Question

Calculate the mean of the following frequency distribution:

Class interval	5 – 15	15 – 25	25 – 35	35 – 45	45 – 55
Frequency	2	6	4	8	4

Answer 1

Step 1: Find the class marks (x_i)

The class mark is the midpoint of each interval, calculated as:

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

Step 2: Create a calculation table

We multiply each frequency (f_i) by its corresponding class mark (x_i) to get f_ix_i.

Class Interval	Frequency (fi)	Class Mark (xi)	fi × xi
5 – 15	2	10	20
15 – 25	6	20	120
25 – 35	4	30	120
35 – 45	8	40	320
45 – 55	4	50	200
Total	Σfi = 24		Σfixi = 780

Step 3: Apply the mean formula

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

`barx = (sumf_ix_i)/(sumf_i)`

Substituting the values from our table:

`barx = 780/24`

`barx = 32.5`

The mean of the given frequency distribution is 32.5.