The median and mean of 7 observations are 9 and 11 respectively. If 2 is subtracted from each observation, then the new median and the new mean will respectively be which of the following?

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 $= 7 \times 11$

Sum $= 77$

When 2 is subtracted from each of the 7 observations, the total decrease in sum:

Total decrease $= 7 \times 2$

Total decrease $= 14$

New sum $= 77 - 14$

New sum $= 63$

New mean $= \dfrac{63}{7}$

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.