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 :

Question :

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

The class (40 – 50) has the maximum frequency frequency. Therefore, this is the modal class.

Here, l = 40, h = 10, \(f_1\) = 20, \(f_0\) = 12 and \(f_2\) = 11

Now, let us substitute these values in the formula

Mode = l + (\(f_1 – f_0\over 2f_1 – f_0 – f_2\)) \(\times\) h

Mode = 40 + (\(20 – 12\over 40 – 12 – 11\)) \(\times\) 10

Mode = 40 + 4.7 = 44.7

Hence, mode = 44.7 cars