The table shows the scores of 100 players in a game…

Contributed by StemPy Lab

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

The table shows the scores of $100$ players in a game. Two frequencies, $x$ and $y$ , are missing, because the page was torn. The organiser remembers that the median score was $32$ . The total of $100$ players is certain. Use the median and the total to find both frequencies.

Score	Players
0-10	10
10-20	$x$
20-30	25
30-40	30
40-50	$y$
50-60	10

Find $x$ and $y$ .

Need a reminder? The key ideaShow

The cumulative frequency is a running total. The median class is the first class whose cumulative frequency reaches $\dfrac{N}{2}$ , and

\displaystyle \text{median} = l + \dfrac{\frac{N}{2} - cf}{f} \times h,

with $cf$ the cumulative frequency of the class before it. For inclusive classes use the boundaries.

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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