This document demonstrates how to calculate mean, variance, and standard deviation in R using a dataset containing class frequencies (f) and class midpoints (xi). It loads the data, calculates the mean (47.66667) by taking a weighted average of the midpoints by frequency. It then calculates the sum of squared deviations from the mean weighted by frequency to get the variance (374.2222) and standard deviation (19.34482).

1. USING R IN INTRODUCTION STATISTICS
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DATASET
Kelas f
Nilai Tengah
(xi)
a b c
10-19 9 15
20-29 20 25
30-39 26 35
40-49 35 45
50-59 22 55
60-69 17 65
70-79 11 75
80-89 6 85
90'99 4 95
# Load data from file excel
> library(readxl)
> DATASETCOVAR <- read_excel("D:/R/DATASETCOVAR.xlsx")
> View(DATASETCOVAR)
> dataset.1 <- DATASETCOVAR[,c(2,3)]
> dataset.1
# A tibble: 9 × 2
f `Nilai Tengah (xi)`
<dbl> <dbl>
1 9 15
2 20 25
3 26 35
4 35 45
5 22 55
6 17 65
7 11 75
8 6 85
9 4 95
# Karena data diatas dalam bentuk table maka kita perlu rubah kedalam bent
uk vector, sebagai contoh
F xi
1 2 1
2 1 3
3 1 2
Menjadi [1]1 1 3 2
> rep(DATASETCOVAR$`Nilai Tengah (xi)`,DATASETCOVAR$f)
# Maka mean/nilai tengah akan didapat
> mean(rep(DATASETCOVAR$`Nilai Tengah (xi)`,DATASETCOVAR$f))
[1] 47.66667
# kemudian kita akan cari |xi-xrata|

2. > abs(DATASETCOVAR$`Nilai Tengah (xi)`- mean(rep(DATASETCOVAR$`Nilai Tenga
h (xi)`,DATASETCOVAR$f)))
[1] 32.666667 22.666667 12.666667 2.666667 7.333333 17.333333 27.333333
37.333333 47.333333
# kemudian kita akan cari |xi-xrata|^2
> (abs(DATASETCOVAR$`Nilai Tengah (xi)`- mean(rep(DATASETCOVAR$`Nilai Teng
ah (xi)`,DATASETCOVAR$f))))^2
[1] 1067.111111 513.777778 160.444444 7.111111 53.777778 300.44444
4 747.111111
[8] 1393.777778 2240.444444
# kemudian kita akan cari |xi-xrata|^2 * f
> (abs(DATASETCOVAR$`Nilai Tengah (xi)`- mean(rep(DATASETCOVAR$`Nilai Teng
ah (xi)`,DATASETCOVAR$f))))^2*DATASETCOVAR$f
[1] 9604.0000 10275.5556 4171.5556 248.8889 1183.1111 5107.5556 821
8.2222 8362.6667
[9] 8961.7778
#Maka Ragam atau variance, dan Standar deviasi atau simpangan bakunya dida
pat
> sum((abs(DATASETCOVAR$`Nilai Tengah (xi)`- mean(rep(DATASETCOVAR$`Nilai
Tengah (xi)`,DATASETCOVAR$f))))^2*DATASETCOVAR$f)
[1] 56133.33
> b <- sum((abs(DATASETCOVAR$`Nilai Tengah (xi)`- mean(rep(DATASETCOVAR$`N
ilai Tengah (xi)`,DATASETCOVAR$f))))^2*DATASETCOVAR$f)
> a <- sum(DATASETCOVAR$f)
> a
[1] 150
# Ragam atau Variance
> b/a
[1] 374.2222
# Simpangan baku atau standard deviasi
> sqrt(b/a)
[1] 19.34482