10.Calculate mean, standard deviation and its coefficient for the following frequency distribution: Class : 50-55 45-50 40-45 35-40 30-35 25-30 Freq. 22 29 31 47 51 70 (Ans. X = 36.78, 0 = 8.19, V = 22.27%)
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Answer:
SD = √Var(X)
Class
F₁
Xi
xi-mean 4
f¡u¡
fiu²
31-35
2
-8
32
-4
-3
36-40
3
27
41-45
-2
8
12 16
32
33
38
43
48 53
58
-9
-16
-12
46-50 51-55
-1 0
12
0
5
1
0
5
5
56-60
61-65
66-70
8
2
2
63
68
2
3
4
6
18
= 50
Σuifi = -30
Σ uffi = 134
Now,
N=50₂ Σu₁f₁ = -30 Σu²f₁ = 134
Mean, X = A + h (fi) N
X = 53+5 5(-30) 30
= 50
Var(X) = h²
4²² - ( 12 ) u;f; i=1 i=1
9
[134
Var(X) = 25
25.
Variance=58
Standard Deviation, 0 = √58
= 7.62 .. The standard deviation is 7.62
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