Question

The median of a set of $9$ distinct observations is $20.5$. If each of the largest $4$ observations of the set is increased by $2$, then the median of new set :

• A. is increased by $2$.
• B. is decreased by $2$.
• C. is two times the original median.
• D. remains the same as that of the original set.

Answer 1

Answer: (D)

remains the same as that of the original set.

Given that number of observations is $9$

Therefore median is $(\frac{n+1}{2}{)}^{th}$ value $=\frac{10}{2}=5^{th}$ value

Given that the largest $4$ observations is increased by $2$

The last four observations are $9^{th},8^{th},7^{th},6^{th}$

Therefore, the median doesn't change.