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	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

From the given data, it can be observed that the maximum class frequency is 20, belonging to 40 − 50 class intervals.

Therefore, modal class = 40 − 50

Lower limit (l) of modal class = 40

Frequency (f₁) of modal class = 20

Frequency (f₀) of class preceding modal class = 12

Frequency (f₂) of class succeeding modal class = 11

Class size = 10

`"Mode" = l + ((f_1-f_0)/(2f_1-f_0-f_2))xxh`

= `40+[(20-12)/(2(20)-12-11)]xx10`

= `40+((80)/(40-23))`

= 40 + 4.7

= 44.7

Therefore, the mode of this data is 44.7 cars.