Question

find the standard deviation for this data set 9, 15, 13, 9, 15 round your answer to the nearest tenth

Answer 1

• 3.0

Explanation:

Sample standard deviation is found by steps below.

Find the mean:

• μ = (9 + 15 + 13 + 9 + 15)/5 = 12.2

Find deviations from the mean and their squares:

• 9 - 12.2 = - 3.2 ⇒ (-3.2)² = 10.24
• 15 - 12.2 = 2.8 ⇒ 2.8² = 7.84
• 13 - 12.2 = 0.8 ⇒ 0.8² = 0.64
• 9 - 12.2 = - 3.2 ⇒ (-3.2)² = 10.24
• 15 - 12.2 = 2.8 ⇒ 2.8² = 7.84

Sum the squares:

• 10.24*2 + 7.84*2 + 0.64 = 36.8

Divide by N - 1 (N - number of samples):

• 36.8/(5 - 1) = 9.2

Square root is the sample standard deviation:

• σ = √9.2 = 3.0 (rounded)