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# Percentiles

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Author: Sophia Tutorial
##### Description:

This lesson will explain percentiles.

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Tutorial

This tutorial will cover percentiles. You’ll learn about:

1. Percentiles

## 1. Percentiles

You probably heard of percentiles before, or percentile rank.

Percentile

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

Percentile is the same as a relative cumulative frequency. That means the percent of data points in, or below, some other bin of data.

IN CONTEXT

You may have seen percentiles reporting standardized test scores. If you were in the 95th percentile on a standardized test, it doesn't mean you scored a 95 on the test. It means that your score was at least as good as 95% of test takers.

Often, large data sets are given in frequency tables, frequently with rounded values.

Here is a table showing heights (in inches) of 333 sixth-grade students, along with the frequency, relative frequency, and relative cumulative frequencies.

How do we read this? Notice the first two rows have a relative frequency of 3% and 6%, respectively. But cumulatively, the amount is 10%, as you see in the 2nd row of the Rel. Cum. Freq. column. Where did the 10 come from? You'd think it would be 3% and 6% put together to make 9%, but the combined amount of 32 (which is the frequency amounts from the first two rows) is actually closer to 10% that it is to 9%. You know this because you can divide the cumulative amount, which is 32, by the total amount of students, 333, and you'll get 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.

Now you can use this chart to answer many questions:

1. Which percentile will a student with a height of 62 inches fall into? A student who is 62 inches tall is at or above the height for what percent of people? You can see, from this chart, that 62 inches falls in the 85th percentile. That means that a 62 inch student is at least as tall as 85% of his/her fellow classmates.
2. What about a student in the 94th percentile? How tall is that person? 63 inches tall.

Where's the median height for sixth graders?

This question is 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 is 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.

Percentiles are the same as relative cumulative frequency. 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.

Thank you and good luck!

Source: THIS WORK IS ADAPTED FROM SOPHIA AUTHOR JONATHAN OSTERS

Terms to Know
Percentile

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