Question

The formula for the standard deviation of a sample is:

Answer 1

Answer:

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

Step-by-step 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