Given 7 observations with Mean = 10 and Median = 9.
When 2 is subtracted from each observation, both the mean and median decrease by the same constant value.
Original Mean = 10
Subtracting 2 from each observation decreases the mean by 2.
New Mean = 10 - 2 = 8
The original sum of all observations = 10 × 7 = 70
After subtracting 2 from each of the 7 observations:
New sum = 70 - (2 × 7)
New sum = 70 - 14
New sum = 56
New Mean = 756 = 8
Original Median = 9
For 7 observations, the median is the 4th value when arranged in order.
Subtracting 2 from each observation decreases the median by 2.
New Median = 9 - 2 = 7
The new Median = 7 and new Mean = 8