Continuous Standard Deviation
The formula for the continuous standard deviation is:
= √ Σ fd2 / N - (Σ fd / N)2 xi
Where d = (m - A) / I I = class interval
Illustration:
Calculate the mean and standard deviation of following frequency distribution of marks:
|
Marks
|
no .of students
|
Marks
|
no .of students
|
|
0-10
|
5
|
40-50
|
50
|
|
10-20
|
12
|
50-60
|
37
|
|
20-30
|
30
|
60-70
|
21
|
|
30-40
|
45
|
|
|
Solution:
|
Marks
|
m. p .m
|
F
|
(m - 35)/10 d
|
Fd
|
Fd2
|
|
0-10
|
5
|
5
|
-3
|
-15
|
45
|
|
10-20
|
15
|
12
|
-2
|
-24
|
48
|
|
20-30
|
25
|
30
|
-1
|
-30
|
30
|
|
30-40
|
35
|
45
|
0
|
0
|
0
|
|
40-50
|
45
|
50
|
+1
|
+50
|
50
|
|
50-60
|
55
|
37
|
+2
|
+74
|
148
|
|
60-70
|
65
|
21
|
+3
|
+63
|
189
|
|
|
|
N = 200
|
|
Σ fd = 118
|
Σfd2 = 510
|
X = A + Σ fd / N xi = 35 + 118 / 200 x 10 = 35 + 5.9 = 40.9
Σ √Σfd2 / N - (Σ fd /N)2 x 10 = √510/200- (118/200)2 x 10
= √2.55 - 3481 x 10 = 1.4839 x 10 = 14.839.