Question

mr. ruiz asked a group of students how many books they read last month. the number of books read is listed: 3,2,5,2,3,2,4,2. when mr. ruiz included the number of books he read last month, the range increased by 1, but the interquartile range remained the same. drag numbers to the blanks to determine the number of books mr. ruiz read. since the range increases by 1, mr. ruiz must have read either __ or books(s). however, since the interquartile range did not change, he must have read __ book(s). 1 2 3 4 5 6

Explanation:

Step1: Find original range

First, order the data set: 2, 2, 2, 2, 3, 3, 4. The original range is \(4 - 2=2\). Since the new range is \(2 + 1=3\), Mr. Ruiz must have read either \(2-1 = 1\) or \(4 + 1=5\) books.

Step2: Analyze inter - quartile range

The inter - quartile range (IQR) is the difference between the third quartile (\(Q_3\)) and the first quartile (\(Q_1\)). For the data set 2, 2, 2, 2, 3, 3, 4, \(Q_1 = 2\), \(Q_3=3\), \(IQR=3 - 2 = 1\). If Mr. Ruiz read 1 book, it won't change the position of \(Q_1\) and \(Q_3\). If he read 5 books, it will change the data set and may change the \(Q_1\) and \(Q_3\) values. So he must have read 1 book.

Answer:

1, 5, 1