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Five numbers are 4, 7, 9, 12 and an unknown number k…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Five numbers are $4, 7, 9, 12$ and an unknown number $k$ . First suppose that $k$ is at least 12. Then $k$ is the largest of the five. Find the value of $k$ that makes the mean equal to the median. Next suppose that $k$ is at most 4, so it is the smallest. Find the value of $k$ that makes the mean equal to the median in this case. For a value of $k$ larger than your first answer, which average is larger, and why?

Need a reminder? The key ideaShow

The mean is the balance point and follows a long tail; the median is the middle value and hardly moves. Usually a right skew gives mean > median and a left skew gives mean < median. Report the median for skewed data.

\displaystyle \bar{x} = \dfrac{\text{total}}{n}

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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