Question

The mean of the following distribution is 50. Find the unknown frequency:

Class	0 – 20	20 – 40	40 – 60	60 – 80	80 – 100
Frequency	6	f	8	12	8

Answer 1

Step 1: Set up the calculation table

First, we need to find the class mark (x_i) for each interval, which is the midpoint of the class. Then, we calculate the product of the frequency (f_i) and the class mark (x_i).

Class	Frequency (fi)	Class Mark (xi)	fi × xi
0 – 20	6	10	60
20 – 40	f	30	30f
40 – 60	8	50	400
60 – 80	12	70	840
80 – 100	8	90	720
Total	Σfi = 34 + f		Σfixi = 2020 + 30f

Step 2: Apply the mean formula

The formula for the mean `(barx)` is:

`barx = (sumf_ix_i)/(sumf_i)`

Given that the mean `(barx) = 50`, we can substitute the values from our table into the equation:

`50 = (2020 + 30f)/(34 + f)`

Step 3: Solve for f

1. Multiply both sides by (34 + f):

50(34 + f) = 2020 + 30f

2. Expand the left side:

1700 + 50f = 2020 + 30f

3. Rearrange the terms to group the f variables on one side:

50f – 30f = 2020 – 1700

20f = 320

4. Divide by 20:

f = `320/20`

f = 16

The unknown frequency f is 16.