Question

The table given below shows the age distribution of 1000 persons who visited a marketing centre on a Sunday.

Age (in years)	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70
Number of persons	105	222	220	138	102	113	100

Find the mean age of the persons visiting the marketing centre on that day.

Answer 1

1. Identify class marks

The class mark (x_i) for each age interval is calculated by taking the average of its lower and upper boundaries using the formula:

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

2. Tabulate data and products

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

Age Interval (in years)	Number of persons (fi)	Class Mark (xi)	Product (fixi)
0 – 10	105	5	105 × 5 = 525
10 – 20	222	15	222 × 15 = 3,330
20 – 30	220	25	220 × 25 = 5,500
30 – 40	138	35	138 × 35 = 4,830
40 – 50	102	45	102 × 45 = 4,590
50 – 60	113	55	113 × 55 = 6,215
60 – 70	100	65	100 × 65 = 6,500
Total	Σfi = 1,000		Σfixi = 31,490

3. Compute mean age

Use the direct method formula for the mean of grouped data:

Mean = `(sumf_ix_i)/(sumf_i)`

Substitute the calculated sums into the formula:

Mean = `(31,490)/(1,000) = 31.49`