Question

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​

Answer 1

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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