Question

use the box - and - whisker plot to answer the questions below.(a) which of the following intervals gives the middle 50% of the data?24 to 33 24 to 27 27 to 33 22 to 27(b) what is the difference of the longest distance and the shortest distance training ride? (that is, what is the range of the data?)16(c) which of these best describes the distances (in kilometers) of donnas training rides?there were more rides with a distance under 27 than with a distance over 27.there were more rides with a distance over 27 than with a distance under 27.the same number of rides had a distance under 27 as had a distance over 27.

Explanation:

Step1: Recall box - and - whisker plot properties

The middle \(50\%\) of the data is represented by the inter - quartile range (IQR). The IQR is the difference between the third quartile (\(Q_3\)) and the first quartile (\(Q_1\)). In a box - and - whisker plot, the box starts at \(Q_1\) and ends at \(Q_3\).

Step2: Identify \(Q_1\) and \(Q_3\) from the plot

From the box - and - whisker plot, \(Q_1 = 24\) and \(Q_3=33\). So the middle \(50\%\) of the data is from \(Q_1\) to \(Q_3\), which is the interval \(24\) to \(33\).

Step3: Calculate the range

The range of a data set is given by \(R=\text{Max}-\text{Min}\). From the whisker plot, assume \(\text{Max} = 40\) and \(\text{Min}=24\). Then \(R = 40 - 24=16\).

Step4: Analyze the symmetry around the median

The median is the line inside the box. In a box - and - whisker plot, the number of data points below \(Q_1\) is \(25\%\), between \(Q_1\) and the median (\(Q_2\)) is \(25\%\), between \(Q_2\) and \(Q_3\) is \(25\%\), and above \(Q_3\) is \(25\%\). The median (\(Q_2 = 27\)). The number of data points below \(27\) (\(Q_2\)) is \(50\%\) ( \(25\%\) below \(Q_1\) and \(25\%\) between \(Q_1\) and \(Q_2\)) and the number of data points above \(27\) (\(Q_2\)) is \(50\%\) (\(25\%\) between \(Q_2\) and \(Q_3\) and \(25\%\) above \(Q_3\)).

Answer:

(a) \(24\) to \(33\)
(b) \(16\)
(c) The same number of rides had a distance under \(27\) as had a distance over \(27\).