SolutionIn this question, you are given a graph of the frequency distribution of 50 integer values and are asked to compare the average (arithmetic mean) with the median of the distribution.

In general, the median of a group of n values, where n is even, is obtained by ordering the values from least to greatest and then calculating the average(arithmetic mean) of the two middle values. So, for the 50 values shown in the graph, the median is the average of the 25th and 26th values, both of which are equal to 5. Therefore, the median of the 50 values is 5.

Once you know that the median of the 50 values is 5, the comparison simplifies to comparing the average of the 50 values with 5. You can make this

comparison without actually calculating the average by noting from the graph that of the 50 values, 11 values are 1 unit above 5,

- 16 values are equal to 5,

- 10 values are 1 unit below 5, and

- 13 values are more than 1 unit below 5.

Since the part of the distribution that is below 5 contains 23 values—13 of which are more than 1 unit below 5—and the part of the distribution that is above 5 contains 11 values—none of which is more than 1 unit above 5—the average (arithmetic mean) of the 50 values must be less than 5. The correct answer is

Choice B.
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Sandy

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