Question

a data set has a lower quartile of 3 and an interquartile range of 5. which box plot could represent this data set?

Explanation:

Step1: Recall the formula for inter - quartile range

The inter - quartile range (IQR) is given by \(IQR = Q_{3}-Q_{1}\), where \(Q_{1}\) is the lower quartile and \(Q_{3}\) is the upper quartile. We know that \(Q_{1} = 3\) and \(IQR=5\). So, \(Q_{3}=Q_{1}+IQR\).

Step2: Calculate the upper quartile

Substitute \(Q_{1} = 3\) and \(IQR = 5\) into the formula \(Q_{3}=Q_{1}+IQR\). Then \(Q_{3}=3 + 5=8\).

Step3: Analyze the box - plots

In a box - plot, the left - hand side of the box represents \(Q_{1}\) and the right - hand side of the box represents \(Q_{3}\).
We need to look for a box - plot where the left - hand side of the box is at \(x = 3\) and the right - hand side of the box is at \(x=8\).

Answer:

The box - plot where the left - hand side of the box (lower quartile) is at \(3\) and the right - hand side of the box (upper quartile) is at \(8\) (by calculating \(Q_{3}=Q_{1}+IQR=3 + 5 = 8\)) is the correct one.