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 :

Explanation

Modal Class is the class with the highest frequency
Mode = `l + [(f_1 - f_0)/(2f_1 - f_0 - f_2)] × h`
Here,
Class size, h
Lower limit of modal class, l
Frequency of modal class, `f_1`
Frequency of class preceding modal class, `f_0`
Frequency of class
succeeding the modal class, `f_2`
From the table, it can be observed that the maximum class frequency is 20, belonging to class interval 40 − 50
Therefore, modal class = 40 − 50
Class size, h = 10
Lower limit of modal class, l = 40
Frequency of modal class, `f_1 = 20`
Frequency of class preceding modal class, `f_0 = 12`
Frequency of class
succeeding the modal class, `f_2 = 11`
Mode = `l + [(f_1 - f_0)/(2f_1 - f_0 - f_2) ]× h`
`= 40 + [(20 - 12)/(2 × 20 - 12 - 11)] xx 10`
`= 40 + [8/(40 - 23)] xx 10`
`= 40 + (8/17) xx 10`
`= 40 + 4.705`
`= 44.705`
`≈ 44.7`
`"Hence, the mode is 44.7"`