The interquartile range of the data set will be 33.
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 [tex] (\frac{52+55}{2})= \frac{107}{2} = 53.5 [/tex] .
Now two sets are {28, 36, 48, 52} and {55, 70, 80, 86}. The median of the first set is [tex] (\frac{36+48}{2})=\frac{84}{2}=42 [/tex] and median of the second set is [tex] (\frac{70+80}{2})=\frac{150}{2}=75 [/tex]
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
