Question

a data set has a maximum of 200, a minimum of 115, a median of 145, an upper quartile of 150, and a lower quartile of 120. which statement is true of the box plot of this data set? the right whisker will go from 150 to 200. the left whisker will go from 115 to 145. a line dividing the box will be at 135. the box will go from 145 to 150.

Explanation:

Step1: Recall box - plot components

A box - plot has the following components: the left whisker (from the minimum to the lower quartile), the box (from the lower quartile \(Q_1\) to the upper quartile \(Q_3\)), a line inside the box (the median \(M\)), and the right whisker (from the upper quartile to the maximum).
Given: \(Min = 115\), \(Q_1=120\), \(M = 145\), \(Q_3 = 150\), \(Max=200\)

Step2: Analyze each option

• Option 1: The right whisker will go from 150 to 200

Since the upper quartile \(Q_3 = 150\) and the maximum \(Max = 200\), the right whisker (which connects the upper quartile to the maximum) will go from \(150\) to \(200\).

• Option 2: The left whisker will go from 115 to 145

The left whisker should go from the minimum (\(115\)) to the lower quartile (\(120\)), not to the median (\(145\)).

• Option 3: A line dividing the box will be at 135

The line dividing the box is the median. Given \(M = 145\), not \(135\).

• Option 4: The box will go from 145 to 150

The box should go from the lower quartile (\(Q_1 = 120\)) to the upper quartile (\(Q_3=150\)), not from the median (\(145\)) to the upper quartile (\(150\)).

Answer:

The right whisker will go from 150 to 200.