Question

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

• A. increases by 2
• B. decreases by 2
• C. doubles
• D. remains the same

Answer 1

The correct option is D remains the same

We know that the median is found when we arrange the observations in ascending or descending order. If the number of observations is odd, then it is the $\frac{n+1}{2}th$ term.
When 9 observations are arranged, the 5th will be the median.
Changing 4 observations on any side of the median won't affect the median and it'll remain the same.