Question

The standard deviation of 20 observations is √6. If each observation is multiplied by 3, find
the standard deviation and variance of the resulting observations.
​

Answer 1

Standard deviation will become $3\sqrt{6}$ and variance will become 54

Step-by-step explanation:

Let the initial observation are $x_1,x_2,x_3........x_{20}$

We have given standard deviation as $\sqrt{6}$

And standard deviation is equal to $SD=\sqrt{\frac{(x-\bar{x})^2}{N}}$

Here SD = $\sqrt{6}$ and N is 20

Now it is given that each observation is multiplied by 3

So let new observation are $y_1,y_2,y_3........y_{20}$

Here $y_1=3x_1$

Now from the relation we can see that standard deviation will become 3 times

So new standard deviation will be $3\sqrt{6}$

As variance $=SD^2$

So variance $=(3\sqrt{6})^2=54$

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Answer 2

Answer:

you see in picture

Step-by-step explanation:

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