Question

The median and standard deviation (S.D) of a distribution are 20 and 4 respectively. If each item is increased by 2, then

• A. median will increase by 2.
• B. median will remain same.
• C. standard deviation will remain same
• D. standard deviation will increase by 2.

Answer 1

Answer: (A), (C)

median will increase by 2.
standard deviation will remain same

The terms used in calculating standard deviation are deviations from the mean of the observations.
As each number/observation is increased by 2, the mean and thus the deviations from the mean remain the same.
Hence standard deviation remains the same.
On the other hand, median gives the middle term or the average of the two middle terms accordingly when the total number of terms is odd or even.
Thus, it has to increase by 2.