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?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 7 and 9
Subtracting the same number from every observation moves every value down by that number and does not change their order. So the middle value and the average both fall by the same number.
New median: the middle (4th) observation is still the middle one, \(9-2=7\)
New mean: the total falls by \(7\times2=14\), so the mean falls by \(14\div7=2\), \(11-2=9\)