Question

The marks scored by 60 students in a mathematics test are given below.

Marks (X)	10	20	30	40	50	60
No. of students (f)	8	12	20	10	7	3

Find the Variance and Standard Deviation of the marks.

Answer 1

Table of calculation
Marks X	Frequency f	fX	Deviation	Square of Deviation D2	f.D2
10	8	80	–20.83	433.8889	3471.1112
20	12	240	–10.83	117.2889	1407.4668
30	20	600	– 0.83	0.6889	13.778
40	10	400	9.17	84.0889	840.889
50	7	350	19.17	367.4889	2572.4223
60	3	180	29.17	850.8889	2552.6667
	= 60	1850			=10858.334

Sum of the frequencies = N = = 60

Mean = = = 30.83

Average marks scored = 30.83

(i) = =

(ii)