Tentukan Koefisien Variasi (Variance) masing-masing dan jelaskan hasil perhitungan tersebut.

Question

Seorang peneliti ingin mengetahui variasi nilai mahasiswa laki-laki dan perempuan, maka diambil sampel masing-masing sebanyak 6 orang dan hasilnya adalah sebagai berikut :

Laki-laki   : 6 8 6 10 9 9

Perempuan : 8 4 9 10 10 7

Tentukan Koefisien Variasi (Variance) masing-masing dan jelaskan hasil perhitungan tersebut.

Answer 1

Here is the problem in English:

(I use Google Translate, please let me know if there is something wrong with the translation):

A researcher wants to know the variation in the grades of male and female students, so a sample of 6 people each is taken and the results are as follows:

Male: 6 8 6 10 9 9

Female: 8 4 9 10 10 7

Determine the coefficient of variation (Variance) for each and explain the results of the calculation

Male(y) Female(x) x-x̅ y-ȳ (x-x̅)² (y-ȳ)²

6 8 0 -2 0 4

8 4 -4 0 16 0

6 9 1 -2 1 4

10 10 2 2 4 4

9 10 2 1 4 1

9 7 -1 1 1 1

------------------------------------------------------------------------

∑ = 48 48 26 14

x̅ = 8 8

n = 6 6

∑(x-x̅)² = 26

∑(y-ȳ)² = 14

The formula for the variance is:

s² = ∑(x_i-x̅)²/(n-1)

The following variances for x and y are:

s_x² = 26/5 = 5.2

s_y² = 14/5 = 2.8

Since the variance of the grades of female is greater than male, the grades of female(ranging from 4 to 10) are more spread out than the grades of men (ranging from 6 to 10).