Question

Find the mean and modal class:

Class	50 – 55	55 – 60	60 – 65	65 – 70	70 – 75	75 – 80	80 – 85	85 – 90
Frequency	5	20	10	10	9	6	12	8

Answer 1

1. Finding the mean

To find the mean of grouped data, we use the formula:

`barx = (sum(f_i xx x_i))/(sumf_i)`

where f_i is the frequency and x_i is the class mark (midpoint) of each interval.

Class	Frequency (fi)	Class Mark (xi)	fi × xi
50 – 55	5	52.5	262.5
55 – 60	20	57.5	1150.0
60 – 65	10	62.5	625.0
65 – 70	10	67.5	675.0
70 – 75	9	72.5	652.5
75 – 80	6	77.5	465.0
80 – 85	12	82.5	990.0
85 – 90	8	87.5	700.0
Total	Σfi = 80		Σ(fi × xi) = 5520

Mean calculation:

`barx = 5520/80`

`barx = 69`

2. Finding the modal class

The modal class is the class interval with the highest frequency.

Looking at the table, the highest frequency is 20.

This frequency corresponds to the class interval 55 – 60.