a The range is the difference of the greatest value and the least value of the data set. The interquartile range is the difference of the third quartile, Q_3, and the first quartile, Q_1.
B
b In a box-and-whisker plot, each whisker represents 25 % of the data. The box represents 50 % of the data.
C
c Which side of the box is longer?
A
a See solution.
B
b See solution.
C
c See solution.
Practice makes perfect
a We are told that a baseball player scores 101 runs in a season. Let's begin by looking at the given box-and-whisker plot that represents the numbers of runs the player scores against different opposing teams.
We are asked to find and interpret the range and interquartile range of the data. Let's first find the range and then the interquartile range.
Range
To find the range, we need to calculate the difference of the greatest and least value of the data. In a box-and-whisker plot, the rightmost point represents the greatest value of the data. It is 17. The leftmost point represents the least value. It is 0. Let's calculate the range.
Range: 17- 0=17Runs
The range is 17 runs. This means that the number of runs the player scores against different opposing teams varies by no more than 17 runs.
Interquartile Range
The interquartile range (IQR) is given by the difference of the third quartile, Q_3, and the first quartile, Q_1. In a box-and-whisker plot, the left point of the right whisker represents Q_3, which is 9. The right point of the left whisker represents Q_1, which is 2. Let's calculate the difference of these values to find the IQR.
IQR: 9- 2=7Runs
The interquartile range is 7 runs. This means that the middle half of the numbers of runs the player scores against different opposing teams vary by no more than 7 runs.
b In this part we are asked to describe the distribution of the data set. In a box-and-whisker plot, each whisker represents 25 % of the data. The box represents 50 % of the data. With this in mind, we can state the following facts about the distribution of the data.
25 % of the number of runs scored are between 0 and 2 runs.
50 % of the number of runs scored are between 2 and 9 runs.
25 % of the number of runs scored are between 9 and 17 runs.
c To find if the data is more spread out between Q_1 and Q_2 or between Q_2 and Q_3, let's look which side of the box is longer. By looking at the given graph, we can see that the length of the box between Q_2 and Q_3 is longer. Therefore, the data is more spread out between Q_2 and Q_3.
