Question

Compute the mean of the following frequency distribution:

Class	10 – 30	30 – 50	50 – 70	70 – 90	90 – 110
Frequency	15	18	25	10	2

Answer 1

1. Identify class midpoints

The midpoint (x_i) for each continuous class interval is computed by taking the average of its lower and upper boundaries:

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

For 10 – 30: `x_1 = (10 + 30)/2 = 20`

For 30 – 50: `x_2 = (30 + 50)/2 = 40`

For 50 – 70: `x_3 = (50 + 70)/2 = 60`

For 70 – 90: `x_4 = (70 + 90)/2 = 80`

For 90 – 110: `x_5 = (90 + 110)/2 = 100`

2. Formulate product values

Next, multiply each class frequency (f_i) by its corresponding midpoint (x_i) to find f_ix_i:

Class Interval	Frequency (fi)	Midpoint (xi)	Product (fixi)
10 – 30	15	20	15 × 20 = 300
30 – 50	18	40	18 × 40 = 720
50 – 70	25	60	25 × 60 = 1500
70 – 90	10	80	10 × 80 = 800
90 – 110	2	100	2 × 100 = 200

3. Compute total sums

Sum the frequencies and the products to obtain `sumf_i` and `sumf_ix_i`:

`sumf_i = 15 + 18 + 25 + 10 + 2 = 70`

`sumf_ix_i = 300 + 720 + 1500 + 800 + 200 = 3520`

4. Calculate final mean

Substitute the compiled sums into the arithmetic mean formula:

`bar(x) = (sumf_ix_i)/(sumf_i)`

`bar(x) = 3520/70 ≈ 50.2857`