Question

Compute the mean of the following frequency distribution: 

Class	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100	100 – 120	120 – 140
Frequency	6	8	10	12	6	5	3

Answer 1

1. Calculate class marks

The class mark (x_i) for each interval is found by taking the average of its lower and upper limits:

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

For 0 – 20: `x_1 = (0 + 20)/2 = 10`

For 20 – 40: `x_2 = (20 + 40)/2 = 30`

For 40 – 60: `x_3 = (40 + 60)/2 = 50`

For 60 – 80: `x_4 = (60 + 80)/2 = 70`

For 80 – 100: `x_5 = (80 + 100)/2 = 90`

For 100 – 120: `x_6 = (100 + 120)/2 = 110`

For 120 – 140: `x_7 = (120 + 140)/2 = 130`

2. Multiply frequency by marks

Multiply each class frequency (f_i) by its corresponding class mark (x_i):

Class Interval	Frequency (fi)	Class Mark (xi)	Product (fixi)
0 – 20	6	10	6 × 10 = 60
20 – 40	8	30	8 × 30 = 240
40 – 60	10	50	10 × 50 = 500
60 – 80	12	70	12 × 70 = 840
80 – 100	6	90	6 × 90 = 540
100 – 120	5	110	5 × 110 = 550
120 – 140	3	130	3 × 130 = 390
Total	Σfi = 50		Σfixi = 3120

3. Sum the values

Calculate the total frequency and the total sum of products:

Σf_i = 6 + 8 + 10 + 12 + 6 + 5 + 3 = 50

Σf_ix_i = 60 + 240 + 500 + 840 + 540 + 550 + 390 = 3120

4. Compute the mean

Use the direct method formula for grouped data:

Mean `(barx) = (sumf_ix_i)/(sumf_i)`

Substitute the calculated values into the formula:

`barx = 3120/50 = 62.4`