Question

Find the mean:

Marks (below)	10	20	30	40	50	60	70	80	90	100
No. of students	5	9	17	29	45	60	70	78	83	85

Answer 1

Step 1: Create a frequency distribution table

The “Marks (below)” represent the upper limits of class intervals. Since they increase by 10, our intervals will be 0 – 10, 10 – 20, etc. To find the frequency (f) for each interval, we subtract the previous cumulative frequency from the current one.

Class Interval (Marks)	Midpoint (xi)	No. of students (cf)	Frequency (fi)	fi × xi
0 – 10	5	5	5	25
10 – 20	15	9	9 – 5 = 4	60
20 – 30	25	17	17 – 9 = 8	200
30 – 40	35	29	29 – 17 = 12	420
40 – 50	45	45	45 – 29 = 16	720
50 – 60	55	60	60 – 45 = 15	825
60 – 70	65	70	70 – 60 = 10	650
70 – 80	75	78	78 – 70 = 8	600
80 – 90	85	83	83 – 78 = 5	425
90 – 100	95	85	85 – 83 = 2	190
Total			Σfi = 85	Σfixi = 4115

Step 2: Calculate the mean

The formula for the mean `(barx)` of grouped data is:

`barx = (sumf_ix_i)/(sumf_i)`

Substituting the values from our table:

`barx = 4115/85`

`barx ≈ 48.41`

The mean marks of the students is approximately 48.41.