A student noted the number of cars passing through a spot on a road for 100 periods, each of 3 minutes, and summarized this in the table given below.

Step 1: Recall the mode formula for the grouped data
Mode = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} * h
l - The lower boundary of the modal class,
h - The class size,
f_1 - The frequency of modal class
f_0 - the frequency of the class preceding the modal class,
f_2 - the frequency of the class succeeding the modal class.
Step 2: Identify the modal class and locate the values of the frequencies.
NOTE: Locate a class with the maximum frequency, called the modal class.
(The mode is a value inside the modal class)
Here the maximum class frequency is 20, and the class corresponding to this
frequency is 40 - 50,
So, the modal class is 40 - 50.
lower boundary l = 40
Class size h = 50 - 40 = 10
The frequency of modal class f_1 = 20
The frequency of the class preceding the modal class f_0 = 12
The frequency of the class succeeding the modal class. f_2 = 11
Step 3: Substitute the values in the formula and calculate the mode.
Mode = l + \frac{f_1 - f_0}{2f_1 - f_0 - f_2} * h
= 40 + \frac{20 - 12}{2*20 - 12 - 11} * 10
= 40 + \frac{8}{17} * 10
= 40 + 0.470588 * 10
= 40 + 4.7058
= 44.7058
Hence, mode = 44.7058