Mean and Standard Deviation

Question

Calculate the mean and standard deviation for the set of numbers
{11,16, 20,17}

Answer 1

Step 1. We find the mean of the numbers:

 

x_bar=1/4(11+16+20+17)

      =1/4•64 = 16.

 

Step 2. We calculate the deviations for the four numbers:

x - x_bar

11 -> 11 - 16 = -5

16 -> 16 - 16 = 0

20 -> 20 - 16 = 4

17 -> 17 - 16 = 1.

 

Step 3. We square the deviations:

 

(-5)² =25

0² =0

4² = 16

1² =1

 

Step 4. We add the squared deviations found in Step 3.

25 + 0 + 16 + 1 = 42.

 

Step 5. We divide the sum from Step 4 by (4-1=3).

 

42÷3=14.

 

Step 6. We take square root of the quotient found in Step 5.

 

√14 = 3.74

 

The standard deviation of the numbers {11, 16, 20, 17} is approximately 3.74.