Given the following data set with an even number of values:
$100, 100, 105, 113, 129, 132, 146, 152, 176, 200$
The value representing the 30th percentile, using the formula n(p/100) where n = sample size and p = percentile, is at position 10(0.30) = 3. So the 30th percentile of this data is 105.
Given the following data set with an odd number of values:
$100, 100, 105, 113, 129, 132, 146, 152, 176, 200, 300$
The value representing the 30th percentile, using the formula n(p/100) where n = sample size and p = percentile, is at position 11(0.30) = 3.3. So now what does one do?
I realize that this formula can yield a decimal even if the data set has an even amount of values, say if n = 36, and you want the 10th percentile, 36(.10) = 3.6.
In this situation, do you average the 3rd and 4th values? Or is it the 3rd value? or the 4th value? How do you decide? What if the position was 3.2 or 3.7? Does it matter in choosing which value is represents the given percentile?
Thanks for any help ahead of time.
Best Answer
As noted in the other responses, there is disagreement.
In practice, with such a small data set, using percentiles isn't particularly useful. So it's really an artificial test question.
I'd say if the test question allows free-form answer, you should demonstrate that you know the general concept of percentiles, and also that you know it's controversial. The answer then would be "either 113, or 109, or 105, depending on the calculation method chosen."
If the question is multiple choice, then there are a few possibilities:
a) A thoughtful test author will not include more than one of 113/109/105 among the permitted choices. Easy.
b) A dogmatic test author who is your own teacher will have given a specific definition in class and will expect you to follow that definition. Predictable at least.
c) A dogmatic test author who is not your own teacher, and who offers more than one of the three choices, puts you in an unwinnable position. Take your best guess, and if it matters enough, be prepared to appeal.