Question

Find the value of mode from the following frequency distribution.

Size of item	0 – 5	5 – 10	10 – 15	15 – 20	20 – 25	25 – 30	30 – 35
Frequency	3	7	15	30	20	10	5

Answer 1

To find the value of the mode for this grouped frequency distribution, we follow these steps:

1. Identify the modal class

The modal class is the class interval with the highest frequency.

Looking at the table, the highest frequency is 30.

Therefore, the modal class is 15 – 20.

2. Use the mode formula

For grouped data, the formula for the mode is:

Mode = `l + ((f_1 - f_0)/(2f_1 - f_0 - f_2)) xx h`

Where:

l = Lower limit of the modal class = 15

f₁ = Frequency of the modal class = 30

f₀ = Frequency of the class preceding the modal class = 15 

f₂ = Frequency of the class succeeding the modal class = 20 

h = Class width (size of the interval) = 20 – 15 = 5

3. Calculation

Substitute the values into the formula:

Mode = `15 + ((30 - 15)/(2(30) - 15 - 20)) xx 5`

Mode = `15 + (15/(60 - 35)) xx 5`

Mode = `15 + (15/25) xx 5`

Mode = 15 + (0.6 × 5)

Mode = 15 + 3

Mode = 18

The value of the mode for the given distribution is 18.