Question

what is the standard deviation of the following data set rounded to the nearest tenth? 30, 26, 28, 32, 28, 30

Answer 1

σ = √ 110 / 5 is your standard deviation

Answer 2

Standard deviation = 1.9

Explanation:

We have to calculate the standard deviation of the following data set.

30, 26, 28, 32, 28, 30

To find standard deviation first we have to calculate the mean of the data set.

Mean =
`(30+26+28+32+28+30)/(6)`

=
`(174)/(6)`

Mean = 29

Now we subtract the mean from all units and square the result.

30 - 29 = 1² = 1

26 - 29 = -3² = 9

28 - 29 = -1² = 1

32 - 29 = 3² = 9

28 - 29 = -1² = 1

30 - 29 = 1² = 1

Now take the mean of squared result.

Mean =
`(1+9+1+9+1+1)/(6)` =
`(22)/(6)` = 3.67

Now standard deviation will be the under root of mean
`√(3.67)`

Standard deviation = 1.915 ≈ 1.9