Question

Find the mode for the following distribution: 

Monthly wages	200 – 220	220 – 240	240 – 260	260 – 280	280 – 320	320 – 340
No. of workers	7	15	20	20	10	2

Answer 1

To find the mode for the given distribution, we first identify the modal class, which is the class with the highest frequency.

1. Identify the data

From the table, we have:

Monthly Wages (Class)	No. of Workers (Frequency f)
200 – 220	7
200 – 240	15
240 – 260	20
260 – 280	20
280 – 320	10
320 – 340	2

2. Determine the modal class

In this case, the maximum frequency is 20, which occurs for two adjacent classes: 240 – 260 and 260 – 280.

When two adjacent classes have the same maximum frequency, the mode effectively falls on the boundary between them. We can verify this by applying the mode formula to either class.

3. Calculate the mode

Let’s use the first modal class, 240 – 260:

Lower limit (l): 240

Frequency of modal class (f₁): 20 

Frequency of preceding class (f₀): 15 

Frequency of succeeding class (f₂): 20 

Class width (h): 20

The formula for the mode is:

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

Substitute the values:

Mode = `240 + ((20 - 15)/(2(20) - 15 - 20)) xx 20`

Mode = `240 + (5/(40 - 35)) xx 20`

Mode = `240 + (5/5) xx 20`

Mode = 240 + 20

Mode = 260

The mode for the distribution is 260.