Question

What is the interquartile range of the data set?

{36, 52, 48, 86, 80, 28, 55, 70}
Enter the answer in the box.


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Answer 1

The interquartile range of the data set is going to be 33.

Answer 2

The interquartile range of the data set will be 33.

Step-by-step explanation

Given data set: { 36, 52, 48, 86, 80, 28, 55, 70 }

First we will rearrange the data in numeric order. So...

{ 28, 36, 48, 52, 55, 70, 80, 86 }

Here middle two numbers are 52 and 55, so the Median will be
`((52+55)/(2))= (107)/(2) = 53.5` .

Now two sets are {28, 36, 48, 52} and {55, 70, 80, 86}. The median of the first set is
`((36+48)/(2))=(84)/(2)=42` and median of the second set is
`((70+80)/(2))=(150)/(2)=75`

That means, Lower quartile(Q₁) = 42 and Upper quartile(Q₃) = 75

So, the interquartile range of the data set: IQR= Q₃ - Q₁ = 75 - 42 = 33