12 calculate mean -
wages
10
20
30
40
50
No. of worless
4
5
3
2
5
Answers
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=ΣXN=9688=121
Calculation of mean by short cut method
X=A+ΣdNor, X=75+3688or, X=75+46⇒X=121
So, mean monthly income of a family is Rs 121.
Page No 162:
Question 2:
Students of Class XI secured following marks in their Statistics paper.
Calculate arithmetic mean using Direct Method and Short-cut Method.
20, 44, 65, 28, 45, 67, 30, 50, 68, 39, 53, 70, 40, 60, 75
ANSWER:
Sr. No. Marks
(X) Deviation from the Assumed mean
d = X − A where A = 50
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15. 20
44
65
28
45
67
30
50 (A)
68
39
53
70
40
60
75 -30
-06
15
-22
-05
17
-20
0
18
-11
3
20
-10
10
25
N = 15 ΣX = 754 Σd = -104 + 108 = 4
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=ΣXNor, X¯=75415or, X¯=50.27⇒X¯ =50.27
Calculation of mean by short cut method
X=A+ΣdNor, X=50+415or, X=50+0.27=50.27⇒X=50.27
So, mean marks in statistics is 50.27.