Welcome to a lesson
on quartiles and percentiles.
Percentiles are used in statistics to indicate a value
at or below which a certain percent of data values fall.
For example, quartile one is the 25th percentile,
because 25% of the data values are at or below Q1.
This also means that 75% of the data values
are at or above the 25th percentile.
Looking at the graph above, Q1 is the 25th percentile,
because 25% of data values, these data values here,
are at or below Q1,
which also means that 75% of the data values,
these data values here, are at or above the 25th percentile.
The median, or Q2, is the 50th percentile,
because 50% of the data values are at or below the median.
This also means that 50% of the data values
are at or above the 50th percentile.
So looking back at the graph,
again the median is the 50th percentile,
because 50% of the data values, these data values here,
are at or below the median,
which also indicates that 50% of the data values,
these values here, are at or above the 50th quartile.
And then quartile three, or Q3, is the 75th percentile,
because 75% of the data values are at or below Q3,
which also means 25% of the data values
are at or above the 75th percentile.
Going back to the graph one last time,
Q3 is the 75th percentile, because 75% of the data values,
these data values here, or at or below Q3,
which also indicates 25% of the data values,
these data values here, are at or above the 75th percentile.
Now let's look at some questions
not involving the quartiles.
These first two statements involve the 28th percentile.
Looking at the graph above, the 28th percentile
would be the data value approximately here,
where 28% of the data values, these data values here,
are at or below the 28th percentile,
which also means that 100% minus 28%,
or 72% of the data values,
are at or above the 28th percentile.
The first question is what percent of data values
in a data set lie at or below the 28th percentile,
which would be 28%.
And the second question is what percent of data values
in a data set lie at or above the 28th percentile,
which is 72%.
The next two questions involve the 70th percentile.
So going back to the graph, the 70th percentile
would be the data value approximately here,
where 70% of the data values, these data values here,
are at or below the 70th percentile,
which means 30% of the data values
are at or above the 70th percentile.
So reading carefully, we're asked to find the percent
of data values in a data set that lie
at or above the 70th percentile,
which are these data values here, which is 30%.
And now we're asked to find the percent
of data values in a data set that lie
at or below the 70th percentile, which is 70%.
Next, if a sample consists of 800 test scores,
how many of them would be at or below the 32nd percentile?
The 32nd percentile is approximately here,
where 32% of the data values, these data values here,
are at or below the 32nd percentile, which means 68%
of the data values are at or above the 32nd percentile.
So if the sample consists of 800 tests,
how many of them would be at or below the 32nd percentile?
That would be 32% of 800,
which is equal to 0.32 times 800,
which is 256.
So if the sample consists of 800 test scores,
256 of them would be at or below the 32nd percentile.
And for the last question,
if a sample consists of 800 tests,
how many of the tests would be
at or above the 56th percentile?
The 56th percentile would be approximately here,
where 56% of the data values, these data values here,
or at or below the 56th percentile,
which means 44% of the data values
are at or above the 56th percentile.
And the question is asking how many test scores
would be at or above the 56th percentile,
which is going to be 44% of the 800 tests.
So 44% of 800 is equal to 0.44 times 800,
which is 352.
If a sample consists of 800 test scores,
352 of them would be at or above the 56th percentile.
I hope you found this helpful.