This will only load the package if it is already installed
# installing/loading the package:
if(!require(moments)) { install.packages("moments"); require("moments")}
#load or install+load 'moments'package
if(!require(modeest)) { install.packages("modeest"); require("modeest")}
#load or install+load 'modeest'package#Importing the dataset from the current directory assuming that the text file has already been saved in the current working directory.
text<-read.table("table6.4.txt",header=TRUE)
#seeing the structure of the data set
str(text)## 'data.frame': 64 obs. of 4 variables:
## $ CM : int 128 204 202 197 96 209 170 240 241 55 ...
## $ FLR : int 37 22 16 65 76 26 45 29 11 55 ...
## $ PGNP: int 1870 130 310 570 2050 200 670 300 120 290 ...
## $ TFR : num 6.66 6.15 7 6.25 3.81 6.44 6.19 5.89 5.89 2.36 ...#Detailed summary statistics
library(psych)
describe(text)## vars n mean sd median trimmed mad min max range
## CM 1 64 141.50 75.98 138.50 139.00 84.51 12.00 312.00 300.0
## FLR 2 64 51.19 26.01 48.00 51.17 31.88 9.00 95.00 86.0
## PGNP 3 64 1401.25 2725.70 620.00 837.69 578.21 120.00 19830.00 19710.0
## TFR 4 64 5.55 1.51 6.04 5.66 1.45 1.69 8.49 6.8
## skew kurtosis se
## CM 0.27 -0.70 9.50
## FLR 0.08 -1.39 3.25
## PGNP 5.16 30.51 340.71
## TFR -0.61 -0.27 0.19#aliter way to summarise
library(fBasics)
basicStats(text)## CM FLR PGNP TFR
## nobs 64.000000 64.000000 6.400000e+01 64.000000
## NAs 0.000000 0.000000 0.000000e+00 0.000000
## Minimum 12.000000 9.000000 1.200000e+02 1.690000
## Maximum 312.000000 95.000000 1.983000e+04 8.490000
## 1. Quartile 82.000000 29.000000 3.000000e+02 4.607500
## 3. Quartile 192.500000 77.250000 1.317500e+03 6.615000
## Mean 141.500000 51.187500 1.401250e+03 5.549688
## Median 138.500000 48.000000 6.200000e+02 6.040000
## Sum 9056.000000 3276.000000 8.968000e+04 355.180000
## SE Mean 9.497258 3.250982 3.407120e+02 0.188624
## LCL Mean 122.521244 44.690930 7.203915e+02 5.172752
## UCL Mean 160.478756 57.684070 2.082109e+03 5.926623
## Variance 5772.666667 676.408730 7.429417e+06 2.277060
## Stdev 75.978067 26.007859 2.725696e+03 1.508993
## Skewness 0.272827 0.076110 5.160060e+00 -0.606093
## Kurtosis -0.695406 -1.393872 3.051475e+01 -0.270432#lets calculate skewness & kurtosis using 'moments' package
library(moments)
#??moments
#??skewness #getting help about skewness function
skewness(text$PGNP)## [1] 5.16006
## attr(,"method")
## [1] "moment"kurtosis(text$PGNP)## [1] 30.51475
## attr(,"method")
## [1] "excess"#??kurtosis #getting help about kurtosis function
#Aliter way using 'e1071' package
#It takes only vector values
library(e1071)
skewness(text$PGNP, na.rm = FALSE, type =1)## [1] 5.16006
## attr(,"method")
## [1] "moment"kurtosis(text$PGNP, na.rm = FALSE, type = 2) #there are various ways to calculate kurtosis/skewness and hence the answer may be slightly different## [1] 30.51475
## attr(,"method")
## [1] "excess"#Lets calculate mode of all the variables using 'modeest' package
library(modeest)
#?modeest
mfv(text$CM)## [1] 142mfv(text$FLR)## [1] 22 31 45 85 88mfv(text$PGNP)## [1] 300 420mfv(text$TFR)## [1] 6.5#or better way to get the output
mlv(text$CM,method="mfv")## Mode (most frequent value): 142
## Bickel's modal skewness: -0.046875
## Call: mlv.integer(x = text$CM, method = "mfv")mlv(text$FLR,method="mfv")## Mode (most frequent value): 22 31 45 85 88
## Bickel's modal skewness: -0.171875
## Call: mlv.integer(x = text$FLR, method = "mfv")mlv(text$PGNP,method="mfv")## Mode (most frequent value): 300 420
## Bickel's modal skewness: 0.390625
## Call: mlv.integer(x = text$PGNP, method = "mfv")mlv(text$TFR,method="mfv")## Mode (most likely value): 6.5
## Bickel's modal skewness: -0.390625
## Call: mlv.default(x = text$TFR, method = "mfv")#some of the variables in the dataset are multimodal