The mode and median of a set of 7 observations are 22.72 and 49.28, respectively. If each of the largest 3 observations of the set is increased by 4, then the median of the new set?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → remains the same as that of the original set
Step 1: Recall facts about median
- The median of a set of 7 observations = 4th observation when arranged in ascending order.
- Median of original set = 49.28 → the 4th observation = 49.28
Step 2: Effect of increasing largest 3 observations
- Largest 3 observations = 5th, 6th, 7th in ascending order.
- Each of these is increased by 4.
- 4th observation (median) is unchanged because it is not among the largest 3.
Step 3: Conclusion
$\text{New median} = \text{Original median} = 49.28$