Question

Consider a sample with data values of 26, 27, 20, 15, 30, 34, 28, and 20. Compute the range, interquartile range, variance, and standard deviation (to a maximum of 2 decimals, if decimals are necessary).

Answer 1

`r=19`

`IQR=9`

`SD=5.81`

Explanation:

Given the following data set:

`26, 27, 20, 15, 30, 34, 28,20`

To find the range of a data set we have to find the largest and the smallest number of the set and then subtract them.

`26, 27, 20, 15, 30, 34, 28,20`

`34-15=19`

`r=19`

To find the interquartile range we have to subtract the third quartile by the first quartile.

`26, 27, 20, 15, 30, 34, 28,20`

`IQR=Q3-Q1`

`Q1=20`

`Q3=29`

`IQR=29-20=9`

`IQR=9`

To find the standard deviation of a data set we have to use the formula to calculate standard deviation with the given values.

`SD=((26-25)^2+...+(20-25)^2)/(8)`

`SD=(270)/(8) =√(33.75) =5.8094750193111`

`5.8094750193111`

`9>5`

`SD=5.81`

Hope this helps.