Question

If the mean of the following distribution is 24, find the value of m.

Marks	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50
No. of Students	7	m	8	10	5

Answer 1

1. Data preparation

First, let’s identify the mid-value (x) for each class interval and calculate the product of the frequency (f) and the mid-value (fx).

Marks (Class)	Mid-value (x)	No. of Students (f)	f × x
0 – 10	5	7	35
10 – 20	15	m	15m
20 – 30	25	8	200
30 – 40	35	10	350
40 – 50	45	5	225
Total		Σf = 30 + m	Σfx = 810 + 15m

2. Calculating the value of m

We are given that the mean `(barx)` = 24. 

Using the formula:

Mean `(barx) = (sumfx)/(sumf)`

Substitute the values into the equation:

`24 = (810 + 15m)/(30 + m)`

1. Cross-multiply:

24(30 + m) = 810 + 15m

2. Expand the brackets:

720 + 24m = 810 + 15m

3. Group variables (m) on one side and constants on the other:

24m – 15m = 810 – 720

9m = 90

4. Solve for m:

`m = 90/9`

m = 10

The value of m is 10.