Find the sample variance and standard deviation. , , , , , , , , , Choose the correct answer below. Fill in the answer box to complete your choice. (Round to two decimal places as needed.)

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Find the sample variance and standard deviation.

7, 55, 14, 49, 32, 23, 30, 32, 34,27

Choose the correct answer below. Fill in the answer box to complete your choice. (Round to two decimal places as needed.)

Sample Variance S² = 205.79

Sample standard deviation S = 14.35

Step-by-step explanation:

Given that;

the observation are;  7, 55, 14, 49, 32, 23, 30, 32, 34,27

First we calculate Sample Mean

⁻x = (∑xi) / n

⁻x = ( 7 + 55 + 14 + 49 + 32 +  23 + 30 + 32 + 34 + 27 ) / 10

⁻x  = 303 / 10 = 30.3

mean ⁻x  = 30.3

now to calculate Sample  variance;

Sample Variance S² = (∑(xi  - ⁻x )²) / (n-1)

⁻x is sample mean

xi is element in the sample

n is sample size

so

Xi                (xi  - ⁻x )                (xi  - ⁻x )²

7                   -23.3                   542.89

55                 24.7                    610.09

14                 -16.3                    265.69

49                 18.7                    349.69

32                  1.7                     2.89

23                -7.3                     53.29

30                -0.3                     0.09

32                  1.7                     2.89

34                 3.7                     13.69

27                -3.3                     10.89

TOTAL ∑                               1852.1  

Sample Variance S² = (∑(xi  - ⁻x )²) / (n-1)

So we substitute

Sample Variance S² =   1852.1  / ( 10 - 1)

Sample Variance S² =  1852.1  / 9

Sample Variance S² = 205.79

Sample standard deviation S = √ [ (∑(xi  - ⁻x )²) / (n-1)]

i.e Sample standard deviation S = √ ( Sample Variance )

Sample standard deviation S = √ 205.79

Sample standard deviation S = 14.35