This video will show how to determine
whether a set of data has any outliers.
An outlier is a data value
that is significantly greater than or less than
the other data values.
Before we determine any outliers, though,
it's important to be aware of the methods used
to determine quartile one, quartile three, and the outliers.
In this video, we will use the Moore and McCabe method
to determine the quartiles where according to this method,
quartile one if the median of the lower half
of the data, not including the median,
and quartile three is the median
of the upper half of the data,
again, not including the median.
And then we use Tukey's method to determine the outliers
where according to this method, outliers are values
that are less than quartile one minus 1.5
times the inner quartile range
or greater than quartile three plus 1.5
times the inner quartile range.
And the inner quartile range is Q three minus Q one.
So going back to our example,
the first step is to order the data from least to greatest,
which I've already done here to save time.
There are a total of 14 data values,
and therefore, we say n is equal to 14.
Before we find quartile one and quartiule three,
we have to find the median.
The median is the data value in the middle,
but here, because we have an even number data values,
there are two middle values,
and therefore, we'll have to find the mean
of the two middle values.
Notice if we drew a line segment here
between the 28 and 30, we have seven values to the left
and seven values to the right,
and therefore, we have two middle values of 28 and 30.
The median is the mean of 28 and 30.
Well, the quantity 28 plus 30
divided by two is equal to 29.
The median is 29.
And now we need to find quartile one and quartile three.
Quartile one is the median of the data values on the left,
and because we have seven data values on the left,
which is odd, quartile one is a data value in the list.
It is the 24.
Notice how there are three values to the left
and right of 24 in the lower half of the data.
So this is Q1.
Now looking at the upper half of the data,
there are seven data values,
and therefore, 40 is the median of the upper half.
40 is quartile three.
And now to determine if we have any outliers,
we need to determine the values of Q one minus 1.5
times the inner quartile range,
as well as Q three plus 1.5 times the inner quartile range
where the inner quartile range is Q three minus Q one
or in our case 40 minus 24,
which is equal to 16.
So Q one minus 1.5 times the inner quartile range
is 24 minus 1.5 times 16,
and Q three plus 1.5 times the inner quartile range is 40
plus 1.5 times 16.
And now let's compute these two values,
which are zero and 64,
which means if any data values are less than zero,
it would be considered an outlier,
or if there are any values greater than 64,
it would be considered an outlier.
But we don't any data values less than zero,
but we have two values greater than 64,
and therefore, we have two outlier.
The outliers are 65 and 77.
65 and 77 are considered significantly greater than
the other data values.
I hope you found this helpful.