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