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  • Give answer! The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is : 

  • Option 1)

    3

  • Option 2)

    1

  • Option 3)

    7

  • Option 4)

    5

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}

y=\frac{3+4+4+x_{4}+x_{5}}{5}\\\\\Rightarrow x_{4}+x_{5}=9\\\\5.2=\frac{\sum x_{i}^{2}}{5}-\mu ^{2}\\\\\\\Rightarrow 5.2=\frac{9+16+16+x_{4}^{2}+x_{5}^{2}}{16}-16\\\\\Rightarrow x_{4^{2}}+x_{5}^{2}=65\\\\\Rightarrow 81-2x_{4}x_{5}=65\\\\\Rightarrow x_{4}x_{5}=8\\\\(x_{1}-x_{5})^{2}=(x_{4}+x_{5})^{2}-4x_{4}x_{5}\\\\81-32=49\\\\\\\: \left | x_{4}-x_{5} \right |=7

-

 

 


Option 1)

3

Option 2)

1

Option 3)

7

Option 4)

5

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