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Question

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5,7,10,12,14,15 then the absolute difference of the remaining two observations is:


A

3

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B

9

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C

7

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D

5

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Solution

The correct option is C

7


Explanation for the correct option:

Step 1: Find the relation between the remaining two observations.

Since, it is given that the mean of 8 observations is 10 and six observations are 5,7,10,12,14,15.

Assume that, the remaining two observations are x1 and x2.

Therefore,

(x)i=188=10(x)i=18=805+7+10+12+14+15+x1+x2=80x1+x2=17...1

Also, it is given that the variance of 8 observations is 13.5.

(x2)i=188-(10)2=13.5(x2)i=188=113.5(x2)i=18=90852+72+102+122+142+(15)2+x12+x22=908x12+x22=169...2

Step 2: Find the absolute difference between the remaining two observations.

Since, we know that (x1+x2)2-2x1x2=x12+x22

From equation 1 and equation 2.

(17)2-2x1x2=169289-2x1x2=1692x1x2=120...3

Since, x1-x22=(x1+x2)2-4x1x2.

From equation 1 and equation 3.

x1-x22=(17)2-2·120x1-x22=289-240x1-x22=49x1-x2=7

Therefore, the absolute difference between the remaining two observations is 7.

Hence, option C is the correct answer.


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