ShmoopTube

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You can't handle the Shmoop!

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In which of the following data sets are the arithmetic mean and the median equal?

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And here are the potential answers…

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To solve this problem, we just have to compare the mean and median

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in each of the answer choices, until we find a match.

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Remember that we can find the arithmetic mean, a fancy term for average, by adding up all

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of the values, and dividing by the total number of values we've added.

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The median is simply the value in the middle of all of the data.

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In the answer choices given, there are 6 values, so there’s no one single value in the middle.

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When this happens, we take the midpoint of the two middle values.

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Let's start looking at our answers. In data set A, we have 40, 40, 41, 42, 43, and 45.

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To find the median, we cross out the min and the max values.

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Then we do it again. We’re left with two values, so the mean of the two is the median.

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Between 41 and 42 is 41.5.

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Now for the mean. We add up all of the values, and get 251. Then, we divide by 6 to get 41.833.

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The mean is 41.83, and the median is 41.5. They’re not the same.

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So we can cross off answer choice A. Our next set is 40, 41, 42, 43, 43, 45.

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Applying the same method to find the median, we get 42.5.

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When we find the mean, we add up our numbers to get 254, and divide by 6 to get 42.3.

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Still not the same. Onto C, which is 40, 41, 42, 43, 44, 45.

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The median is 42.5.

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When we add up all of the values, we get 255. When we divide by 6, we get 42.5.

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The mean and median of C is the same. We’ve found our answer.

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