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Author: Jonathan Osters

Calculate the percentile of a specific value from a data set.

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Source: Tables and charts created by the author; Standardized Test, Creative Commons:

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In this tutorial, you're going to learn about percentiles. You probably heard of percentiles before, or percentile rank. Percentile is the same as a relative cumulative frequency. And that means the percent of data points in, or below, some other bin of data. You may have seen percentiles reporting standardized test scores. If you were in the 95th percentile on a standardized test, that doesn't mean you scored a 95 on the test. That means that your score was at least as good as 95% of test takers.

So, let's look at an example. When you have large data sets, often you see it in a frequency table right off the bat. So what we can do is we can look at relative frequency instead. Now these are rounded values, just be aware. So we can also look at relative cumulative frequencies. That means the percent of data points that are in or below this bin. Now notice, this says 3% and this says 6%. But cumulatively, the amount is 10%? Where did that come from? You'd think it would be 3 and 6% put together to make 9. But the combined amount of 32 is actually closer to 10% that it is to 9%.

So what we did was divided the cumulative amount, which was 32, by 333 and got a number close to 10%. By the time we get to 65 inches, we will have accounted for all of the sixth graders in the data set.

All right, so we can continue to use this chart to answer the questions. So a student with a height of 62 inches would fall in which percentile? That means that a student who's a height of 62 is at or above the height for what percent of people? Well, you should have recognized that it's the 85th percentile. That means that a 62 inch student is at least as tall as 85% of his fellow classmates.

What about a student in the 94th percentile? How tall is that person? So what's the height of someone who is at least as tall as 94% of classmates? Well that's someone who's 63 inches tall.

And then where's the median height for sixth graders? This one's a little tricky. By the time you finish counting up all of the 59 inch students, you still haven't accounted for half the grade yet. But by the time you're done counting all the 60 inch students, you've accounted for 62% of the grade. That means that somewhere within that 60 inch range was the median height of 60 inches. Half the students are at or above 60 inches. And half the students are at or below 60 inches.

And so to recap. Percentiles are the same as relative cumulative frequency. And so, they can be used to compare where individuals rank relative to their group. Percentiles measure what percent of data points fall in a bin or below that. bin. So we're going to use the word percentile to describe that.

Good luck, and we'll see you next time.

Terms to Know

Relative Cumulative Frequency; the amount of data points at or below a particular value.