Question

a data set has a median of 12, an upper quartile of 15, a lower quartile of 10, a minimum of 4, and a maximum of 20. which statement is true of the box plot of this data set? the left whisker will go from 4 to 15. the right whisker will go from 12 to 20. the box will go from 10 to 12. a line dividing the box will be at 12.

Explanation:

Step1: Recall box - plot components

A box - plot (box - and - whisker plot) has the following components: the left whisker represents the minimum value to the lower quartile (\(Q_1\)), the box represents the lower quartile (\(Q_1\)) to the upper quartile (\(Q_3\)), and a line inside the box represents the median (\(M\)), and the right whisker represents the upper quartile (\(Q_3\)) to the maximum value.
Given \(M = 12\), \(Q_1=10\), \(Q_3 = 15\), \(min = 4\), \(max=20\).

Step2: Analyze each option

• Option 1 (Left whisker from 4 to 15):

The left whisker should go from the minimum value (\(4\)) to the lower quartile (\(Q_1 = 10\)), not to \(15\). So this option is wrong.

• Option 2 (Right whisker from 12 to 20):

The right whisker should go from the upper quartile (\(Q_3=15\)) to the maximum value (\(20\)), not from the median (\(12\)) to \(20\). So this option is wrong.

• Option 3 (Box from 10 to 12):

The box should go from the lower quartile (\(Q_1 = 10\)) to the upper quartile (\(Q_3=15\)), not from \(10\) to \(12\). So this option is wrong.

• Option 4 (Line dividing the box at 12):

Since the median of the data set is \(12\), the line that divides the box (which represents the median in a box - plot) is at \(12\). This option is correct.

Answer:

A line dividing the box will be at 12.