Question

the five values for a data set are:
minimum = 0
lower quartile = 2
median = 3.5
upper quartile = 5
maximum = 10
bruno created the box plot using the five values. what error did he make?
the right whisker should go from 3.5 to 10.
the box should go from 3.5 to 5.
the box should go from 2 to 3.5.
the left whisker should go from 0 to 2.

Explanation:

Step1: Recall box - plot structure

A box - plot has a box that goes from the lower quartile (\(Q_1\)) to the upper quartile (\(Q_3\)), and a line inside the box representing the median (\(Q_2\)). The whiskers go from the minimum to \(Q_1\) (left whisker) and from \(Q_3\) to the maximum (right whisker).
Given: minimum \(=0\), \(Q_1 = 2\), \(Q_2=3.5\), \(Q_3 = 5\), maximum \(=10\).

Step2: Analyze each option

• For the left whisker: It should go from the minimum (\(0\)) to \(Q_1(2)\).
• For the box: It should go from \(Q_1(2)\) to \(Q_3(5)\), with the median (\(3.5\)) inside the box.
• For the right whisker: It should go from \(Q_3(5)\) to the maximum (\(10\)).

Answer:

The left whisker should go from \(0\) to \(2\).