Congo, Dem. Rep. Africa 259.3589
## 12 Congo, Rep. Africa 3558.3099
## 13 Cote d'Ivoire Africa 1596.7755
## 14 Djibouti Africa 1995.3712
## 15 Egypt Africa 5167.8927
## 16 Equatorial Guinea Africa 9928.7928
## 17 Eritrea Africa 703.3598
## 18 Ethiopia Africa 610.4296
## 19 Gabon Africa 12864.0992
## 20 Gambia Africa 706.6677
## 21 Ghana Africa 1219.7967
## 22 Guinea Africa 944.1189
## 23 Guinea-Bissau Africa 577.4682
## 24 Kenya Africa 1375.3820
## 25 Lesotho Africa 1422.2580
## 26 Liberia Africa 472.9949
## 27 Libya Africa 10796.0884
## 28 Madagascar Africa 969.7036
## 29 Malawi Africa 712.3865
## 30 Mali Africa 996.9957
## 31 Mauritania Africa 1691.0855
## 32 Mauritius Africa 9989.4035
## 33 Morocco Africa 3539.3354
## 34 Mozambique Africa 728.6518
## 35 Namibia Africa 4441.6926
## 36 Niger Africa 610.3757
## 37 Nigeria Africa 1814.6318
## 38 Reunion Africa 6993.1439
## 39 Rwanda Africa 824.3711
## 40 Sao Tome and Principe Africa 1475.7637
## 41 Senegal Africa 1616.0537
## 42 Sierra Leone Africa 781.0152
## 43 Somalia Africa 904.1114
## 44 South Africa Africa 8490.3021
## 45 Sudan Africa 2297.8967
## 46 Swaziland Africa 4320.7988
## 47 Tanzania Africa 1003.2782
## 48 Togo Africa 884.5953
## 49 Tunisia Africa 6407.9093
## 50 Uganda Africa 992.0506
## 51 Zambia Africa 1171.4128
## 52 Zimbabwe Africa 570.8740
## 53 Argentina Americas 10788.5102
## 54 Bolivia Americas 3617.6999
## 55 Brazil Americas 8598.5068
## 56 Canada Americas 34824.1000
## 57 Chile Americas 11975.2113
## 58 Colombia Americas 6380.9202
## 59 Costa Rica Americas 8684.2543
## 60 Cuba Americas 7644.3748
## 61 Dominican Republic Americas 5294.5915
## 62 Ecuador Americas 6323.1534
## 63 El Salvador Americas 5539.9611
## 64 Guatemala Americas 5022.1987
## 65 Haiti Americas 1236.0010
## 66 Honduras Americas 3324.0298
## 67 Jamaica Americas 7157.8276
## 68 Mexico Americas 11360.0077
## 69 Nicaragua Americas 2611.9349
## 70 Panama Americas 8582.6088
## 71 Paraguay Americas 3978.2564
## 72 Peru Americas 6658.9628
## 73 Puerto Rico Americas 19092.1576
## 74 Trinidad and Tobago Americas 14734.5547
## 75 United States Americas 41024.3763
## 76 Uruguay Americas 9169.2325
## 77 Venezuela Americas 10010.4268
## 78 Afghanistan Asia 850.6572
## 79 Bahrain Asia 26599.8038
## 80 Bangladesh Asia 1263.8221
## 81 Cambodia Asia 1305.0024
## 82 China Asia 4039.1979
## 83 Hong Kong, China Asia 34966.9969
## 84 India Asia 2099.4899
## 85 Indonesia Asia 3207.2822
## 86 Iran Asia 10423.2382
## 87 Iraq Asia 4430.8896
## 88 Israel Asia 23714.4361
## 89 Japan Asia 30130.3300
## 90 Jordan Asia 4182.1892
## 91 Korea, Dem. Rep. Asia 1619.9118
## 92 Korea, Rep. Asia 21291.0640
## 93 Kuwait Asia 41208.5477
## 94 Lebanon Asia 9887.4988
## 95 Malaysia Asia 11329.3169
## 96 Mongolia Asia 2618.2558
## 97 Myanmar Asia 777.5000
## 98 Nepal Asia 1074.2830
## 99 Oman Asia 21045.5149
## 100 Pakistan Asia 2349.3300
## 101 Philippines Asia 2920.7010
## 102 Saudi Arabia Asia 20334.6866
## 103 Singapore Asia 41583.1425
## 104 Sri Lanka Asia 3492.7371
## 105 Syria Asia 4137.7367
## 106 Taiwan Asia 25976.8501
## 107 Thailand Asia 6685.7919
## 108 Vietnam Asia 2103.0165
## 109 West Bank and Gaza Asia 3770.4187
## 110 Yemen, Rep. Asia 2257.7954
## 111 Albania Europe 5270.6206
## 112 Austria Europe 34272.0502
## 113 Belgium Europe 32089.2444
## 114 Bosnia and Herzegovina Europe 6732.6370
## 115 Bulgaria Europe 9188.7853
## 116 Croatia Europe 13123.8058
## 117 Czech Republic Europe 20214.7594
## 118 Denmark Europe 33722.4594
## 119 Finland Europe 30705.8375
## 120 France Europe 29698.0245
## 121 Germany Europe 31103.0882
## 122 Greece Europe 25026.3333
## 123 Hungary Europe 16426.4400
## 124 Iceland Europe 33671.9956
## 125 Ireland Europe 37376.5229
## 126 Italy Europe 28268.9089
## 127 Montenegro Europe 7905.5452
## 128 Netherlands Europe 35261.3455
## 129 Norway Europe 47020.5827
## 130 Poland Europe 13696.0819
## 131 Portugal Europe 20240.2778
## 132 Romania Europe 9346.9178
## 133 Serbia Europe 8511.3050
## 134 Slovak Republic Europe 16158.5464
## 135 Slovenia Europe 23214.1385
## 136 Spain Europe 26828.2677
## 137 Sweden Europe 31600.6896
## 138 Switzerland Europe 35993.6884
## 139 Turkey Europe 7483.1811
## 140 United Kingdom Europe 31341.1302
## 141 Australia Oceania 32561.5611
## 142 New Zealand Oceania 24187.4052Using sapply(), tapply(), and apply()
sapply(), checks data type of every column
sapply(gapminder, class)## country continent year lifeExp pop gdpPercap
## "factor" "factor" "integer" "numeric" "integer" "numeric"Gapminder is a datatype and class is a function it can be anything which you want to know
To find mean for each column
sapply(gapminder, mean)## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA
## Warning in mean.default(X[[i]], ...): argument is not numeric or logical:
## returning NA## country continent year lifeExp pop gdpPercap
## NA NA 1.979500e+03 5.947444e+01 2.960121e+07 7.215327e+03Mean can’t be calculated as there are character entries in some columns
As we saw above some columns are character some are numeric and if we want to perform some function on some specific column, so we can use apply function
apply(gapminder, 2, class)## country continent year lifeExp pop gdpPercap
## "character" "character" "character" "character" "character" "character"NOTE: Here 2= column
Calculating mean only for numeric columns
apply(gapminder[,5:6], 2, mean)## pop gdpPercap
## 29601212.325 7215.327perform function on each row
apply(gapminder[,5:6], 1, mean)## [1] 4213056.22 4620877.43 5133968.05 5769401.10 6540099.99
## [6] 7440579.06 6441397.01 6934404.70 8159285.17 11114025.17
## [11] 12634565.87 15945448.79 642149.03 739223.64 865224.94
## [16] 993410.10 1133433.71 1256290.50 1391863.94 1539529.97
## [21] 1664497.72 1715615.53 1756558.11 1803230.01 4640987.00
## [26] 5136934.99 5501749.41 6381873.00 7382484.83 8578857.21
## [31] 10019749.08 11630318.68 13151698.11 14538406.15 15646215.02
## [36] 16669719.68 2117807.81 2282594.47 2415142.14 2626495.89
## [41] 2950165.64 3082841.82 3509570.48 3938330.10 4369307.92
## [46] 4938650.57 5434439.64 6212636.62 8941433.66 9808697.43
## [51] 10645458.08 11471138.98 12394621.02 13496953.51 14675185.95
## [56] 15815028.84 16984127.71 18107215.14 19169959.32 20157353.19
## [61] 4350625.80 4861759.32 5403592.61 5943395.06 6596894.31
## [66] 7046217.10 7601838.50 8139568.94 8752700.88 9296120.47
## [71] 9788739.88 10234305.68 3466954.54 3487351.30 3570307.36
## [76] 3694916.30 3780431.31 3794089.71 3798105.04 3801295.41
## [81] 3971005.51 4049485.96 4090364.80 4117954.75 65157.04
## [86] 75145.40 92308.14 108493.34 124534.33 158375.05
## [91] 198589.07 236568.01 274263.29 309426.51 339900.28
## [96] 369184.52 23443771.62 25683064.82 28419987.67 31411302.59
## [101] 35379962.62 40214482.94 46537541.49 51882496.49 56852708.41
## [106] 61658130.39 67828963.20 75224865.13 4369374.05 4499412.98
## [111] 4614695.60 4784824.52 4862886.07 4920458.99 4938641.42
## [116] 4946362.78 5035598.79 5113674.10 5171227.94 5212959.30
## [121] 869688.88 963066.30 1076422.25 1214184.92 1381246.40
## [126] 1584648.08 1821440.45 2122506.93 2491431.10 3033656.49
## [131] 3513742.94 4039877.64 1442996.16 1606932.84 1798049.49
## [136] 2021625.94 2284426.17 2541632.05 2822690.26 3079561.35
## [141] 3448206.35 3848257.07 4224273.63 4561487.07 1395986.77
## [146] 1538676.99 1675354.84 1793586.18 1910930.08 2044764.24
## [151] 2088409.81 2171645.56 2129279.89 1805883.18 2085717.49
## [156] 2279822.15 221579.62 237778.62 256873.83 277377.85
## [161] 310807.31 392343.43 487449.07 578694.94 675284.06
## [166] 772591.57 820675.30 825850.43 28302334.47 32776829.18
## [171] 38021363.29 44026626.43 50422521.86 57160305.56 64484984.92
## [176] 71472941.55 77991462.14 84277338.49 89961171.61 95009856.40
## [181] 3638672.14 3827131.34 4008600.17 4157901.50 4291398.75
## [186] 4402317.12 4450161.10 4490098.93 4332404.31 4036013.69
## [191] 3834747.89 3666769.40 2235261.13 2357016.59 2460177.26
## [196] 2564364.91 2717370.37 2945158.69 3317701.60 3793731.53
## [201] 4439617.38 5176894.65 6126123.32 7163710.02 1222978.65
## [206] 1333948.78 1481135.10 1665700.99 1765223.55 1917485.55
## [211] 2290484.80 2563322.41 2904933.85 3061036.56 3510762.20
## [216] 4195467.54 2347102.23 2661485.02 3042057.96 3480295.22
## [221] 3725513.81 3489565.99 3636554.74 4186237.45 5075388.15
## [226] 5891848.14 6463801.61 7066785.89 2505119.83 2680618.02
## [231] 2897516.30 3168507.23 3511356.07 3980824.22 4626599.49
## [236] 5391634.83 6234482.08 7098751.67 7965961.01 8849167.55
## [241] 7398475.58 8511321.98 9499655.74 10417921.79 11151735.29
## [246] 11909245.44 12612399.40 13288163.26 14274922.44 15167398.96
## [251] 15967798.48 16713230.12 646383.16 696737.42 762335.53
## [256] 867387.03 964165.01 1084321.19 1238963.88 1420426.94
## [261] 1632935.95 1848626.75 2024375.85 2184872.01 1341820.33
## [266] 1448081.75 1575903.41 1748581.91 1950086.05 2194696.99
## [271] 2437957.95 2749953.69 3215237.53 3781507.98 4418447.59
## [276] 5120255.53 3190779.49 3526370.81 3982888.55 4432007.33
## [281] 4861509.01 5302274.88 5746103.83 6234450.53 6790295.06
## [286] 7305023.53 7753912.39 8148956.32 278131963.72 318704287.99
## [291] 332885243.84 377275306.35 431015338.45 471727870.62 500140981.21
## [296] 542018189.45 582485827.89 615038644.62 640201559.64 659344027.56
## [301] 6176457.56 7244158.40 8506188.68 9883352.86 11273077.33
## [306] 12549113.90 13884520.79 15484574.11 17104082.82 18831973.68
## [311] 20506991.13 22117278.29 77519.50 86069.57 96547.82
## [316] 109627.01 125982.29 152955.80 174955.05 198214.99
## [321] 227837.95 264577.81 307728.91 355973.07 7050392.77
## [326] 7789418.93 8743665.16 9970967.30 11504286.95 13240832.88
## [331] 15323584.37 17741158.89 20836300.36 23899649.09 27690046.58
## [336] 32303518.28 428505.31 471386.53 525194.39 591218.97
## [341] 671835.58 770014.09 889807.25 1034148.10 1206544.62
## [346] 1402215.58 1666139.53 1902121.28 464472.00 557645.01
## [351] 674323.97 796439.36 919957.07 1057191.94 1214814.87
## [356] 1402720.46 1589688.21 1762392.02 1921328.72 2071764.53
## [361] 1489203.80 1650750.45 1917068.43 2373461.03 3037037.10
## [366] 3731045.87 4514276.86 5381627.48 6387122.04 7313876.63
## [371] 8127187.40 9007476.88 1942674.12 1997790.12 2041017.45
## [376] 2090663.15 2117237.05 2164989.19 2213294.91 2249066.29
## [381] 2251230.40 2227235.30 2246324.19 2253965.61 3006691.77
## [386] 3323422.09 3629776.88 4072511.13 4418326.72 4772184.25
## [391] 4898270.46 5123685.96 5364426.42 5494219.50 5616669.82
## [396] 5712967.55 4566029.57 4761007.17 4815209.43 4923254.22
## [401] 4937633.23 5088357.58 5159540.61 5163953.72 5164999.51
## [406] 5158377.76 5136945.61 5125788.65 2171846.19 2249465.33
## [411] 2330241.16 2427368.61 2505231.10 2554420.95 2569749.02
## [416] 2576070.09 2598899.87 2656733.67 2703429.75 2751699.21
## [421] 32909.26 37357.98 46459.49 65318.53 91271.11
## [426] 115887.88 154435.23 156952.55 193266.58 209901.51
## [431] 224662.13 249228.24 1246371.86 1462365.20 1727548.07
## [436] 2025399.86 2336759.44 2652740.99 2985605.05 3329098.42
## [441] 3677112.61 3997985.55 4327442.90 4662823.69 1776137.56
## [446] 2031082.77 2342896.56 2718501.54 3151966.00 3642772.81
## [451] 4186531.90 4775819.89 5377748.85 5959624.23 6463503.52
## [456] 6881276.63 11112363.91 12505599.96 14087501.17 15841501.44
## [461] 17404720.50 19393324.25 22842657.36 26401473.73 29702996.38
## [466] 33069232.09 36658656.80 40135062.09 1022956.65 1179613.26
## [471] 1375731.90 1618642.80 1897711.62 2143862.46 2239485.67
## [476] 2423167.22 2639546.62 2894296.91 3179516.28 3472708.18
## [481] 108669.82 116674.05 124901.42 130389.80 139137.71
## [486] 96816.78 143205.41 171105.45 194485.03 221392.74
## [491] 251665.25 281677.54 719544.47 771477.58 833499.50
## [496] 910393.90 1130350.66 1256573.88 1318910.94 1458240.07
## [501] 1834511.43 2029616.24 2207815.18 2453613.18 10430651.57
## [506] 11407996.45 12572895.73 13930406.56 15385469.12 17309177.90
## [511] 19056166.93 21500051.87 26044490.18 29930908.44 33973663.53
## [516] 38256288.90 2048462.26 2165772.71 2250407.42 2308332.82
## [521] 2327007.94 2377253.71 2422733.08 2476435.01 2530843.08
## [526] 2579064.98 2610621.80 2635833.54 21233348.40 22159762.92
## [531] 23567280.24 24790999.96 25874053.60 26591655.82 27226929.45
## [536] 27826083.22 28699441.40 29324658.89 29976980.52 30557193.01
## [541] 212497.74 219940.10 231146.23 248681.38 274689.47
## [546] 364056.29 384493.68 446130.70 499630.58 570455.92
## [551] 655912.86 734036.74 142402.62 161835.46 187309.83
## [556] 220163.89 258928.54 304579.38 358179.40 424508.83
## [561] 513024.81 618210.37 729213.29 844555.87 34576548.06
## [566] 35514628.41 36876009.73 38191599.31 39367552.09 39090642.96
## [571] 39178648.77 38871468.59 40312134.65 41019430.94 41190353.40
## [576] 41216583.19 2790956.15 3196165.78 3678219.02 4245669.35
## [581] 4677649.11 5269543.11 5700607.02 7084474.00 8139831.53
## [586] 9209646.62 10275931.49 11437332.80 3868390.35 4050567.15
## [591] 4227125.10 4362477.05 4450676.41 4661337.26 4900874.21
## [596] 4995305.26 5171485.25 5260559.85 5313188.63 5366914.21
## [601] 1574404.62 1821746.58 2105804.18 2347007.77 2576806.20
## [606] 2854155.00 3200225.25 3665326.24 4245694.23 4904279.66
## [611] 5591754.17 6289057.03 1332379.60 1438651.13 1570344.69
## [616] 1726063.38 1906064.33 2113950.34 2355677.13 2825533.79
## [621] 3495684.17 4024851.72 4404381.79 4974378.33 290476.43
## [626] 300763.40 314171.02 301001.29 313090.61 372996.36
## [631] 413412.56 464130.21 525841.77 597252.33 666517.35
## [636] 736310.12 1601664.18 1754713.94 1940963.29 2159794.53
## [641] 2349977.73 2455214.15 2600205.08 2879013.01 3164069.15
## [646] 3457443.36 3804460.68 4252007.82 759823.96 886305.24
## [651] 1046226.58 1251613.63 1483837.92 1529219.10 1836284.88
## [656] 2187613.05 2540214.35 2935558.73 3340213.86 3743655.67
## [661] 1064477.21 1369964.54 1654946.32 1864498.98 2062007.96
## [666] 2297443.07 2639530.27 2802274.24 2927226.80 3262147.82
## [671] 3396342.51 3510068.49 4754631.84 4922520.09 5035275.18
## [676] 5116374.32 5202129.83 5324422.92 5359040.50 5312863.24
## [681] 5179609.81 5128198.39 5049078.47 4987058.47 77614.84
## [686] 87177.00 96201.58 105997.95 112536.53 120738.98
## [691] 128633.30 135799.60 142078.20 149626.55 159596.60
## [696] 169055.89 186000273.28 204500295.03 227000329.17 253000350.39
## [701] 283500362.02 317000406.67 354000427.86 394000488.26 436000582.20
## [706] 479500729.41 517087146.88 555199391.61 41026374.84 45062429.45
## [711] 49514424.64 54671881.22 60641555.55 68363191.35 76672258.44
## [716] 84638874.18 92409191.57 99640559.67 105531436.96 111775270.33
## [721] 8637517.66 9897645.13 11439093.66 13271953.37 15311806.91
## [726] 17746283.80 21540179.67 25948169.44 30202604.33 31668125.30
## [731] 33458533.38 34732587.86 2722947.88 3127436.17 3624300.87
## [736] 4264106.73 5035541.02 5948802.12 7093917.95 8277416.29
## [741] 8932825.32 10389389.62 12003103.36 13752054.53 1478683.14
## [746] 1441909.54 1418315.80 1453877.78 1516965.39 1641525.49
## [751] 1746309.16 1776886.43 1787659.91 1845877.47 1956616.02
## [756] 2074881.00 812500.26 974893.14 1159004.82 1350989.37
## [761] 1554339.97 1754612.31 1936894.01 2110135.24 2477300.76
## [766] 2776141.80 3025717.30 3226101.14 23835465.70 24594124.33
## [771] 25425721.79 26338561.20 27188916.64 28036750.49 28276086.74
## [776] 28374455.12 28431430.32 28752072.01 28977483.55 29088151.36
## [781] 714496.77 769923.26 835187.05 933610.35 1002524.94
## [786] 1081732.10 1152188.53 1166478.62 1193011.46 1269216.46
## [791] 1335826.89 1393726.44 43231120.98 45783663.35 47919166.82
## [796] 50417563.39 53601525.89 56944541.69 59237179.05 61056850.47
## [801] 62178046.95 62992657.79 63547222.80 63749814.03 304730.45
## [806] 374222.54 467953.50 628899.90 807830.93 970252.18
## [811] 1175596.21 1412245.34 1935420.30 2264940.19 2655657.46
## [816] 3028856.23 3232449.77 3727861.72 4339726.98 5096284.37
## [821] 6023003.68 7250835.81 8831400.11 10599721.97 12510940.46
## [826] 14132593.74 15694064.76 17805820.12 4433288.14 4706476.07
## [831] 5459557.85 6309576.27 7392471.31 8164713.15 8825812.26
## [836] 9535830.25 10357550.53 10793397.88 11108505.88 11651659.03
## [841] 10474300.80 11306519.80 13210921.67 15066514.61 16754015.44
## [846] 18220328.61 19665811.47 20815266.54 21908777.14 23094904.76
## [851] 23994191.99 24534069.07 134191.18 163184.57 226862.06
## [856] 327948.94 475640.93 599811.24 764424.02 959802.71
## [861] 726513.96 902822.81 1073335.55 1276432.99 722181.90
## [866] 826750.89 946281.28 1096450.49 1343752.19 1562223.35
## [871] 1547258.26 1547365.05 1613442.40 1719571.48 1843546.97
## [876] 1965869.53 374522.92 406837.00 446777.40 498439.32
## [881] 558637.79 626134.68 706302.13 799987.00 902086.24
## [886] 992004.57 1024023.59 1007109.17 431941.79 488285.48
## [891] 556715.10 640059.80 741715.50 852128.66 978723.60
## [896] 1134960.06 956805.31 1100667.09 1407591.24 1597178.25
## [901] 511058.27 602513.14 724310.02 888998.38 1102444.25
## [906] 1371867.11 1680719.14 1905807.79 2187070.57 2384568.72
## [911] 2689059.84 3024485.75 2382177.51 2591634.10 2852483.69
## [916] 3168095.02 3542089.28 4004355.11 4586389.94 5284898.72
## [921] 6105717.84 7083050.15 8237185.82 9584349.39 1459085.58
## [926] 1610827.18 1814517.95 2073873.76 2365790.81 2818954.61
## [931] 3251728.90 3912691.26 5007406.10 5210341.64 5912580.21
## [936] 6663919.17 3375104.57 3870522.53 4454210.94 5078577.87
## [941] 5722155.55 6424604.46 7223418.18 8168517.40 9163389.96
## [946] 10243111.95 11336285.99 12416868.83 1919310.17 2121187.19
## [951] 2345434.09 2606480.50 2914369.68 3246167.70 3499437.01
## [956] 3817346.09 4208477.01 4692887.13 5290563.70 6016418.79
## [961] 511649.56 538849.06 573906.45 615981.57 667186.43
## [966] 729092.75 811808.58 921330.80 1060413.18 1223112.07
## [971] 1415218.51 1635934.08 259261.98 305925.02 351772.53
## [976] 395892.19 426954.74 458367.99 497864.02 523723.29
## [981] 551130.13 578621.85 604613.91 630919.50 15073897.56
## [986] 17509839.77 20563033.30 24000656.87 27995551.70 31883825.46
## [991] 35825257.57 40065590.08 44060251.19 47952456.65 51245334.72
## [996] 54356434.29 400724.78 441523.33 505668.18 575363.02
## [1001] 660960.87 764823.76 879016.30 1008735.50 1157293.70
## [1006] 1248352.63 1338187.37 1438611.39 208240.79 223255.63
## [1011] 239588.80 253471.43 267728.21 284834.46 286885.29
## [1016] 290602.76 314312.17 349558.31 363393.60 346994.95
## [1021] 4970452.60 5703996.00 6529085.18 7386003.52 8331300.10
## [1026] 9199655.81 10100716.31 11495076.02 12900593.52 14266241.55
## [1031] 15585520.75 16880497.59 3223392.26 3519265.29 3894750.34
## [1036] 4340737.83 4905160.46 5564185.16 6293842.61 6446170.94
## [1041] 6580570.95 8301903.17 9237206.81 9976239.84 10046663.50
## [1046] 10866097.00 11817412.00 12935310.00 14233373.50 15764229.00
## [1051] 17340433.00 19014481.50 20273442.50 21624141.00 22799346.00
## [1056] 23881462.00 244127.39 275350.72 312282.61 355216.85
## [1061] 412764.04 490451.24 551600.55 640938.87 779028.77
## [1066] 889332.76 988112.66 1029945.53 4591540.93 4841467.97
## [1071] 5166354.70 5631183.22 6206633.89 6966946.06 7898516.19
## [1076] 8958977.82 10163553.37 11501061.95 12937487.10 14451440.68
## [1081] 5195464.79 5518829.60 5909239.92 6306092.63 6674334.37
## [1086] 6937099.03 7165900.23 7344464.66 7600517.47 7817355.07
## [1091] 8078277.38 8303705.47 1002675.29 1120827.20 1250862.84
## [1096] 1371306.96 1472573.02 1590566.86 1614141.21 1668086.60
## [1101] 1728018.66 1848618.71 1965613.40 2070478.00 584451.18
## [1106] 681142.71 797115.68 935066.70 1093798.30 1280042.19
## [1111] 1491446.67 1673654.49 2010054.58 2305912.51 2574661.27
## [1116] 2839052.66 1690114.94 1846509.76 2038502.88 2267558.19
## [1121] 2530608.10 2841447.45 3219048.86 3666653.15 4196699.59
## [1126] 4833416.15 5570628.04 6447742.34 16560086.64 18587220.30
## [1131] 20936250.96 23644383.26 26870891.69 31105577.48 36520476.49
## [1136] 40776452.51 46682931.92 53104731.97 59951444.64 67516588.99
## [1141] 1668911.71 1751795.99 1826184.70 1901190.44 1975984.53
## [1146] 2033258.17 2070542.82 2108843.99 2160161.33 2223477.58
## [1151] 2290137.49 2338641.60 254830.62 282109.87 315544.32
## [1156] 359747.97 419834.02 508190.67 657001.40 805998.61
## [1161] 966912.35 1151668.53 1366618.42 1613606.60 20673622.30
## [1166] 23340345.54 26550737.17 30321420.70 34663485.47 39076930.96
## [1171] 45731765.71 52594292.84 60033487.91 67783441.68 76702808.36
## [1176] 84636611.47 471280.19 533233.90 609630.77 704953.50
## [1181] 810874.12 922566.96 1021657.30 1130336.89 1245807.87
## [1186] 1370822.35 1499115.52 1625991.09 778914.15 886474.08
## [1191] 1005980.51 1145142.19 1308313.67 1493871.19 1685348.75
## [1196] 1945255.44 2244070.71 2579185.20 2944137.34 3335659.92
## [1201] 4014729.26 4575172.63 5260728.52 6068994.05 6980318.91
## [1206] 7998190.15 9065781.75 10101142.47 11217447.69 12376980.17
## [1211] 13387672.51 14341082.95 11219981.94 13036870.97 15163456.78
## [1216] 17679207.06 20426065.19 23426667.60 26729688.64 30009988.82
## [1221] 33594022.66 37507762.27 41498869.46 45540238.74 12867290.16
## [1226] 14120040.13 15167477.88 15895967.58 16523775.75 17315381.07
## [1231] 18117916.27 18874896.18 19189217.94 19332558.29 19318989.12
## [1236] 19266815.46 4264559.16 4410712.29 4512263.98 4554680.76
## [1241] 4489736.12 4836386.24 4935701.92 4964164.15 4971943.63
## [1246] 5087028.02 5226918.95 5331672.82 1115040.98 1131953.58
## [1251] 1226577.17 1327945.14 1428127.52 1545299.26 1644665.99
## [1256] 1728374.67 1799908.79 1888214.72 1939230.80 1980909.85
## [1261] 130209.44 155734.73 181036.86 209022.59 233340.33
## [1266] 248207.40 261538.61 283669.19 314146.13 345440.97
## [1271] 375148.58 402882.06 8316572.31 8916635.19 9342728.00
## [1276] 9645642.43 10335329.71 10833976.70 11183165.66 11348033.64
## [1281] 11401812.70 11284902.27 11206111.18 11143432.24 1267710.16
## [1286] 1411311.14 1525919.74 1725794.98 1996355.79 2328871.04
## [1291] 2754223.29 3175106.50 3645470.03 3606586.47 3926593.33
## [1296] 4430725.54 30445.29 31092.87 33208.28 36085.92
## [1301] 39063.99 44266.78 50241.61 56164.26 63669.89
## [1306] 73473.54 85862.55 100588.72 2006068.28 2213903.80
## [1311] 2477327.71 2817550.52 3248796.71 4081336.38 5644182.59
## [1316] 7320471.63 8485349.31 10625172.85 12260272.27 13811346.42
## [1321] 1378519.68 1528057.33 1715948.99 1983726.70 2295146.86
## [1326] 2631208.38 3074650.74 3586394.36 4154643.95 4768353.18
## [1331] 5435778.32 6134602.74 3431864.23 3638058.05 3811174.81
## [1336] 3989606.85 4161905.03 4349673.83 4524002.55 4623326.94
## [1341] 4917861.03 5172254.16 5059397.54 5080025.77 1072064.39
## [1346] 1148341.24 1234505.82 1331698.02 1440183.38 1571122.64
## [1351] 1732993.51 1935099.72 2130976.35 2289393.32 2679895.74
## [1356] 3072712.27 564657.57 724386.05 876937.37 991288.71
## [1361] 1080498.88 1168255.04 1333519.08 1406706.77 1630317.45
## [1366] 1917914.24 2116899.55 2300076.09 1781605.83 1925185.13
## [1371] 2122432.55 2225325.45 2301553.58 2419362.83 2529695.77
## [1376] 2605677.63 2656193.23 2697568.12 2711845.39 2733090.16
## [1381] 746866.52 769466.14 795182.15 828158.74 853446.74
## [1386] 881098.02 939559.36 982274.27 1006712.36 1014386.55
## [1391] 1016078.51 1017506.63 1264064.87 1390836.57 1540761.24
## [1396] 1715061.87 1920707.79 2177558.50 2915034.40 3461475.62
## [1401] 3050362.98 3317222.30 3877096.04 4559849.57 7134830.15
## [1406] 8078518.05 9181212.86 10502217.74 11971787.98 13568980.33
## [1411] 15574298.63 17970602.41 19985692.03 21421242.09 22220666.47
## [1416] 22003548.83 14276852.02 14923089.40 15581877.42 16429134.26
## [1421] 17261899.88 18226118.46 18998618.08 19448233.49 19784020.53
## [1426] 19937943.65 20088676.24 20238506.03 3991712.77 4564809.27
## [1431] 5211505.24 5869265.76 6508973.20 7059092.39 7705899.54
## [1436] 8248590.38 8794606.87 9350659.74 9789899.19 10191104.55
## [1441] 4253141.50 4877581.17 5592593.30 6358908.50 7299339.33
## [1446] 8553594.49 10184474.27 12363733.91 14114540.10 16081180.61
## [1451] 18546145.70 21147765.70 145695.69 163992.85 185931.09
## [1456] 211651.55 241734.92 277603.21 326898.19 391666.42
## [1461] 482948.51 529181.38 567198.56 568789.74 3566600.42
## [1466] 3686856.94 3786958.72 3941594.65 4070062.51 4135251.86
## [1471] 4172963.69 4222494.96 4371373.51 4461442.80 4491758.32
## [1476] 4532473.87 2414867.12 2571954.74 2843215.55 3042983.07
## [1481] 3214297.56 3171703.15 3248261.86 3340111.85 3513659.27
## [1486] 3612948.16 3698118.98 3796083.71 1831596.24 2076012.62
## [1491] 2418407.02 2841346.96 3351871.71 3967849.24 4707127.92
## [1496] 5622981.89 6611201.27 7542515.12 8579952.46 9659465.77
## [1501] 4275784.47 5082861.43 5960380.44 6825667.93 7615050.76
## [1506] 8395396.26 9254408.18 9884426.78 10351066.83 10824405.91
## [1511] 11238737.21 11601506.14 4161820.83 4726762.27 5432340.00
## [1516] 6304080.11 7353754.49 8565263.75 9922628.12 11520730.91
## [1521] 13303149.34 15343839.09 17297339.04 19070373.74 10645079.90
## [1526] 12521355.29 14632199.60 17012772.23 19638838.68 22075123.11
## [1531] 24414776.61 26456662.33 28335855.95 30111264.81 31406330.59
## [1536] 32537803.70 609986.40 679185.45 764582.77 868513.80
## [1541] 1029000.33 1155057.39 1323054.79 1577733.10 1874293.65
## [1546] 2160936.14 2489132.11 2851230.98 332936.64 384500.20
## [1551] 446247.76 482888.18 490909.28 523454.28 562799.26
## [1556] 599362.30 595520.00 573446.79 556646.30 537308.25
## [1561] 1824601.74 1976122.12 2144106.15 2394459.18 2653130.14
## [1566] 3004090.94 3368829.12 3864393.21 4263704.86 4618272.90
## [1571] 4888148.95 5141625.46 11118823.05 12836578.88 14895508.93
## [1576] 16707071.68 18748201.85 21204151.06 23666516.18 26443208.52
## [1581] 29092411.17 31527124.21 33657718.04 35583552.64 2912765.88
## [1586] 3338137.69 3844782.14 4450601.46 5095617.87 5729300.87
## [1591] 6470041.13 7641833.86 9126417.09 10605535.28 12370398.36
## [1596] 14585727.19 25219989.75 25720641.59 26652238.59 27486571.43
## [1601] 28047447.56 28098214.37 28178968.21 28501642.39 28944527.05
## [1606] 29417170.27 29970955.00 30404720.63 78783495.24 85999423.56
## [1611] 93277086.57 99365765.18 104958903.02 110131536.32 116106422.28
## [1616] 121416708.68 128463096.47 136473763.72 143857311.55 150591449.33
## [1621] 1129340.88 1215554.89 1302034.68 1377011.81 1417614.70
## [1626] 1440012.17 1480458.61 1526302.70 1578699.50 1636034.12
## [1631] 1685406.00 1729053.73 2723628.90 3356235.23 4075898.99
## [1636] 4859546.74 5763077.13 6758353.48 7815959.21 8960032.79
## [1641] 10138148.46 11192281.75 12148137.52 13048038.90 13123722.03
## [1646] 14499609.64 16898456.02 19732273.56 22327856.75 25267109.77
## [1651] 28071444.12 31413655.90 34970858.51 38025190.95 40454955.73
## [1656] 42632398.79 516050.30 536133.03 567666.48 572642.86
## [1661] 546352.70 632386.92 715106.02 848158.60 1055398.33
## [1666] 1416578.33 1697046.74 2010678.67 2482305.36 2749447.42
## [1671] 3060453.31 3370823.72 3704170.02 4202909.88 4829797.78
## [1676] 5610655.87 6684938.25 7914307.24 9351745.91 11107011.88
## [1681] 1336573.69 1508655.98 1711226.36 1950888.54 2254135.25
## [1686] 2609069.34 3050907.84 3636809.66 4191186.94 4709430.18
## [1691] 5298441.31 5873653.11 1540656.94 1823429.38 2139131.64
## [1696] 2498000.90 2930967.18 3321396.29 3818656.43 4608562.08
## [1701] 5352516.71 5702870.22 5963617.52 6155806.35NOTE: Here 1 denotes it’s calculating mean on rows
tapply also works as aggregate but differs in output format
tapply(gm.subset$gdpPercap, gm.subset$country, FUN= mean) -> tapplycheck
str(tapplycheck)## num [1:142(1d)] 851 5271 5756 3785 10789 ...
## - attr(*, "dimnames")=List of 1
## ..$ : chr [1:142] "Afghanistan" "Albania" "Algeria" "Angola" ...Q: Difference between aggregate and tapply?
ANs: aggregate gives vector as an output whereas tapply gives list in output.