Question

If the S.D of a set of observations is 4 and if each observation is divided by 4, the S.D of the new set of observations will be

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

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 the old mean.
And the variance of these numbers will be multiple of "$k^2$".
Since standard deviation is nothing but the square root of variance, s.d will be multiple of "k" of the old standard deviation.
We are given the s.d was 4.
So after multiplying each observation by (1/4), the s.d will also be multiplied by (1/4), thus giving the value = 4.$\frac{1}{4}$ = 1