Example
The list shows marks for 25 students on a test out of 40.
31 28 28 30 20
25 38 40 26 28
15 21 28 36 25
16 21 34 37 30
23 24 36 32 25
a) calculate the 80th percentile b) what percentile is a mark of 25? c) what percentile is a mark of 40?
Solution
a) calculate the rank first. We want to know what rank gets us that 80th percentile mark. = 20.8 We round down. = 20 The 20th highest number is the basis for our 80% percentile. 34 is the 80th percentile
b) data point is 25. there are 7 marks lower than 25. and 3 marks equal to 25. 100(7+0.5(3))/25 = 34 25 is within 34% percentile
c) data point is 40. 24 marks lower than 40. 1 mark equal to 40 100(24+0.5)/25 = 98 40 is within the 98% percentile