Find the standard deviation for the group of data items. 11​, 11​, 11​, 16​, 21​, 21​, 21

Question

Find the standard deviation for the group of data items.
11, 11, 11, 16, 21, 21, 21

Answer 1

Hi Sapphron,

 

First, calculate the mean.

mean = 11+11+11+16+21+21+21/7

mean = 16

now calculate the variance, which is the sum of differences squared divided by n-1.

s^2 =((16-11)^2+(16-11)^2+(16-11)^2+(16-16)^2+(16-21)^2+(16-21)^2+(16-21)^2)/(n-1)

= (25+25+25+0+25+25+25)/(7-1)

= 150/6

= 25 this is variance

now take its square root to calculate the standard deviation

s = sqrt(25)

= 5