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 (*f*_{1}) of modal class = 20

Frequency (*f*_{0}) of class preceding modal class = 12

Frequency (*f*_{2}) 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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