Question

the box plots show the data distributions for the number of laps two students run around a track each day. number of laps 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:

Step1: Find the range of Liam's data

The range is the difference between the maximum and minimum values. For Liam, the minimum is \(4\) and the maximum is \(22\). So the range is \(22 - 4=18\).

Step2: Find the range of Samuel's data

For Samuel, the minimum is \(10\) and the maximum is \(20\). So the range is \(20 - 10 = 10\).

Step3: Calculate the difference between the ranges

The difference between the ranges is \(18-10 = 8\). This option is not relevant. Now for the median:

Step4: Find the median of Liam's data (the middle - value of the box - and - whisker plot)

The median of Liam's data (the line inside the box) is \(14\).

Step5: Find the median of Samuel's data

The median of Samuel's data (the line inside the box) is \(10\).

Step6: Calculate the difference between the medians

The difference between the medians is \(14 - 10=4\).

Answer:

The difference between the medians of both data sets is 4.