# If the standard deviation of 0,1,2, 3............9 in K, the standard deviation of 10,11,12,13......19 is  Option 1) $K$ Option 2) $K+10$ Option 3) $K+\sqrt{10}$ Option 4) $10K$

Using

Standard Deviation -

In case of discrete frequency distribution

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

-

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

and each data increases by $\lambda \left ( \lambda =10 \right )$ then there will be no change in standard deviation because $\left ( x_{i}-\bar{x} \right )$ will be same.

So, new standard deviation is K.

Option 1)

$K$

This option is correct

Option 2)

$K+10$

This option is incorrect

Option 3)

$K+\sqrt{10}$

This option is incorrect

Option 4)

$10K$

This option is incorrect

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