# How To Calculate Percentiles (With Examples)

Jun. 27, 2020
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Whether you enjoyed math classes or not, your math teachers weren’t lying when they said you’d use the things you were learning in the future.

Even though most people don’t use the complex formulas and algebra equations they learned in high school in their daily lives, some smaller facets of math come in handy, especially in the professional world.

Many of these come from your statistics classes, and one of the most prominent examples is the percentile.

## What Is a Percentile?

A percentile is a statistic that reports relative standing. In other words, it shows you how a piece of data relates to the rest of the group of data.

Percentiles are regularly used in standardized test score reports because they show the test takers how their score compares to others’ scores.

If you get your test back and see that you’re in the 85th percentile, that means that your score is better than 85% of the rest of the test takers.

This is important because if you got a 90% on a test, you know that you did pretty well, but you don’t know if that was better or worse than the rest of the class. If you know what percentile you’re in, though, you’ll know how your test score relates to your classmates’.

## Percentiles vs. Percentages

Percentiles and percentages are easily confused. As stated before, a percentile is a statistic that shows where one data point stands in relation to the other data points.

A percentage denotes a part of a whole and is what we usually use when we talk about how we scored on a test or when we talk about a percentage change, like an increase in sales.

Percentiles are helpful for more than just seeing how good you are at taking tests. They’re also useful when you’re organizing research results, interpreting data, or gauging performance standards.

1. In organizing research results. Say you’re looking at a job opening at a specific company that you’d want to work for, but you don’t know how the salary you’d make there compares to what you’d make at other organizations in the area.

For example, let’s say a large company in La Crosse, Wisconsin gives you a job offer. If you find that the position pays \$75,000 a year, that might sound low to you if you’re making \$90,000 a year at a similar job in New York.

Upon further research, though, you might find that a \$75,000 salary would put you into the 90th percentile of people in La Crosse. This means that you’d actually be making pretty good money compared to the rest of the population and that the decrease in salary is only because the cost of living in La Crosse is less than it is in New York.

Percentiles can give you a more complete and accurate picture of the results of your research.

Or, say you want to move to a big city, and you want to research the jobs you might apply for there. You do a quick Google for “worst jobs in Chicago,” “best jobs in Chicago,” and “best jobs in Atlanta,” and you quickly find the information you’re looking for.

The results listed in articles like these usually involve percentiles, as they can help statisticians and authors quickly organize their data into the “top ten” lists you read on virtually any subject.

This is a more simplified application of percentiles, but it’s used all the same.

2. In interpreting data. If you work in a job that requires handling a lot of data, percentiles can help you see the less obvious stories the data is telling you.

For example, if you are a realtor, you might have a list of statistics of the different neighborhoods in your area and their rankings based on those statistics.

Your first instinct is probably to look at that data to see which areas are the best and worst. This is a great place to start and can be helpful, but it isn’t all that data can do for you.

Knowing the best neighborhood to live in is good to know so that you can direct your clients there if they can afford the housing, but if they can’t, what do you do?

You know they wouldn’t appreciate you directing them to the areas with the highest crime rates and worst schools, but they also don’t want to be looking at homes they can’t afford.

Instead, you might look at your data again and pay attention to the neighborhoods ranked between the 75th and 85th percentiles. These aren’t as expensive as those in the 90th percentile and above, but they are better than most neighborhoods in the area.

This can help you narrow down your list pretty quickly and allow you to explain the benefits of these locations to your clients. Telling them that their new neighborhood is ranked higher than 75% of the others in the area is more appealing than telling them, “it isn’t the best one out there, but it isn’t the worst, either.”

If you want another example, here is an article listing some of the most above-average cities in America using this exact method.

If you manage sales representatives, for example, you need to know how much they’re selling in order to manage them effectively.

You can use percentiles to better understand how your employees are performing in relation to one another and how they’re doing compared to different branches of the company or salespeople in general.

This method also allows you to create very clear performance-based incentive programs. For example, you can say that those in the top 90th percentile at the end of the month get a grand prize, while those in the 85th to 89th get a different award.

Using percentiles makes it easier to gauge how your employees are performing and communicate your standards and expectations to them.

## Other Percentile Terms

Many terms you might be familiar with from math class relate to percentiles. For example:

• Median. The median is the middle number in a data set. Expressed another way, that’s the 50th percentile. Knowing the median is more useful than knowing the average in many cases.

• Quartile. Because percentiles span a 0-100 range, they can be divided into quarters at every 25th percentile. The first quartile extends from 0-25, the second from 25-50, and so on. Quartiles are often represented as simply a Q and a number, like Q1. Q1 is also referred to as the lower quartile, while Q3 is known as the upper quartile.

• Percentile range. If you’re interested in finding the range between two percentiles, you’ll want to find the percentile range. For example, you might be curious what the range of values between the 20th and 40th percentile is.

• Interquartile range. The interquartile range is a specific percentile range between Q1 and Q3. This shows the middle half of the data, with a quarter below and a quarter above. A bigger IQR means your values are more spread out.

## How to Calculate a Percentile

Now that you know a little bit about why percentiles are useful, you need to know how to calculate them. There are a few methods for how to do this, but here are the steps to one of the most common ones:

1. Arrange all of your data in order from smallest to largest. Whether it’s test scores, salaries, or city rankings, arrange your findings from the worst to the best or the lowest to the highest.

2. Decide what percentile you’re trying to calculate. Whether you’re trying to find the 80th percentile or the 10th, we’ll refer to this number from now on as k.

3. Find n. Now you need to determine the number of data points you have, which we’ll refer to as n. For instance, if you collected 50 test scores, n would be 50.

4. Multiply k percent by n. This means if you’re trying to find the 80th percentile and you have 50 different test scores, you’re going to be calculating 0.8 times 50. Don’t forget that k is a percentage. That means you can’t multiply 80 times 50 and expect it to work.

The result of this calculation is known as the index, and in this example, the index is 40.

5. Round the index, if you need to. If your index isn’t a pretty whole number like 40 and is instead a decimal like 39.7, you’ll need to round it either up or down.

6. Count the values in your dataset. Once your index is no longer a decimal, go back to your dataset and count the values from left to right (lowest to highest) until you reach the number that is your index.

In this case, you’d count test scores from left to right until you hit 40 test scores since that was your index. Once you hit the 40th test score from the bottom, you’ve found the 80th percentile.

## Example of Calculating a Percentile

To illustrate these steps, here’s an example of what finding the 90th percentile would look like with 50 test scores:

Here are the example scores already arranged from lowest to highest:

54, 57, 61, 62, 64, 65, 68, 69, 70, 70, 73, 75, 76, 78, 80, 81, 81, 81, 82, 82, 82, 84, 84, 85, 85, 86, 86, 87, 87, 88, 88, 89, 89, 90, 90, 90, 91, 91, 92, 92, 93, 93, 94, 94, 95, 97, 98, 99, 99, 100

Next, you’ll find k, which is 90 in this case, since you want to find the 90th percentile.

Then, you find n, which equals 50, since you have 50 test scores.

Now you get to do some math and find your index by multiplying the percentage of k by n, which would be 0.90 x 50 = 45.

Since our index is 45, we now count up to the 45th test score, which is 95. So, if you got a 95 on your test, you’re in the 90th percentile.

## Example of Calculating a Percentile Range

If you understand the concepts from above, finding a percentile range is fairly straightforward. Let’s say you want to find the 30-60 percentile range from the same data set as above:

Start by finding the 30th percentile: .3 x 50 = 15
Then find the 60th percentile: .6 x 50 = 30
Now find the 15th and 30th numbers in the set (80 and 88)
Subtract the larger number from the smaller (88-80=8)

The percentile range between the 30th and 60th percentiles is 8.

## Final Thoughts

Between standard deviations, normal distributions, and percentiles, several lessons from high school math classes are relevant in a number of fields. Data is everywhere, and understanding how to break it down and analyze it is a valued skill in any industry.

Percentiles offer a different perspective on a data set that can provide insights beyond the story that the numbers tell initially.

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Abby is a writer who is passionate about the power of story. Whether it’s communicating complicated topics in a clear way or helping readers connect with another person or place from the comfort of their couch. Abby attended Oral Roberts University in Tulsa, Oklahoma, where she earned a degree in writing with concentrations in journalism and business.

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