Number of observations = 7
Original Median = 9
Original Mean = 11
Operation: 2 is subtracted from each observation
The sum of the original 7 observations:
Sum =7×11
Sum =77
When 2 is subtracted from each of the 7 observations, the total decrease in sum:
Total decrease =7×2
Total decrease =14
New sum =77−14
New sum =63
New mean =763
New mean =9
The median is the middle value (4th observation when arranged in order).
When 2 is subtracted from every observation, all values shift down by 2, but their order remains unchanged.
The middle value decreases by 2:
New median =9−2
New median =7
Therefore, the new median and new mean are 7 and 9 respectively.