Question

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

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

Answer 1

Modal class $=30–35,$

$l=30,$

Class width $\left(h\right)=5,$ and the frequencies are

$f_m=10,f_1=9and{f}_2=3$

Formula

Mode Formula:

Mode $=l+\left[\right(f_m-f_1)/(2f_m-f_1-f_2\left)\right]\times h$

Substitute the values in the given formula

Mode $=40+\left(\right(20-12)/(40-12-11\left)\right)\times 10$

$$\begin{gathered} =40+(80/17) \\ =40+4.7 \\ =44.7 \end{gathered}$$

Thus, the mode of the given data is $44.7$cars.