Question

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised in the table given below. Find the mode of the data:

Number of cars:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	7	14	13	12	20	11	15	8

Answer 1

The given data is shown below.

Number of cars	Frequency
0−10	7
10−20	14
20−30	13
30−40	12
40−50	20
50−60	11
60−70	15
70−80	8

Here, the maximum frequency is 20 so the modal class is 40−50.

Therefore,

$$\begin{gathered} \therefore \mathrm{Mode}=l+\frac{f-f_1}{2f-f_1-f_2}\times h \\ =40+\frac{20-12}{2\times 20-12-11}\times 10 \\ =40+\frac{8}{17}\times 10 \\ =40+4.7 \\ =44.7 \end{gathered}$$

Thus, the mode of the data is 44.7.