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

Therefore, modal class = 40−50
Lower limit (\(l\)) of modal class = 40
Frequency (\(f_1\)) of modal class = 20
Frequency (\(f_0\)) of class preceding the modal class = 12
Frequency (\(f_2\)) of class succeeding the modal class = 11
Class size (\(h\)) = 10

Mode = \(l\) + \((\frac{f_1 - f_0 }{2f_1 - f_0 - f_2)} \times h\)

Mode = \(40 + (\frac{10 - 12 }{ 2(20) - 12 - 11}) \times1000\)

Mode =\(400+ [\frac{80}{40 - 23}]\)

Mode = 4000 + \(\frac{80}{18}\)
Mode = 40 + 4.7
Mode = 44.7

Therefore, mode of this data is 44.7 cars.