Instructor: Hello, students.
Now we will go over a new problem,
that is, problem 20.
First, I'm going to read the problem.
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.
The values are: 7, 35, 5, 9, 8, 3, 10, 12, and 8.
The question is, are there any outliers?
And we need to justify our answer.
So, as we know, to identify our outliers,
we first need to calculate the Tukey fences.
And in order to do that we first have to identify Q1, Q3
IQR, and of course, part of the Tukey fences,
we have to calculate the lower and the upper limits.
So, let's get started.
So the formula for Q1 is,
as we know, K here will be 25,
because we are looking at the Q1.
And n is our sample size, which is nine.
So when we do the algebra here, what do we get?
We get 2.25.
Now, as we know, 2.25 is not a whole number,
so, as part of the formula,
we have to go to the next whole number, and that is three.
So now, the third value of the ordered set will be our Q1,
and that is going to be seven.
So, Q1 is equal to seven.
Now we need to calculate Q3.
To calculate Q3,
all we have to do is replace the K, which we had 25 before,
with 75, because Q3 is also the 75th percentile.
So, again, when we crunch the numbers, what do we get?
We get 6.75.
As we know, 6.75 is not a whole number.
So, what is the next whole number?
It is seven.
So, now let's go back to the ordered data set.
What is the seventh value here?
That is going to be 10,
so Q3 is 10.
So now, let's go ahead and calculate
the upper and lower limits for our Tukey fences.
As always, at first I'm going to write the formula,
and I always encourage my students
to write the formula first.
And when we do the algebra,
we get that the lower limit is 2.5.
Now we will calculate the upper limit.
Again, when we do the algebra, what do we get?
We get 14.5.
So now the question is,
do we have a value that is below 2.5 or above 14.5?
So, no, we do not have a value below 2.5,
because our lowest value is three.
However, do we have a value above 14.5?
And that answer is yes, we do, and that is 35.
Because 35 is greater than 14.5,
we must identify that as our outlier.
So we do have an outlier,
and that is 35.
I hope this helps,
and I'm going to see you in the next video.