>> In this video, we're going to talk about outliers.
Definition, an outlier are data, value or values that lie outside
of the overall pattern of the distribution.
What does this mean?
So, think about distribution as a picture of your data
and let's say you're collecting data through some type
of dot plot and you notice some points that don't conform
to the overall pattern right, to the overall picture,
to the overall distribution.
And you might think hey, these could be outliers.
By looking at it, it does look like they don't conform
to the overall pattern, but there's a math way to figure
out if these are outliers.
What we're going to do is we're going
to calculate something called the upper bound value.
And when we do this any value
above the upper bound value we're going
to consider that an outlier.
On the other side the same thing,
we're going to calculate something called the lower
bound value.
Anything below that we're going
to consider any data points to be outliers.
Let's do an example to figure out how to do this.
So, let's say I have these data points
and I also have the five number summary, you're always going
to need the five number summary on these data points.
If you don't know how to do that not a problem I've got a video
for you that you can watch.
Okay the first thing we need to do is to calculate IQR.
Again, we're trying to figure out if any
of my data points are outliers.
So, I need to calculate this IQR which is the interquartile range
and that's going to equal to Q3 take away Q1
and I have those values right there.
So, I'm going to write them down 73 take away 65
and that's going to equal to 8.
Okay not a problem I'm going to need that value.
Let's calculate the upper bound value
that has a formula Q3 plus 1.5 times IQR,
1.5 is always going to be there.
IQR you have to calculate which we already did.
Q3 we have that value with our five number summary.
Okay, let's plug it in, Q3 is 73 plus 1.5 times 8
and 1.5 times 8 I believe is 12 and so 73 plus 12 equals 85.
Note that the upper bound value the formula has a plus sign Q3
plus 1.5 okay.
So, 73 plus 12 gives you 85.
All right, let's move on.
Let's look at the lower bound value
and we'll look at the formula first.
That's going to be Q1 take away 1.5 times IQR.
Notice that this one has a subtraction.
Q1 we already have in our five number summary,
1.5 that's automatic, IQR we calculated already,
let's plug it in, 65 take away 1.5 times 8 that's going
to be what, that's right 65 take away 12 which equals 53.
So again, upper bound value formula has a plus sign,
lower bound value has a takeaway sign.
Okay, so any data values not falling between 53
through 85 are suspected to be outliers.
So, between 53 through 85 any data points that go
in there we don't consider them outliers.
Any data values that go outside below 53
or above 85 are considered outliers.
In this dataset do you consider any points to be outliers?
That's right 90, 90 is a possible outlier.
So, what we do is we can draw a box plot to show
that there's an outlier.
What we want to do is we want to draw a number line
and the way I do it I'll draw a dot for the minimum,
I'll draw a dot for Q1, another dot
for the median, another dot for Q3.
And we know we can't use 90 for the max
because that's an outlier, so we're going to get rid of that
and consider the next highest which will be 74
and so I'm going to put a dot for 74 there.
And I'm going to put a star above 90 because that's going
to tell everybody hey there's an outlier here.
The next thing I'm going to do is draw a box right,
that's going to be -- basically that's my IQR right.
That's going to be my Q1, median, Q3.
Okay and then I draw the whiskers
and that's it, I've got my box plot.
Now if you want more information on how
to draw a box plot go ahead and watch my video.