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  • Help me answer: The mean of five observation is 5 and their variance is 9.20. If three of the given five observation are 1,3and 8, then a ratio of other two observation is:

The mean of five observation is 5 and their variance is 9.20. If three of the given five observation are 1,3and 8, then a ratio of other two observation is:

  • Option 1)

     

    10:3

  • Option 2)

     

    4:9

  • Option 3)

     

    5:8

  • Option 4)

     

    6:7

Answers (1)

best_answer

 

ARITHMETIC Mean -

For the values x1, x2, ....xn of the variant x the arithmetic mean is given by 

\bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}

in case of discrete data.

-

 

 

Variance -

In case of discrete data 

\dpi{100} \sigma ^{2}= \left ( \frac{\sum x_{i}^{2}}{n} \right )-\left ( \frac{\sum x_{i}}{n} \right )^{2}

-

Let 5 bservation are 1,3,8,1 and b

mean = \frac{\Sigma x_{i}}{5} = 5

\Rightarrow 1 + 3 + 8 + a + b = 25

\Rightarrow a+ b = 13 ..... (1)

Variance (\sigma^{2}) = \frac{\Sigma x_{i}^{2}}{5} -2 5 = 9.20

\Rightarrow \Sigma x_{i}^{2} = 171

\Rightarrow a2 + b2  = 97..... (2)

from (1) and (2)

(a+b)2 - 2ab = 97

ab = 36

\therefore a:b = 9:4 or 4:9

 


Option 1)

 

10:3

Option 2)

 

4:9

Option 3)

 

5:8

Option 4)

 

6:7

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