What is the standard deviation of {4, 5, 8, 3, 6, 2, 1, 5, 9, 5, 4, 2}?

1 Answer
Feb 21, 2016

Standard Deviation is 2.2913

Explanation:

Set of numbers are {4, 5, 8, 3, 6, 2, 1, 5, 9, 5, 4, 2}. As there are 12 terms whose sum is 54, mean is 54/12 or 4.5.

Hence deviations from mean are {-0.5, 0.5, 3.5, -1.5, 1.5, -2.5, -3.5, 0.5, 4.5, 0.5, -0.5, -2.5} and sum of there squares is

0.25+0.25+12.25+2.25+2.25+6.25+12.25+0.25+20.25+0.25+0.25+6.25=63

Hence Standard Deviation is sqrt(63/12)=sqrt(21/4)=1/2sqrt21=4.5826/2 i.e. 2.2913