|
Q. 6. Calculate the variance for the class-frequency
distribution given below: (Dec.
2001)
| Marks obtained |
Number of students |
| 0-10 |
15 |
| 10-20 |
20 |
| 20-30 |
25 |
| 30-40 |
17 |
| 40-50 |
12 |
Solution.
| Marks obtained |
Mid point
(M) |
Number of students (f) |
f X M |
x = M - mean
|
x2
|
f X x2
|
| 0-10 |
5
|
15 |
75
|
-18.98 |
360.2404
|
5403.606
|
| 10-20 |
15
|
20 |
300
|
-8.98 |
80.6404
|
1612.808
|
| 20-30 |
25
|
25 |
625
|
1.02 |
1.0404
|
26.01
|
| 30-40 |
35 |
17 |
595 |
11.02 |
121.4404 |
2064.4868 |
| 40-50 |
45
|
12 |
540
|
21.02 |
441.8404
|
5302.0848
|
|
Total |
|
å
N = 89 |
å
fM = 2135 |
|
|
å
fx2 = 14408.9956 |
Mean = å fM/å
N = 2135/89 = 23.98
| |
 |
å
fx2
|
| s = |
|
| |
å
N
|
| |
|
14408.9956
|
| or
s = |
|
| |
89
|
or s = 12.72
Variance, s2
= 160.79
|
