what is the standard deviation for the numbers 1,6,6,3,7,4,and10

Question

I need to know how to find the standard deviation for the numbers 1,6,6,3,7,4,and10.

Show me the steps

 

Answer 1

Given numbers are 1,6,6,3,7,4,10.

Mean of gven numbers is (1+6+6+3+7+4+10)/7

Mean = 37/7

= 5.28

To calculate the given numbers standard deviation, first compute the difference of each data point from the mean,and square the result of each.

(1-5.28)^2= (-4.28)^2 = 18.31

(6-5.28)^2 = (0.72)^2 = 0.51

(6-5.28)^2 = (0.72)^2 = 0.51

(3-5.28)^2 = (-2.28)^2 = 5.19

(7-5.28)^2 = (1.72)^2 = 2.95

(4-5.28)^2 = (-1.28)^2 = 1.63

(10-5.28)^2 = (4.72)^2 = 22.27

Next compute the mean of these values and take the square root.

Mean =(18.31+0.51+0.51+5.19+2.95+1.63+22.27)/7

= 51.37/7

= 7.33

Sqrt(7.33) = 2.709

Given numbers standard deviation is 2.7.