Statistcs help

Question

Below are 36 sorted ages of an acting award winner. Find the percentile corresponding to age
37 using the method presented in the textbook.

18 19 19 20 21 23 26 27 29 30
30 30 33 34 35 35 37 39 40 41
43 44 46 46 46 50 50 50 53 58
62 70 70 72 72 73

percentile of value 37 =

Answer 1

It's tough to know what method the textbook used, but 37 is greater than 16 of the 36 nicely-sorted numbers.  This makes the percentile (per cent meaning per hundred) 16/36 or 44/100 (rounded) or 44%.  That is, the number 37 is larger than 44% of the numbers in this list.

 

Now, if the textbook is really savvy and is teaching estimating without a calculator, then it might say that there are 36 sorted values, that the number 40 in position 19 is above half of the values (18 is 50% of 36; at the 50 percentile point) and that each of the 36 numbers is roughly 3% of 100%  (that is, 3/36) and 2 positions is roughly 6%, thus, the answer is very roughly 44%.