Question

What is the interquartile range for the data set?

27, 4, 54, 78, 27, 48, 79, 64, 5, 6, 41, 71

Answer 1

it's 51! i just took the test :)

Answer 2

The interquartile range for the data set is 65

Solution-

We have to calculate IQR or interquartile range for the given data set,

27, 4, 54, 78, 27, 48, 79, 64, 5, 6, 41, 71

Placing the data set from least to greatest,

4, 5, 6, 27, 27, 41, 48, 54, 64, 71, 78, 79

Now, the median or the middle of the data set, as there are even number of data points, is

`=(41+48)/(2)=44.5`

Q₁ = median of the first half of the data =
`(6+27)/(2) =16.5`

Q₃ = median of the second half of the data =
`(64+71)/(2) =67.5`

Then, IQR = Q₃-Q₁ = 67.5-16.5 = 51

Therefore, the interquartile range for the data set is 65