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

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.\nnumber of pages elias read during the summer\nlast summer: 140, 220, 190, 180, 190\nthis summer: 150, 170, 150, 190, 180\n\nwhich statement comparing the modes to the ranges is true?\nthe modes differ by 40 and the ranges differ by 40.\nthe modes differ by 20 and the ranges differ by 20.\nthe modes differ by 40, but the ranges differ by 20.\nthe modes differ by 20, but the ranges differ by 40.
Answer
Explanation:
Step1: Find last summer's mode
The mode is the most frequent value. For last summer: 140, 220, 190, 180, 190. The value 190 appears twice, so mode = 190.
Step2: Find this summer's mode
For this summer: 150, 170, 150, 190, 180. The value 150 appears twice, so mode = 150.
Step3: Calculate mode difference
Subtract the two modes: $190 - 150 = 40$
Step4: Find last summer's range
Range = max - min. Last summer max=220, min=140. $\text{Range} = 220 - 140 = 80$
Step5: Find this summer's range
This summer max=190, min=150. $\text{Range} = 190 - 150 = 40$
Step6: Calculate range difference
Subtract the two ranges: $80 - 40 = 40$
Answer:
The modes differ by 40 and the ranges differ by 40.