Percentile Rules from Triola’s Elementary Statistics:
Math 11
Percentile rules are not all uniformly accepted, and I defined one of the rules differently than our
textbook during Monday’s class. For the first exam, I will hold you responsible for the percentile rules as
stated in the text and the following example is provided to make it clear how those rules work.
Consider the ranked data set:
Scores on a Recent Mathematics Comprehensive Exam (22 Students)
2
2
5
6
8
8
8
9
13
14
18
22
23
29
31
31
35
38
40
51
63
64
1. Find the percentile of the student who scored 23 on the exam.
Answer: To find the percentile of a data point, you count the number of data points below that value,
then express that number as a percentage of the entire data set. The score of 23 has 12 points below it,
so the percentile is (12/22)*100 = 54.55. It is standard to round to the nearest whole number, which is
55. The score of 23 is at the 55th percentile.
2. Find the percentile of a student who scored 31 on the exam.
Answer: The number of values less than 31 is 14. 31 is repeated, but you just count the number of
values strictly less than 31. The percentile for a score of 31 is (14/22)*100 = 63.6, which rounds to the
64th percentile.
3. Find the test score for the 29th percentile.
Answer: Since there are 22 data points, you find 29% of 22 which is .29*22 = 6.4. What we mean is that
“29% of the data is below the 6.4th position in the data set”. Since the 6.4th position doesn’t actually
make sense, we round UP to the 7th position. 7 is called the locator. What we mean is that “at least
29% of the data set is below the 7th position”. There is an 8 in the 7th position, so 8 is the test score
corresponding to the 29th percentile.
Note that this rule is a little bit fishy! If you compute the percentile for a score of 8, you actually get
4/22 = 0.182 which rounds to 18th percentile!
4. Find the test score for the 50th percentile.
Answer: 50% of the data set is exactly 11 data points. We want the test score that has at least 50% of
the data below it, and the rule (in our book) is that you average the scores from the 11th and 12th
positions (this is different from the rule I gave in class!). The 11th position is 18 and the 12th position is
22, so the score for the 50th percentile is actually 20.
To go from percentile to a data value, just remember: if the location is between two whole numbers,
move up to the next highest location. If the location is exactly a whole number, average the data points
from that position and the next highest position.