Question

Find mean of the following table.

Difference in ages (in years)	No. of couples (fi)
0 – 2	1
2 – 4	2
4 – 6	8
6 – 8	5
8 – 10	3
10 – 12	1

Answer 1

1. Calculation table

First, find the class mark (midpoint x_i) for each interval using the formula:

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

Difference in ages (in years)	No. of couples (fi)	Class Mark (xi)	fi × xi
0 – 2	1	1	1 × 1 = 1
2 – 4	2	3	2 × 3 = 6
4 – 6	8	5	8 × 5 = 40
6 – 8	5	7	5 × 7 = 35
8 – 10	3	9	3 × 9 = 27
10 – 12	1	11	1 × 11 = 11
Total	Σfi = 20		Σfixi = 120

2. Formula and Final Steps

Using the direct method formula for calculating the mean:

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

`barx = 120/20`

`barx` = 6