9. Given below the four sets of observations. Which set has the
minimum variation?
a) 46, 48, 50, 52,54
(b) 30, 40, 50, 60, 70
(C) 40, 50, 60, 70, 80
(c) 48, 49, 50, 51,52
With proper explanation plz
Answers
Given : four sets of observations
To Find : Which set has the minimum variation
Solution:
a) 46, 48, 50, 52,54
Mean = (46 + 48 + 50 + 52 + 54)/5 = 50
x x-mean (x -mean)²
46 -4 16
48 -2 4
50 0 0
52 2 4
54 4 16
40
Variance = 40/5 = 8
b) 30, 40, 50, 60, 70
Mean = (30 + 40 + 50 + 60 + 70)/5 = 50
x x-mean (x -mean)²
30 -20 400
40 -10 100
50 0 0
60 10 100
70 20 400
1000
Variance = 1000/5 = 200
c) 40, 50, 60, 70 , 80
Mean = ( 40 + 50 + 60 + 70 + 80)/5 = 60
x x-mean (x -mean)²
40 -20 400
50 -10 100
60 0 0
70 10 100
80 20 400
1000
Variance = 1000/5 = 200
d) 48, 49, 50, 51,52
Mean = (48 + 48 + 50 + 51 + 52)/5 = 50
x x-mean (x -mean)²
48 -2 4
49 -1 1
50 0 0
51 1 1
52 2 4
10
Variance = 10/5 =2
Variance 8 , 50 , 50 , 2
Minimum variance = 2 for 48, 49, 50, 51,52
Hence 48, 49, 50, 51,52 has minimum variation
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