Question

Find the standard deviation of the data set below. Round to the nearest tenth,
6, 5, 2, 5,8

Answer 1

The standard deviation = 1.9

Explanation:

standard deviation, ρ = sqrt (
`(sum(x_(i) - u)^(2) )/(N)`)

Where u is the mean of the data,
`x_(i)` each given value, and N is the number of data given.

Mean, u =
`(6+5+2+5+8)/(5)`

= 5.2

So that;

`(6-5.2)^(2)` =
`(0.8)^(2)` = 0.64

`(5-5.2)^(2)` =
`(-0.2)^(2)` = 0.04

`(2-5.2)^(2)` =
`(-3.2)^(2)` = 10.24

`(5-5.2)^(2)` =
`(-0.2)^(2)` = 0.04

`(8-5.2)^(2)` =
`(2.8)^(2)` = 7.84

Sum = 18.8

So that;

`\sqrt{(18.8)/(5) }` =
`√(3.76)`

= 1.9391

= 1.9

The standard deviation of the given data is 1.9