Question

Find the mean of the following frequency distribution: 

Class	1 – 3	3 – 5	5 – 7	7 – 9
Frequency	9	22	27	18

Answer 1

1. Find the class marks

The class mark (x_i) for each interval is calculated as the average of its lower and upper limits using the formula:

`x_i = ("Lower Limit" + "Upper Limit")/2`

For 1 – 3: `x_1 = (1 + 3)/2 = 2`

For 3 – 5: `x_2 = (3 + 5)/2 = 4`

For 5 – 7: `x_3 = (5 + 7)/2 = 6`

For 7 – 9: `x_4 = (7 + 9)/2 = 8`

2. Calculate the products and sums

Multiply each frequency (f_i) by its corresponding class mark (x_i), then find the total sum of the frequencies (Σf_i) and the products (Σf_ix_i).

Class Interval	Frequency (fi)	Class Mark (xi)	fixi
1 – 3	9	2	18
3 – 5	22	4	88
5 – 7	27	6	162
7 – 9	18	8	144
Total	Σfi = 76		Σfixi = 412

3. Apply the mean formula

The formula for the mean `(barx)` of grouped data is:

`barx = (sumf_ix_i)/(sumf_i)`

Substitute the calculated sums into the formula:

`barx = 412/76 ≈ 5.421`

The mean of the given frequency distribution is 5.42.