Answer: the required variance is 11.6555
Step-by-step explanation:
Given data;
xi = 2 19 23 14 20 16 21 18 14 19
mean x" = 2+19+23+14+20+16+21+18+14+19 / 10
mean x" = 166 / 10 = 16.6
so;
X xi - x" (xi - x")²
12 -4.9 24.01
16 -0.9 0.81
23 6.1 37.21
13 -3.9 15.21
18 1.1 1.21
18 1.1 1.21
19 2.1 4.41
18 1.1 1.21
13 -3.9 15.21
19 2.1 4.41
Total 104.9
Variance = n_i=1∑(xi - x")² / n-1
Variance = 104.9 / 9
Variance = 11.6555
Therefore, the required variance is 11.6555
