Question

If each observation of set is divided by $10$, the S.D of the new observations is ______.

• A. $10$ times of S.D of original obs.
• B. $\frac{1}{100}$th
• C. Not changed
• D. $\frac{1}{10}$th

Answer 1

The correct option is D $\frac{1}{10}$th

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data. So the deviations are affected by division and multiplication. Therefore, if each observation of the set id divided by 10 then the whole standard deviation also becomes 1/10 th of the prior standard deviation.