Question

item 6 sam said the range of the top 50% of the data is greater than the range of the bottom 50% of the data. use the box and whisker plot below to determine which person is correct. harper disagreed and said that the range of the top 50% of the data is less than the range of the bottom 50% of the data. use the box and whisker plot below to determine which person is correct. a sam b harper c they are both right d neither person is right e there is not enough information

Explanation:

Step1: Recall the concept of box - and - whisker plot

In a box - and - whisker plot, the range of the top 50% of the data is the inter - quartile range (IQR) (from the median to the maximum). The range of the bottom 50% of the data (from the minimum to the median) is also considered.

Step2: Analyze the box - and - whisker plot

Let's assume the minimum value is \(m\), the median is \(Q_2\), and the maximum value is \(M\). The range of the bottom 50% of the data is \(Q_2 - m\), and the range of the top 50% of the data is \(M - Q_2\).
Looking at the box - and - whisker plot, we can observe that the length from the minimum to the median (range of the bottom 50% of the data) is shorter than the length from the median to the maximum (range of the top 50% of the data).

Answer:

A. Sam