ShmoopTube

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Here’s your shmoop du jour, brought to you by hypothetical situations.

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Well…let’s just suppose that it is…

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A data set contains nine numbers.

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If the four largest numbers in the set were doubled, what would happen to the median value?

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And here are the potential answers…

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Whenever we’re given a hypothetical data set without many details, we can always make up our own values.

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For example, in this case, we know our data set has 9 numbers.

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So we just need to make up a data set that… works.

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The four largest numbers are doubled. That's 9, 8, 7, and 6 in this case. We're gonna double those.

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So what happens to the median value?

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Remember that the median value is simply the middle value of all of the data.

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We can find it by repeatedly getting rid of the minimum and maximum values until we’re

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left with one number.

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In our first data set, we’d get rid of 1 and 9 first. Then 2 and 8, followed by 3 and 7.

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Finally, we get rid of 4 and 6, to be left with 5.

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What about our second, altered data set?

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First we get rid of 1 and 18, 2 and 16, 3 and 14, and finally 4 and 12.

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We’re left with 5.

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In both cases, we’re left with 5 as the median.

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Our answer is A… the median doesn't change.

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