Question

The formula for the standard deviation of a sample is:

Select the true statement for the following data set that has a mean of 9:

3, 7, 8, 8, 8, 9, 10, 10, 13, 14

Answer choices are rounded to the hundredths place.

a. The variance is 8.50 and the standard deviation is 3.09.
b. The variance is 3.09 and the standard deviation is 9.56.
c. The variance is 9.56 and the standard deviation is 8.50.
d. The variance is 9.56 and the standard deviation is 3.09.

Answer 1

d. The variance is 9.56 and the standard deviation is 3.09.

Explanation:

From the above question, we are given the following data set.

3, 7, 8, 8, 8, 9, 10, 10, 13, 14

a) Mean = 3 + 7 + 8 + 8 + 8 + 9 + 10 + 10 + 13 + 14/ 10

= 90/10

= 9

b) Variance

The formula for sample Variance = (Mean - x)²/ n - 1

Mean = 9

n = 10

Sample Variance =

(3 - 9)² + (7 - 9)² + (8 - 9)² + (8 - 9)² + (8 - 9)² + (9 - 9)² + (10 - 9)² + (10 - 9)² + (13 - 9)² + (14 - 9)² / 10 - 1

= 36 + 4 + 1 + 1 + 1 + 0 + 1 + 1 + 16 + 25/9

= 86/9

= 9.555555556

≈ Approximately 9.56

Variance = 9.56

Sample Standard deviation = √Sample Variance

= √9.56

= 3.0919249667

≈ Approximately 3.09