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प्रश्न
If each observation of a raw data whose standard deviation is σ is multiplied by a, then write the S.D. of the new set of observations.
उत्तर
Standard deviation,
Multiplying each \[x_i\] bay \[a\] : \[x_{new} = \frac{1}{n}\sum_i a . x_i \]
\[ = a \times \frac{1}{n} \sum_i x_i \]
\[ = a . x_{old}\]
\[ = \sqrt{\frac{\sum_i a^2 . \left( x_i - x \right)^2}{n}}\]
\[ = \left| a \right|\sqrt{\frac{\sum_i \left( x_i - x \right)^2}{n}}\]
\[ = \left| a \right| . \sigma\]
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