Question

Suppose a data set consisting of exam scores has a lower quartile QL = 60, a median QM = 75, and an upper quartile QU = 85. The scores on the exam range from 18 to 100. Without having the actual scores available to you, construct as much of the box plot as possible.

Short answer

IQR = Q_U – Q_L

= 85 – 60

= 25

Lower Inner Fence = Q_L - 1.5(IQR)

= 60 – 1.5(25)

= 60 – 37.5

= 22.5

Upper Inner Fence = Q_U + 1.5(IQR)

= 60 + 1.5(25)

= 60 + 37.5

= 122.5

Step-by-step solution

Finding the fences

IQR = Q_U – Q_L

= 85 – 60

= 25

Lower Inner Fence = Q_L - 1.5(IQR)

= 60 – 1.5(25)

= 60 – 37.5

= 22.5

Upper Inner Fence = Q_U + 1.5(IQR)

= 60 + 1.5(25)

= 60 + 37.5

= 122.5

Creating the box plot