Percentiles - Introductory Statistics

This video covers the meaning of percentiles in introductory statistics. A percentile score indicates the percentage of values below a certain point.

Percentiles
Quartiles
Deciles
Median

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Video Transcript:
In this video we'll take a look at percentiles. Percentiles indicate the location of a score in a distribution and percentiles range from 1 to 99. Let's go ahead and take a look at an example. So suppose that John scored at the 59th percentile on an exam. If John scored at the 59th percentile this means that he scored better than approximately fifty-nine percent of the people on the exam. As a second example suppose that Margarita scored at the 85th percentile on a standardized test such as the SAT. As she scored the 85th percentile this indicates that Margarita scored better than 85% of the people on the exam. So percentiles indicate the percentage of scores that a given value is higher or greater than. So for example a person who scored at the 3rd percentile they scored better than three percent of the examinees and a person who scored at the 40th percentile scored better than forty percent of the examinees. Percentiles can also be thought of as dividing scores into two separate groups. So for our example with the 3rd percentile, that indicates once again that 3% scored below that point and if 3% score below that point, then everyone else, or the remaining 97% scored above that point. And for the 40th percentile that indicates once again that 40% of the people scored below that point which means that the remaining 60% of people scored above that point. So percentiles really divide the distribution into two separate parts. Certain percentiles go by other names as well which you should be aware of. For example, the 25th percentile that indicates once again that the person who scored the 25th percentile they scored better than 25% of the examinees. Now that exact percentile is also known as Q1 or the first quartile. The 50th percentile indicates that the person who scored there, scored better than 50% of the examinees. Now the 50th percentile is known as Q2 or the second quartile. And the 50th percentile or Q2 is also equal to the median as it splits the distribution exactly in half. So if someone reports the 50th percentile or if they report the second quartile those two are the same thing and that's also equal to the median. The 75th percentile indicates that the person who scored there did better than 75% of the examinees and this is known as Q3 or the third quartile. So in summary, Q1 is the 25th percentile also known as the first quartile, Q2 is the 50th percentile and known as the second quartile and this is also equal to the median and then finally Q3 or the 3rd quartile is equal to the 75th percentile. Finally there are also deciles which are described in many statistics textbooks. And D1 is the first decile. Now the first decile's equal to the 10th percentile. The second decile is known by D2 and it's equal to the 20th percentile. D3 is the third decile or the 30th percentile and so on until we get to D9 which is the ninth decile or the 90th percentile. So the first decile or the 10th percentile this separates the bottom 10% of examinees from the top 90%. The second decile separates the bottom 20% from the top 80% and so on. The smallest percentile is the first percentile and separates the bottom 1% of scores from the top 99%. And the largest percentile is the 99th percentile and the 99th percentile separates the top 1% of the scores from the bottom 99%. Now recall that the 99th percentile would indicate that 99% of the people scored below that point. So that's why it separates the top 1% from the bottom 99%. And as a note it's important to know that there are no such things as the zero or one hundred percentiles. So as I said at the beginning of this presentation percentiles range from 1 to 99. And one other note, percentiles often cause confusion to people who might receive like their son or their daughter's scores on a standardized test in school. So on a score report a person will get a raw score and then they'll get a percentile and it'll say something like 65 and when they see the 65 many people mistakenly think that that means that their son or daughter scored a 65% on the test but that's just a percentile. So it indicates that they scored better than 65% of their peers on the exam so indicates they did pretty well and it has nothing to do with the percentage of questions that they answered correctly. So on those score reports those are percentiles that are reported and it says that typically it has a column labeled percentile or something to that effect and it will report the exact percentile.