If Each observation of a raw data where  variance  is  \sigma ^{2} is multiplied I , the variance  of new set is 

  • Option 1)

    \sigma ^{2}

  • Option 2)

    \lambda ^{2}\sigma ^{2}

  • Option 3)

    \lambda +\sigma ^{2}

  • Option 4)

    \lambda ^{2}+\sigma ^{2}

 

Answers (1)

Using

Standard Deviation -

In case of discrete frequency distribution 

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

-

 

 Since Standard deviation

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

Is each observation of a raw data is multiplied by \lambda then,

\sigma ^{1}= \lambda \sqrt{\frac{\sum \left ( x_{i} -\bar{x}\right )^{2}}{n}}

So that new variance \left ( \sigma ^{1} \right )^{2} = \lambda ^{2}\sigma ^{2}


Option 1)

\sigma ^{2}

This option is incorrect

Option 2)

\lambda ^{2}\sigma ^{2}

This option is correct

Option 3)

\lambda +\sigma ^{2}

This option is incorrect

Option 4)

\lambda ^{2}+\sigma ^{2}

This option is incorrect

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