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  • I have a doubt, kindly clarify. If the mean of the data : 7, 8, 9, 7, 8, 7, λ, 8 is 8, then the variance of this data is :

If the mean of the data : 7, 8, 9, 7, 8, 7, λ, 8 is 8, then the variance of this data is :

  • Option 1)

    \frac{7}{8}

  • Option 2)

    1

  • Option 3)

    \frac{9}{8}

  • Option 4)

    2

 

Answers (2)

best_answer

As we learned,

 

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.

-

 

 

Standard Deviation -

If x1, x2...xn are n observations then square root of the arithmetic mean of 

\sigma = \sqrt{\frac{\sum \left ( x_{i}-\bar{x} \right )^{2}}{n}}

\bar{}

- wherein

where \bar{x} is mean

 

 mean of data = \frac{7+8+9+7+8+7+7+8}{8}=8

\Rightarrow \: \lambda =10

Variance

V^{2}=\frac{\left ( 7-8 \right )^{2}+\left ( 8-8 \right )^{2}+\left ( 9-8 \right )^{2}+\left ( 7-8 \right )^{2}+0^{2}+\left ( 7-8 \right )^{2}+\left ( 10-8 \right )^{2}+\left ( 8-8 \right )^{2}}{8}

=\frac{8}{8}=1

Variance = 1


Option 1)

\frac{7}{8}

Option 2)

1

Option 3)

\frac{9}{8}

Option 4)

2

Posted by

Himanshu

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