Question

Find sample standard deviation from these values
20, 19, 20, 20, 8, 10 , 16, 13 , 11

Answer 1

The formulas for mean, variance, and standard deviation for sample are given as below:

Sample Mean = X̄ = ∑ X/n

Sample Variance = S² = ∑[ (X - mean)^2]/(n - 1)

Sample Standard deviation = S = Sqrt(S²) = Sqrt(Variance)

The calculation table is given as below:

No.	X	(X - mean)^2
1	20	22.82716262
2	19	14.27160662
3	20	22.82716262
4	20	22.82716262
5	8	52.16049062
6	10	27.27160262
7	16	0.604938617
8	13	4.938270617
9	11	17.82715862
Total	137	185.5555556

From above table, we have

n = 9

Sample Mean = X̄ = 137/9 = 15.22222

Sample Variance = S² = 185.5555556/(9 - 1) = 185.5555556/8 = 23.19444444

Sample Standard deviation = S =sqrt(23.19444444) = 4.816061092

Sample standard deviation = 4.816061092