Question

Find the average age from the following distribution:

Age (in years)	25 – 29	30 – 34	35 – 39	40 – 44	45 – 49	50 – 54	55 – 59
Frequency	4	14	22	16	6	5	3

Answer 1

First, let’s calculate the midpoint (x_i) for each interval using the formula:

Mid-point = `("Lower Limit" + "Upper Limit")/2`

Age (in years)	Midpoint (xi)	Frequency (fi)	fi × xi
25 – 29	27	4	108
30 – 34	32	14	448
35 – 39	37	22	814
40 – 44	42	16	672
45 – 49	47	6	282
50 – 54	52	5	260
55 – 59	57	3	171
Total		Σfi = 70	Σfixi = 2755

Calculating the mean

Now, we use the mean formula for grouped data:

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

Substituting the values from our table:

`barx = 2755/70`

`barx ≈ 39.36`

The average age from the distribution is approximately 39.36 years.