Question

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

Answer 1

Answer:

a) 3.16

Step-by-step explanation:

Explanation:-

Given sample size 'n' =4

mean of x⁻ = ∑x / n

                  = $\frac{13+14+17+20}{4} = \frac{64}{4} =16$

          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

$S^{2} = \frac{30}{4-1} = \frac{30}{3} =10$

The standard deviation of the sample

 S = √10 = 3.1622 ≅3.16