Instructor: Hello, students, and welcome to Problem 20.
So this problem, I'm going to read the problem first.
The following data are sample of white blood counts
in thousands of cells per-cubic-millimeter
for nine participants entering a hospital
in Boston, Massachusetts on a given day.
So the values here, I have already created the ordered set,
as you can see,
which are three, five, seven, eight, eight,
nine, 10, 12, 35.
Now the question here is asking us are there any outliers
in this data set, and if so, justify.
So as you know by now,
when we start the process of identifying the outlier,
we need to go back to first calculating Q1, Q3,
and then the Tukey fences,
basically the upper and lower limits.
And then we need to see if we have any values
above or below the upper and lower limits.
So let's start here.
So Q1 is the first thing we need to calculate.
So as you already know by now,
the formula to calculate Q1 here
is L equal to K divided by 100.
Oops, sorry, should be this here, multiplied by n,
and that is our sample size.
So K here is going to be 25 divided by 100
and multiplied by nine,
and that is going to give us 2.25.
So as you know, 2.25 is not a whole number.
So what we have to do is proceed
and identify the next whole number.
So that will be three.
So now we have to go back to our order data set
and identify the third value,
and that is seven.
So that is our Q1.
Now we need to calculate Q3.
So for Q3, again, we are going to use the same formula.
Only difference now would be instead of 25,
we are going to use 75.
And when we do that,
what we get here is 6.75.
Again, 6.75 is not a whole number,
so we need to proceed to the next whole number,
and that will be seven.
So what is the seventh value of our order set?
When we go down, we can see that is going to be 10.
So our Q3 is 10.
So now we need to calculate the Tukey fences,
basically the upper and lower limits.
So the formula here, as you have seen before,
is going to be Q1 for the lower limits, or lower limit,
is going to be Q1 minus 1.5
multiplied by Q3 minus Q1.
And as I've said before, Q3 minus Q1 is our IQR.
So here, Q1 is going to be seven minus 1.5,
and the IQR is going to be 10 minus seven.
So when we do the calculation,
so let's do it and see what we get.
10 minus seven is three.
So three times 1.5 is 4.5.
So seven minus 4.5 is 2.5.
So for our Tukey fences,
the lower limit is 2.5.
Now we are going to calculate the upper limit.
So here the formula is Q3 plus 1.5,
Q3 minus Q1.
So Q3 is going to be 10, 1.5.
And we already know Q3 minus Q1 is three.
So when we do all this calculation,
what we get is 14.5.
So now the question is do we have any value
[edited] below 2.5?
So the Tukey fences here is 2.5 to 14.5.
Now, do we have any value that is below 2.5?
The answer is no, because our lowest value is three.
Do we have any value that is above 14.5?
Now the answer is yes, we do,
and that is 35.
So because 35 is greater than 14.5,
we have identified that, yes, we do have an outlier here,
and that outlier is 35.
So I hope was helpful,
because I mentioned previously that we are going to go
through a problem where we will have an outlier,
and that's exactly what we had for this problem.
Here we have an outlier,
and we were able to identify by using the Tukey fences.