If the oldest person leaves and is replaced by a person who is even older, what happens to the mean and median?

Question

There are 5 students in a room. The mean age is 20.3 years, and the median age is 19 years.

If the oldest person leaves and is replaced by a person who is even older, what happens to the mean and median?

A.) The median stays the same and the mean increases

B.) Both the median and the mean increase

C.)The median decreases and the mean increases

D.) The mean increases, but it is impossible to determine what happens to the median

E.) The median increases and the mean stays the same.

Answer 1

A) the median stays the same and the mean increases

the median depends only on the order. The order stays the same. The median is still 19.

the mean is the arithmetic average, which increases, when the oldest is replaced by an even older. The mean increases above 20.3

17, 18, 19,20 and 27 1/2 are 5 students with a median age of 19 and mean age of (17+18+19+20+27.5) =101.5/5= 20.3

replace 27 1/2 with 28 and the median (the middle age) is still 19, but the mean is now

(17+18+19+20+ 28)/5 = 102/5= 20.4