Madison claims that two data sets with the same median will have the same variability. Which data set would provide good support for whether her claim is true or false?

Her claim is false, we can prove it with the next data sets 5,5,5,5,5 and 3, 4, 5, 6, 7

Step-by-step explanation:

If we define the first data set as 5, 5, 5, 5, 5; the median is easily found to be 5 and the variability is 0, i. e., there is no variability in this data set. A second data set with a median of 5 is 3, 4, 5, 6, 7 and its variability is greater than 0 because we have different positive numbers. It is possible to compute the variance (sample variance) for both data sets, the variance for the first data set is 0 and the variance for the second data set is 2.5