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Question

A student noted the number of cars passing through a spot on a road for100 periods each of 3minutes and summarised it in the table given below. Find the mode of the data:

Number of carsFrequency
0-107
10-2014
20-3013
30-4012
40-5020
50-6011
60-7015
70-808

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Solution

Modal class =3035,

l=30,

Class width (h)=5, and the frequencies are

fm=10,f1=9andf2=3

Formula

Mode Formula:

Mode =l+[(fm-f1)/(2fm-f1-f2)]×h

Substitute the values in the given formula

Mode =40+((20-12)/(40-12-11))×10

=40+(80/17)=40+4.7=44.7

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


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