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.
Concept: Mode of Grouped Data
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