How to Calculate Percentiles in Statistics

When we speak about percentiles, we are talking about the ranking that someone has based on certain scores or percentages. It is, simply put, your relative standing in a norm group.

For example, if you score in the 98th percentile, this means that you did as well or better than 98 percent of the people who took a particular test. This is an excellent score. If you scored in the 50th percentile, it means you are in the middle of the distribution, and you only did as well or better than 50 percent of the people who took the test.

By figuring your percentile rank, you can figure out where a statistic stands relative to others. This is an important aspect of reporting statistical data.

MicroStockHub / Getty Images

When we are dealing with percentiles, we are dealing with two separate parts of data. The first set of data is the 100th percentile, while the other (missing data that we are trying to solve for) is equivalent to 100-k.

The answer to this algebraic formula is the percentile we are solving for that is unknown. Once we determine this, we will know what percentile a number falls into with the distribution. This is because [100-k]=is the total amount of data being considered in a particular situation.

ismagilov / Getty Images

The median is the average or "midpoint" where the data falls in a distribution. Since 100% is the top of the distribution, then 50% would be absolute average. This is confusing to some students when taking a test. They get back their scores that are around 50%, and they think that they failed the test, when really they scored in the average range.

It is important to understand percentiles to correctly interpret test scores or any other form of data that involves percentages and distributions. Always think of 50 as the midpoint when it comes to a standard distribution, and anything above that is "above average."

leventince / Getty Images

To get started in calculating percentiles, you first need to take all of your raw data and order it from smallest to largest. By doing this, you are creating a logical distribution of numbers in ascending order. This allows you to visually see the median, as well as to manage the raw data scientifically.

YakobchukOlena / Getty Images

You must apply an algebraic formula her to figure out the total number of values in the calculation. The "k" here represents the percentile that you are solving for. For example, if you are trying to find who is in the 90th percentile, then you would multiply 90% x 25 in a distribution of 25 numbers. Always multiply the number of values times the percentile you are solving for to render the solution.

The answer to this equation will give you the index. You will need this for the next step.

Sidekick / Getty Images

If the answer to the previous problem was not a whole number, you need to round up to the nearest whole number to proceed. To find the nearest whole number, you must count the values of your data from left to right until you find the nearest whole number.

The corresponding value is the kth percentile that you are solving for.

PeopleImages / Getty Images

If your number is already a whole number, you can proceed with figuring the percentile. It will be the average of the corresponding value in your data set and the amount that immediately follows it.

Remember to find the index first, then use the above procedures to find the nearest whole number. That will be your percentile that you are solving for.

Like any mathematical procedure, it just takes a little practice to get it right, and you'll be calculating percentiles easily in no time.

SARINYAPINNGAM / Getty Images

To figure percentiles, you should keep in mind the percentile that you are solving for. This will give you the corresponding numbers in your range that correspond to certain means or averages. For example, if your solution renders a 73 score when you are solving for the 50th percentile, then this means that 73 was the average score that was made on this test or statistical study.

You can then take this data a step further and extrapolate to say that anything above the 50th percentile (in the 73 score range) was above average and anything below it was below average.

Remember that, in statistics, it's easy to figure out the math. But it's a bit harder to draw conclusions that are too general. One of the most important aspects of statistical research is in reporting the results. Be specific and succinct when doing this and avoid making too many generalizations.

This will make your research more valid and avoid getting into areas that you cannot support with your research. In statistical analysis, the goal should always be to have your data back up your research without overgeneralizing to areas the data doesn't support.

SARINYAPINNGAM / Getty Images

Once you figure one percentile, you can figure others using the same method you have applied for the previous one. Then you can report various scores or results in magazines, online publications, or white papers to your target audience.

The reporting of statistics is just as critical as the calculation process, so make sure you take care to do it correctly.

PeopleImages / Getty Images