Question 1

How do I convert a score into a percentile?

Accepted Answer

Subtract the mean, divide by the standard deviation, and take the area under the normal curve to the left of that z. With a mean of 65, a deviation of 12 and a score of 78, z is 1.083 and the percentile is 86.

Question 2

What is a z-score?

Accepted Answer

How many standard deviations a score sits from the mean. A z of 1 means one deviation above and corresponds to the 84.13th percentile; a z of −1 to the 15.87th.

Question 3

What is the difference between a percentile and a percentage?

Accepted Answer

A percentage is the share of marks you earned; a percentile is the share of candidates you beat. Eighty percent correct could be the 30th percentile or the 99th, depending entirely on how everyone else did.

Question 4

Where do I find the standard deviation?

Accepted Answer

In the examiner's statistics, where they are published. Failing that, calculate it from the scores themselves if you have them. A guess from the range — say a quarter of the gap between the highest and lowest score — is very rough: how well it works depends on the group size and the spread of marks.

Question 5

Why is the rank only approximate?

Accepted Answer

Because it is derived from a share rather than a list of results. The calculator takes the share above you out of the cohort size; tied scores share places, so the exact position cannot be recovered.

Question 6

When should I not trust the result?

Accepted Answer

When the distribution is not normal — on an easy test with a ceiling, say, or a very hard one. The error can then go either way, and without the real distribution you cannot tell which; a published distribution of scores always beats the estimate.

Question 7

What is a percentile good for?

Accepted Answer

Comparing results across different tests. A score of 78 means nothing on its own, but the 86th percentile is comparable with the 86th percentile anywhere — which is the principle the withdrawn ECTS grading scale was built on.

Score	z-score	Percentile	Above you, %	Below you, %
41	−2	2.28	97.7	2.3
53	−1	15.87	84.1	15.9
65	0	50	50	50
77	+1	84.13	15.9	84.1
78	+1.083	86.07	13.9	86.1
89	+2	97.72	2.3	97.7

Test Score Percentile Calculator

Result

Related tools

Grade Scale Converter

Exam Score Needed Calculator

GPA Calculator

Useful links