Statistics Definitions > Percentiles, Percentile Rank & Percentile Range

Contents:

Percentiles

Percentile Rank

How to Find a Percentile

Percentile Range

  1. What are Percentiles?

“Percentile” is in ordinary use, however, there is no all-inclusive definition for it. The most widely recognized meaning of a percentile is where a specific level of scores fall beneath that number. You may realize that you scored 67 out of 90 on a test. In any case, that figure has no genuine importance except if you recognize what percentile you fall into. On the off chance that you realize that your score is in the 90th percentile, that implies you scored superior to anything 90% of individuals who stepped through the examination. 

Percentiles are generally used to report scores in tests, similar to the SAT, GRE, and LSAT. for instance, the 70th percentile on the 2013 GRE was 156. That implies on the off chance that you scored 156 on the test, your score was superior to 70 percent of test-takers. 

The 25th percentile is additionally called the primary quartile. 

The 50th percentile is commonly the middle (in case you’re utilizing the third definition—see underneath). 

The 75th percentile is likewise called the third quartile. 

The contrast between the third and first quartiles is the interquartile run. 

2. Percentile Rank 

“Percentile” is utilized casually in the above definition. In like manner use, the percentile typically demonstrates that a specific rate falls underneath that percentile. For instance, in the event that you score in the 25th percentile, at that point 25% of test-takers are underneath your score. The “25” is known as the percentile rank. In measurements, it can get somewhat more muddled as there are really three meanings of “percentile.” Here are the initial two (see underneath for definition 3), in light of a subjective “25th percentile”: 

Definition 1: The nth percentile is the most minimal score that is more prominent than a specific rate (“n”) of the scores. In this model, our n is 25, so we’re searching for the most minimal score that is more prominent than 25%. 

Definition 2: The nth percentile is the littlest score that is more noteworthy than or equivalent to a specific level of the scores. To rethink this present, it’s the level of information that falls at or beneath a specific perception. This is the definition utilized in AP insights. In this model, the 25th percentile is the score that is more noteworthy or equivalent to 25% of the scores. 

They may appear to be fundamentally the same as, yet they can prompt huge contrasts in results, despite the fact that they are both the 25th percentile rank. Take the accompanying rundown of test scores, requested by rank:

SCORERANK
301
332
433
534
565
676
687
728

3. The most effective method to Discover a Percentile 

Test question: Discover where the 25th percentile is in the above rundown. 

Stage 1: Ascertain what rank is at the 25th percentile. Utilize the accompanying recipe: 

Rank = Percentile/100 * (number of things + 1) 

Rank = 25/100 * (8 + 1) = 0.25 * 9 = 2.25. 

A position of 2.25 is at the 25th percentile. Be that as it may, there is definitely not a position of 2.25 (at any point known about a secondary school rank of 2.25? I haven’t!), so you should either gather together or round down. As 2.25 is nearer to 2 than 3, I will adjust down to a position of 2. 

Stage 2: Pick either definition 1 or 2: 

Definition 1: The most minimal score is more noteworthy than 25% of the scores. That equivalents a score of 43 on this rundown (a position of 3). 

Definition 2: The littlest score that is more noteworthy than or equivalent to 25% of the scores. That equivalents a score of 33 on this rundown (a position of 2). 

Contingent upon which definition you use, the 25th percentile could be accounted for at 33 or 43! A third definition endeavors to address this conceivable error: 

Definition 3: A weighted mean of the percentiles from the initial two definitions. 

In the above model, here are the means by which the percentile would be worked out utilizing the weighted mean: 

Duplicate the contrast between the scores by 0.25 (the portion of the rank we determined previously). The scores were 43 and 33, giving us a distinction of 10: 

(0.25)(43 – 33) = 2.5 

Add the outcome to the lower score. 2.5 + 33 = 35.5 

For this situation, the 25th percentile score is 35.5, which bodes well as it’s in 43 and 33. 

By and large, the percentile is normally definition #1. Nonetheless, it is savvy to twofold watch that any measurements about percentiles are made utilizing that first definition. 

4. Percentile Range 

A percentile range is a contrast between two determined percentiles. these could hypothetically be any two percentiles, yet the 10-90 percentile range is the most well-known. To locate the 10-90 percentile run: 

Ascertain the tenth percentile utilizing the above advances. 

Compute the 90th percentile utilizing the above advances. 

Subtract Stage 1 (the tenth percentile) from Stage 2 (the 90th percentile).