Question

Calculate the 83^rd percentile of the data shown

x

11.6

12.7

13.1

17

17.4

38.5

40.6

48.2

55.1

56.1

60.5

Answer 1

Step 1 : We will calculate the Rank R of 83rd percentile

Formula for Rank R = P * (N+1) / 100

Where P is the required percentile, here it is 83

N = number of values = 11

Rank R = (83 * 12) / 100

= 996/100

= 9.96

Step 2 : Since Rank is between 9 and 10, the 83rd percentile value will be between 55.1 and 56.1

Ranks are the numbers in the asceding order. For example Rank 3 here is 13.1, Rank 4 is 17 etc.,

Step 3 : We will interplote by subtracting 55.1 fro, 56.1 and then multiplying it by 0.96 which is the fractional part of the Rank and then add the obtained value to 55.1

83rd Percentile = 55.1 + 0.96 * (56.1 - 55.1)

= 55.1 + 0.96

= 56.06

So 83rd Percentile = 56.06