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Chapter 8: Problem 58

In a certain set of scores, the median occurs more often than any other score. It follows that (A) The median and mean are equal. (B) The mean and mode are equal. (C) The mode and median are equal. (D) The mean, mode, and median are all equal.

Short Answer

Expert verified
The correct option is (C) The mode and median are equal, because in the given set of scores, the median occurs more often than any other score, making it also the mode.

Step by step solution

01

Understanding Definitions

In order to solve this problem, it is essential to understand what is meant by median, mean, and mode. 1. Median: The middle value in a given set of data when the data is ordered from least to greatest. If there are two middle values (in the case of an even number of data points), the median is the average of the two middle values. 2. Mean: The average value of a given set of data. It is calculated by adding up all the values and dividing that sum by the number of values. 3. Mode: The value(s) occurring most frequently in the given set of data. Knowing these definitions, let's analyze each option.
02

Option A: The median and mean are equal.

There is no requirement that the median and mean must be equal, even if the median occurs more often than any other score. The mean can differ from the median depending on how the other values in the dataset are distributed.
03

Option B: The mean and mode are equal.

There is no requirement that the mean and mode must be equal in the given set of scores. We are only told that the median occurs more often than any other score. The mean and mode can differ depending on the distribution of the values.
04

Option C: The mode and median are equal.

Let's analyze this statement. We are given that the median occurs more often than any other score; this means that, by definition, the median is the value that occurs the most frequently in this dataset, therefore, the median is also the mode. In this case, it follows that the mode is equal to the median.
05

Option D: The mean, mode, and median are all equal.

As we mentioned before, there is no requirement that mean and mode must be equal, and mean and median must be equal. So, this option cannot be true automatically based on the given information. #Conclusion# Based on the analysis, the correct option is (C) The mode and median are equal.

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