Question

the box plots show the data distributions for the number of laps two students ran around a track each day. which statement is true about the data? the difference between the medians of both data sets is 2. the difference between the medians of both data sets is 4. the difference between the ranges of both data sets is 2. the difference between the ranges of both data sets is 4.

Explanation:

To solve this problem, we analyze the box - plots for Liam and Sumai:

Step 1: Analyze the median

• For a box - plot, the line inside the box represents the median. From the box - plot, we can see that the median of Liam's data set is 10 and the median of Sumai's data set is 14.
• The difference between the medians is calculated as \(14 - 10=4\).

Step 2: Analyze the range

• The range of a data set is calculated as the maximum value minus the minimum value. From the box - plot, the minimum value for both data sets seems to be 4 (since the left - most whisker starts at 4 for both). The maximum value for Liam's data set is 22 and for Sumai's data set is 24.
• The difference between the ranges: The range of Liam's data set is \(22 - 4 = 18\), and the range of Sumai's data set is \(24 - 4=20\). The difference between the ranges is \(20 - 18 = 2\). But we are checking the statements one by one.

Now let's check each statement:

• Statement 1: "The difference between the medians of both data sets is 2" is wrong because \(14 - 10 = 4\).
• Statement 2: "The difference between the medians of both data sets is 4" is correct as we calculated \(14-10 = 4\).
• Statement 3: "The difference between the ranges of both data sets is 2" is wrong. The range of Liam is \(22 - 4=18\), the range of Sumai is \(24 - 4 = 20\), and \(20 - 18=2\) is the difference between the ranges, but let's check the other statement.
• Statement 4: "The difference between the ranges of both data sets is 4" is wrong.

Answer:

The difference between the medians of both data sets is 4 (the option corresponding to this statement)