## Percentiles - Introductory Statistics

In this video we'll, take a look at percentiles indicate the location of a score and 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 at 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 third percentile, they scored better than three percent of the examinees and a person who scored at the 40th percentile scored better than 40 percent of the examinees percentiles can also be thought of as dividing scores into two separate groups.

So. For example, with the third percentile that indicates once again, the three percent scored below that point and a three percent scored below that point, then everyone else or the remaining 97% scored above that point. And for the fortieth 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 twenty-fifth percentile that indicates once again that the person who scored the twenty-fifth percentile, they scored better than 25 percent 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 fiftieth 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 laughs.

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 therapy did better than 75% of the examinees. And this is known as q3 or the third quartile.

So in summary, q1 is the twenty-fifth percentile Allison own is 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 third quartile is equal to the 75th percentile.

Finally, there are also decides, which are described in many statistics textbooks and D 1 is the first decide. Now, the first decide is equal to the 10th percentile. The second decide is known by d 2, and it's equal to the 20th percentile D 3 is the third decide or the 30th percentile. And so on, until we get to D 9, which is the ninth decide or the 90th percentile.

So the first decide or the 10th percentile. This separates the bottom 10% of examinees from the top 90%, the 2nd decide separates the bottom 20% from the top 80%. And so on. The smallest percentile is the first percentile, and it separates the bottom 1% of scores from the top 99. And the largest percentile is a 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 100% titles. So as I had said at the beginning of this presentation, percentiles range from 1 to 99 and one other note, Gentiles often cause confusion to people who might receive like their son or their daughters scores on a standardized test in school. So on a score report, a person will get a raw score, and it'll get a percentile, and it'll say something like 65.

And when they see the 65 many people will. 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 percent of their peers on the exam. So it indicates that 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.

So as another example, the 80th percentile would indicate pretty good performance as it means that the person scored better than 80 percent of their peers with only 20% of the people doing better than them. Okay? That's it. This concludes the video on percentiles. Thanks for watching.

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