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 the new set _________.
(Data is arranged in ascending order)

• 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

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

Since n = 9 (odd observatioons), Median = ${\left(\frac{n+1}{2}\right)}^{th}$
then median will be
Median = ${\left(\frac{9+1}{2}\right)}^{th}=5^{th}$observation
Now, last four observations are increased by 2.
The median is the $5^{th}$ observation, which remains unchanged.

$\therefore$ There will be no change in median.