If the standard deviation of a set of observations is 4 and if each observation is divided by 4, the standard deviation of the new set of observations will be:

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Solution

The correct option is D 1
We know that, if we multiply all numbers of a set by a constant "k" then the mean of these numbers will also be a multiple of "k".
And the variance of these numbers will be multiple of " $k^{2}$ ".
Since standard deviation is nothing but the square root of the variance, the standard deviation will be multiple of "k" of the old standard deviation.
It is given that standard deviation was 4 initially.
So, after multiplying each observation by $\frac{1}{4}$ , the standard deviation will also be multiplied by $\frac{1}{4}$ .
It gives the value $= 4 \times \frac{1}{4} = 1$

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