statistics - 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.

Krishna (last edited 2 years ago) (Expert, Educator @Qalaxia)

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