Question

The median of a set of $11$ distinct observations is $15.5$. If each of the smallest $5$ observations of the set are decreased by $3$, then the median of the new set:

• A. Is increased by $3$
• B. Is decreased by $3$
• C. Is $3$ times the original median
• D. Remains the same as that of the original set

Answer 1

The correct option is D Remains the same as that of the original set

Given, the median of a set of $11$ distinct observations is $15.5$.
Since, Median is the middle most term in given data, so if we have total $11$ terms then middle most term is $6^{th}$ term.
$\therefore 6^{th}$ term $=15.5$
If each of the smallest $5$ observations of the set are decreased by $3$, then $6^{th}$ term of the data still remains same.
Therefore, Median remains same as that of Original set.
Option $D$ is correct.