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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.

\begin{tabular}{|c|c|c|c|c|c|}
\hline \multicolumn{6}{|c|}{Number of Pages Elias Read during the Summer} \\
\hline Last Summer & 140 & 220 & 190 & 180 & 190 \\
\hline This Summer & 150 & 170 & 150 & 190 & 180 \\
\hline
\end{tabular}

Which statement comparing the modes to the ranges is true?

A. The modes differ by 40, and the ranges differ by 40.
B. The modes differ by 20, and the ranges differ by 20.
C. The modes differ by 40, but the ranges differ by 20.
D. The modes differ by 20, but the ranges differ by 40.

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Answer :

GinnyAnswer
Sure, let's solve this step-by-step.

1. Identify the number of pages read both last summer and this summer:

- Last Summer: 140, 220, 190, 180, 190
- This Summer: 150, 170, 150, 190, 180

2. Calculate the mode for each summer:

The mode of a dataset is the number that appears most frequently.

- For Last Summer: The numbers are 140, 220, 190, 180, 190. Here, 190 appears twice, which is more frequently than others. So, the mode for Last Summer is 190.
- For This Summer: The numbers are 150, 170, 150, 190, 180. Here, 150 appears twice, which is more frequently than others. So, the mode for This Summer is 150.

3. Calculate the difference between the modes of last summer and this summer:

- The difference = Mode (Last Summer) - Mode (This Summer)
- Difference in mode = 190 - 150 = 40

4. Calculate the range for each summer:

The range of a dataset is the difference between the maximum and minimum values.

- For Last Summer: The numbers are 140, 220, 190, 180, 190. The maximum is 220, and the minimum is 140. So, the range = 220 - 140 = 80.
- For This Summer: The numbers are 150, 170, 150, 190, 180. The maximum is 190, and the minimum is 150. So, the range = 190 - 150 = 40.

5. Calculate the difference between the ranges of last summer and this summer:

- The difference = Range (Last Summer) - Range (This Summer)
- Difference in range = 80 - 40 = 40

6. Compare the differences:

- The modes differ by 40.
- The ranges differ by 40.

So, the correct statement is: "The modes differ by 40 and the ranges differ by 40."