# 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 :

## Solution :

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