Find the median of these ordered lists without writing out all the numbers. Show and explain briefly what you did to find the median.

Question

(a) 1 2 3 4 5…..97 98 99

(b) 1 2 3 4 5….97 98

Answer 1

The slot number of the median is (n+1)/2.

a) n = 99, so the slot number is (99+1)/2 = 50, and the median is 50.

b) n = 98, so the slot number if (98+1)/2 = 49.5 and the median is the average of the 49th and 50th slot numbers = 49.5

Answer 2

(a) There are an ODD number of statistics, namely 99 of them.

So the median must be 50 : 1-49 less and 51-99 greater

(b) There are an EVEN number of statistics, namely 98 of them.

So the median must be (49+50)/2 = 49.5