Question

Find the standard deviation of the following data. Answers are rounded to the nearest tenth. 5, 5, 6, 12, 13, 26, 37, 49, 51, 56, 56, 84

Answer 1

24.2(to the nearest tenth)

Explanation:

The question is ungrouped data type

standard deviation =√ [∑ (x-μ)² / n]

mean (μ)=∑x/n

=
`(5+5+6+12+13+26+37+49+51+56+56+84)/(12)`

=33.3

x-μ for data 5, 5, 6, 12, 13, 26, 37, 49, 51, 56, 56, 84 will be

-28.3, -28.3, -27.3, -21.3, -7.3, 3.7, 15.7,17.7, 22.7,22.7,50.7

(x-μ)² will be 800.89, 800.89,745.29,453.69,53.29,13.69,246.49,313.29,515.29,515.29,2570.49

∑ (x-μ)² will be = 7028.59

standard deviation = √(7028.59 / 12)

=24.2