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

To do:

We have to find the mean, median and mode of the above data.

Solution:

The frequency of the given data is as given below.

We observe that the class interval of 40-50 has the maximum frequency(20).

Therefore, it is the modal class.

Here,

$l=40, h=10, f=20, f_1=12, f_2=11$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=40+\frac{20-12}{2 \times 20-12-11} \times 10$

$=40+\frac{8}{40-23} \times 10$

$=40+\frac{80}{17}$

$=40+4.70$

$=44.7$

The mode of the given data is 44.7(cars).

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Updated on: 10-Oct-2022

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