This question is incomplete, the complete question is;
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.)
Answer:
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
