Question

The following table shows the frequency distribution of electricity consumption of households in a month.

No. of units of electricity	0-20	20-40	40-60	60-80	80-100
No. of households	4	16	47	65	8

Find the modal number of units of electricity consumed by households in a month.

Answer 1

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No. of units of electricity	No. of households (frequency)
0-20	4
20-40	16
40-60	47
60-80	65
80-100	8

Here, the maximum frequency f_m is 65. So, the corresponding modal class is 60-80.
Mode = L+$\left[\frac{f_m-f_1}{2f_m-f_1-f_2}\right]h$
Here, L = lower limit of the modal class = 60
$f_m=$maximum frequency = 65
$f_1=$frequency of pre-modal class = 47
$f_2=$frequency of post-modal class = 8
h = width of modal class = 20
$$\begin{gathered} \therefore \mathrm{Mode}=60+\left[\frac{65-47}{2\left(65\right)-47-8}\right]\times 20 \\ =60+\left[\frac{18}{75}\right]\times 20 \\ =60+4.8 \\ =64.8 \\ \therefore \mathrm{The}\mathrm{modal}\text{number}\mathrm{of}\mathrm{units}\mathrm{of}\mathrm{electricity}\mathrm{consumed}\mathrm{by}\mathrm{households}\mathrm{in} \\ \mathrm{a}\mathrm{month}\mathrm{is}64.8\mathrm{units}. \end{gathered}$$