Question

The standard deviation of the sample data 13, 14, 17, and 20 equals if you know that the mean

is 16
Select one:
a. 3.16
b. 7.98
c. 2.74
d. 9.16

Answer 1

a) 3.16

Explanation:

Explanation:-

Given sample size 'n' =4

mean of x⁻ = ∑x / n

=
`(13+14+17+20)/(4) = (64)/(4) =16`

x⁻ = 16

Given data

x 13 14 17 20

x - x⁻ -3 -2 1 4

(x-x⁻)² 9 4 1 16

∑(x-x⁻)² = 9 + 4 + 1 +16 =30

The sample Variance

S² = ∑(x-x⁻)²/n-1

`S^(2) = (30)/(4-1) = (30)/(3) =10`

The standard deviation of the sample

S = √10 = 3.1622 ≅3.16