Nine students have obtained the following marks in statistics out of 100 marks. Calculate the standard deviation of marks through short-cut method (Assumed mean method).
S.N 1 2 3 4 5 6 7 8 9. Marks 5 10 20 25 40 45 48 70 80.
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ANSWER:
Families
Monthly income
(X)
Deviation from the Assumed average
(d = X − A) (A = 75)
1
2
3
4
5
6
7
8 70
10
500
75 (A)
13
250
8
42 −5
−65
425
0
−62
175
−67
−33
(N) = 8
(ΣX)=968 Σd = −232 + 600 = 368
where,
N= Number of items
ΣX= Total of monthly income of all the families
Σd= net sum of deviations
Calculation of Mean by Direct Method
X=
ΣX
N
=
968
8
=121
Calculation of mean by short cut method
X=A+
Σd
N
or, X=75+
368
8
or, X=75+46⇒X=121
So, mean monthly income of a family is Rs 121.
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