Question

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

Answer 1

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`