# What Is Percentile Rank? How Is It Different From Percentage?

## Related, but different concepts

Quantitative Specialists define percentile rank as indicating the "location of a score in a distribution," with percentiles ranging from 1 to 99. Percentiles show "the percentage of scores that a given value is higher or greater than."

For example, a test score in the 5th percentile scored better than 5 percent, and worse than 95 percent, of others. In order to calculate a score, or another piece of data's percentile rank, it is necessary to know its position within a distribution of other scores or data. A lone score or piece of data has no percentile rank.

Percentile rank also uses the concept of percentage, which is the notion of rate per 100. For example. a student who correctly gave 90 answers on a test with 120 questions, scored 75 percent, or (90/120)*100 = 75 percent. This is equivalent to saying that the student answered questions correctly at a rate of 75 per 100. On it's own, there is no way to consider this student's percentile rank, unless it is analysed in a distribution of test scores of students from the entire class, school, district, or even state or country.

Business publication *Investor's Business Daily* makes an innovative use of percentile rank with its Relative Strength rating, which is really just the percentile ranking of a given stock, based on its 12-month performance, which is calculated as a percent.

## Percentile ranks and Normal curve equivalents

## Percentile ranking used in many fields

*IBD* calculates how much the shares of companies have gained, or lost, over the past 12 months and then ranks the shares with a percentile ranking. For example, the stock of a company with an IBD Relative Strength rating of 90 has outperformed the stock of 90 percent of all other companies over the past year.

As there are thousands of companies listed on the New York Stock Exchange and Nasdaq, there are equal numbered groups of companies within each percentile rank. The very best performing companies in the stock market belong to the 99th percentile. The next best group is the 98th percentile, all the way down to the 1st percentile, the worst performing group.

In December 2016, *IBD* reported on the Relative Strength, or percentile, ranking of Nvidia Corporation, which was 99. At the time, NVDA stock had returned close to 172 percent over the preceding 12 months: a very strong performance.

The amount NVDA stock returned is a percentage and is calculated as follows: ((price at end of period - price at beginning of period) / price at beginning of period)*100.

## Stocks can be ranked by performance percentile

With the Nvidia example. the stock closed at $32.12 on December 2, 2015 and at a $87.44 on December 1, 2016. Using the formula from above:

(($87.44 - $32.12)/$32.12)*100

=($55.32/$32.12)*100

=1.7222*100

=172.2 percent

From this, the conclusion can be drawn that, because Nvidia stock is in the 99th percentile, and it has returned 172 percent, most other stocks have returned less than 172 percent. On a distribution of returns for the entire market, Nvidia stock might even be viewed as an outlier.

The U.S. Department of Commerce defines an outlier as "an observation that lies an abnormal distance from other values in a random sample from a population." The department continues, "Outliers should be investigated carefully. Often they contain valuable information about the process under investigation or the data gathering and recording process. Before considering the possible elimination of these points from the data, one should try to understand why they appeared and whether it is likely similar values will continue to appear. Of course, outliers are often bad data points."

With many types of data, including test scores and stock performance, individual data points tend to be more relatively tightly clustered in mid-range percentile groups, and more relatively widely spaced in low- and high-numbered, outlying, groups.

**© 2017 Stephen Sinclair**

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