A school garden club measures the heights of 50 plants and groups the heights in the table below…

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

A school garden club measures the heights of $50$ plants and groups the heights in the table below. One frequency was lost, and it is called $x$ . The club remembers that the mode of the grouped data was $36$ cm. Use this to find the lost frequency $x$ of the class $40$ to $50$ . Then check that $30$ to $40$ is really the modal class of your table.

Height (cm)	Plants
10-20	5
20-30	10
30-40	16
40-50	$x$
50-60	7

Find $x$ .

Need a reminder? The key ideaShow

The modal class has the greatest frequency. For equal class widths,

\displaystyle \text{mode} = l + \dfrac{f_1 - f_0}{2f_1 - f_0 - f_2} \times h,

where $f_0$ is the frequency before the modal class and $f_2$ the frequency after it. A missing neighbour has frequency $0$ . 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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