Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.
Both exams had the same range, so they must have had the same median.
Choose the correct answer below.
A. This does not make sense because the range is the most common value or group of values in a distribution. It has nothing to do with the median.
B. This makes sense because the median is equal to the range.
C. This makes sense because the median is equal to half of the range.
D. This does not make sense because the range is the difference between the highest and lowest data values. It has nothing to do with the median.

Question

UpStudy AI · Accepted Answer

**Step 1. Definition of the Range**

The range of a data set is defined as the difference between the maximum and minimum values in the data. That is,  
$$
\text{Range} = \text{Maximum} - \text{Minimum}
$$

**Step 2. Definition of the Median**

The median is the middle value of a data set when the numbers are arranged in order. It is not directly related to the maximum or minimum values; instead, it depends on the central location of the data.

**Step 3. Analysis of the Statement**

The statement "Both exams had the same range, so they must have had the same median" is incorrect because knowing that two data sets have the same range only tells us that the difference between the highest and lowest values is equal. It does not provide any information about the distribution of the values in between or their central tendency.

**Step 4. Conclusion**

Since the range is simply the difference between the highest and lowest values, it has no inherent connection to the median. The median can be vastly different even when the ranges of the two data sets are the same.

**Final Answer:**

D. This does not make sense because the range is the difference between the highest and lowest data values. It has nothing to do with the median.
The statement does not make sense because the range (the difference between the highest and lowest values) does not determine the median (the middle value).

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