Question

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

last summer	140	220	190	180	190
this summer	150	170	150	190	180

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 and the ranges differ by 20.
the modes differ by 40, but the ranges differ by 20.
the modes differ by 20, but the ranges differ by 40.

Explanation:

Step1: Find the mode for last summer

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

Step2: Find the mode for this summer

For this - summer data (150, 170, 150, 190, 180), the mode is 150.

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 data, the maximum is 220 and the minimum is 140. So the range is \(220 - 140 = 80\).

Step5: Find the range for this summer

For this - summer data, the maximum is 190 and the minimum is 150. So the range is \(190 - 150 = 40\).

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.