Question

For the set of data, find the 25th percentile:

41,43,56,57,62,71,74,78,84,92,97

Answer 1

the 25th percentile. We see that the number of observations, n = 11

41    43   56   57   62   71 74 78 84 92 97

We need to find the position (L) of the 25th percentile.

If L is a decimal, then the required percentile is the next value, for eg we get a position of 2.1, then the 3rd value would be the required percentile.

If L is an integer say 3 (that is the 3rd position), then we take the average of the 3rd and 4th positions, and that value will be the required percentile.

For this question, L = (25/100) * 11 = 2.75. Therefore the 3rd value is our required percentile = 56