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A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it - Mathematics

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
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Solution

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, mode of this data is 44.7 cars.

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APPEARS IN

NCERT Class 10 Maths
Chapter 14 Statistics
Exercise 14.2 | Q 6 | Page 276
RD Sharma Class 10 Maths
Chapter 15 Statistics
Exercise 15.5 | Q 12 | Page 46
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