Question

elias likes to read during his summer breaks. the table below shows the number of pages in each book he read this summer and the number of pages in each book he read last summer. number of pages elias read during the summer

this summer	last summer
170	220
150	190
190	180
180	190

which statement comparing the modes to the ranges is true?
o the modes differ by 40 and the ranges differ by 40.
o the modes differ by 40, but the ranges differ by 20.
o the modes differ by 20 and the ranges differ by 20.
o the modes differ by 20, but the ranges differ by 40.

Explanation:

Step1: Find the mode for this - summer

The mode is the number that appears most frequently. For this summer, the numbers are 150, 170, 150, 190, 180. The mode is 150.

Step2: Find the mode for last - summer

For last summer, the numbers are 140, 220, 190, 180, 190. The mode is 190.

Step3: Calculate the difference between the modes

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

Step4: Find the range for this - summer

The range is the difference between the largest and smallest values. For this summer, the largest value is 190 and the smallest is 150, so the range is \(190 - 150 = 40\).

Step5: Find the range for last - summer

For last summer, the largest value is 220 and the smallest is 140, so the range is \(220 - 140=80\).

Step6: Calculate the difference between the ranges

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

Answer:

The modes differ by 40, but the ranges differ by 40.