3) An original frequency table with mean 11 and variance 99 was lost but the following
table derived from it was found. Construct the original table
value of deviation = -2 , -1 , 0 , 1 , 6
frequency = 1 , 6 , 7 , 4 , 2
Answers
Given : An original frequency table with mean 11 and variance 9.9 was lost . value of deviation & Frequency is available
To find : original table
Solution:
value of deviation d = -2 , -1 , 0 , 1 , 2
Frequency f = 1 , 6 , 7 , 4 2
d f d * f fd²
-2 1 -2 4
-1 6 -6 6
0 7 0 0
1 4 4 4
2 2 4 8
20 0 22
A = Assumed Mean
h = Width of Class interval
Mean = A + h (0)/20 = 11
=> A = 11
Variance = h² ( ∑ fd² / N - (∑fd/N)²)
9.9 = h² (22/20 - 0)
=> h² = 9
=> h = 3
Assumed mean = 11
Class width = 3
=> 3/2 on both sides of 11 ( 11 - 1.5 = 9.5 & 11 + 1.5 = 12.5)
=> Assumed Mean interval = 9.5 - 12.5
Original Class frequency
3.5 - 6.5 1
6.5 - 9.5 6
9.5 - 12.5 7
12.5 - 15.5 4
15.5 - 18.5 2
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