Question

elias likes to read during his summer breaks. the table shows the number of pages in each book he read last summer and the number of pages in each book he read this summer. which statement comparing the modes to the ranges is true? the modes differ by 40 and the ranges differ by 40. the modes differ by 20, but the ranges differ by 40. the modes differ by 40, but the ranges differ by 20. the modes differ by 20 and the ranges differ by 20.

Explanation:

Step1: Find the mode for last summer

The mode is the number that appears most frequently. For last summer's data \(140, 220, 190, 180, 190\), the mode is \(190\) (appears twice).

Step2: Find the mode for this summer

For this summer's data \(150, 170, 150, 190, 180\), the mode is \(150\) (appears twice).

Step3: Calculate the difference in modes

The difference in modes is \(190 - 150=40\).

Step4: Find the range for last summer

The range is the difference between the maximum and minimum values. For last summer, range \(=220 - 140 = 80\).

Step5: Find the range for this summer

For this summer, range \(=190 - 150=40\).

Step6: Calculate the difference in ranges

The difference in ranges is \(80 - 40 = 40\).

Answer:

The modes differ by 40 and the ranges differ by 40.