Question

a data set has a maximum of 84, a minimum of 34, a median of 52.5, an upper quartile of 64, and a lower quartile of 44. which statement is true of the box plot of this data set? a line dividing the box will be at 54. the left whisker will go from 34 to 52.5. the right whisker will go from 44 to 84. the box will go from 44 to 64.

Explanation:

Step1: Recall box - plot components

A box - plot has a box from the lower quartile (\(Q_1\)) to the upper quartile (\(Q_3\)), a line inside the box representing the median (\(M\)), and whiskers from the minimum (\(min\)) to \(Q_1\) (left whisker) and from \(Q_3\) to the maximum (\(max\)) (right whisker).
Given \(min = 34\), \(Q_1=44\), \(M = 52.5\), \(Q_3 = 64\), \(max=84\).

Step2: Analyze each option

• Option 1: The line dividing the box is the median. The median is \(52.5

eq54\).

• Option 2: The left whisker goes from \(min = 34\) to \(Q_1 = 44\), not to the median (\(52.5\)).
• Option 3: The right whisker goes from \(Q_3=64\) to \(max = 84\), not from \(44\) to \(84\).
• Option 4: The box goes from \(Q_1 = 44\) to \(Q_3=64\) which is correct according to the definition of a box - plot.

Answer:

The box will go from \(44\) to \(64\).