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Example Calculate s.d. of the marks of 100 students.
|
Marks |
No. of students
(fi) |
Mid-values
(xi) |
fi xi |
fi xi2
|
|
0-2 |
10 |
1 |
10 |
10 |
|
2-4 |
20 |
3 |
60 |
180 |
|
4-6 |
35 |
5 |
175 |
875 |
|
6-8 |
30 |
7 |
210 |
1470 |
|
8-10 |
5 |
9 |
45 |
405 |
| |
n = 100 |
|
Sfi xi = 500 |
Sfi xi2 = 2940 |
Solution
1) 
2) 
Example Calculate s.d. of the marks of 100 students.
|
Marks |
No. of students
(fi) |
Mid-values
(xi) |
fi xi |
fi xi2
|
|
0-2 |
10 |
1 |
10 |
10 |
|
2-4 |
20 |
3 |
60 |
180 |
|
4-6 |
35 |
5 |
175 |
875 |
|
6-8 |
30 |
7 |
210 |
1470 |
|
8-10 |
5 |
9 |
45 |
405 |
| |
n = 100 |
|
Sfi xi = 500 |
Sfi xi2 = 2940 |
Solution
1) 
2) 
Combined Standard deviation : If two sets containing n1 and n2
items having means x1 and x2 and standard deviations s1
and s2 respectively are taken together then,
(1) Mean of the combined data is 
(2) s.d. of the combined set is 
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