Question

Steve and Karla are studying the text messaging habits of middle school students. They collected data about the number of messages sent daily by students in two school districts. The box plots show their results. Which statements about the data sets are true? The IQR of Karla’s data is 13. The IQR of Steve’s data is 16. The difference of the medians is about half the interquartile range of either data set. The difference of the medians is about twice the interquartile range of either data set.

Answer 1

A) The IQR of Karla’s data is 13

Explanation:

Answer 2

The correct answer is A.

A) The IQR of Karla's data in 13.

Explanation:

The interquartile range can be defined as the difference of upper quartile and lower quartile range. If we want to find the IQR from the box plot, we can simply see the length of the box from the box plot, as it represent the IQR.

We can clearly see that:

IQR of Steve's data is 45 - 31 = 14, hence the second statement is incorrect

IQR of Karla's data is 52 - 39 = 13, hence the first statement is CORRECT

The difference of medians is 43 - 36 = 7

Hence the difference of medians is not the half or twice of IQR ranges of both data sets