Instructor: Hello, students.
We are now going to get problem 20.
This is, again, a new problem
and here we have the raw dataset.
The following data are a sample of white blood cell counts
in thousands of cells per cubic millimeter for nine patients
entering a hospital in Boston, Massachusetts on a given day.
So, the question is asking us
are there any outliers in this dataset?
And of course, we have to justify our answer.
So, what do we have to do here?
As you may have understood
from our previous problems that we have solved,
we need to compute the quartiles.
So, we have to first compute the quartiles
and kind of make a plan for this.
We have to compute the quartiles
and then we have to calculate the lower
and our limits, right, for the two (indistinct).
Okay, now,
before we can calculate the quartiles
what's the first thing we have to do?
We need the ordered set.
So, again here I'm going to give you the ordered set.
Again, very easily we can use Excel and calculate this.
So, let's see here
is 3, 5, 7,
8, 8, 9,
10, 12, and 35.
Okay, so again, this is our ordered set.
So, what I want to do is right now number them
using another color so it is easier for us to see it.
So, this is 1, this is 2, this is 3,
this is 4, this is 5,
6, 7, 8, and 9.
And because, again, we have 9,
which is an odd number,
it's very clear that this is going to be our median.
Okay, so the fifth place, which is number 8,
is our median, and this is Q2.
So, now the question is, what is Q1 and what is Q3?
So, the Q1 will be, again,
the median of the upper values,
basically the values that are above our median
and that will be, again, I'm going to use another color.
So, that's basically this data set.
And of this, what's in the middle?
These two
And because it's a even number,
we need to make an average of these two.
So, this is Q1, so it is five plus seven.
And again, I always like to put a parenthesis around
because that makes me realize
I gotta do the addition before doing the division.
So, this will be 12 divided by two.
That is what, six?
Correct, okay.
Now we have to go to the lower part,
and again I'm going to use another color.
Let's see, I'm going to use
maybe blue this time.
Okay, so here this is basically the four values
that are below
our median, which is Q2.
So, here again, what is going to be Q3?
That's going to be the average of these two numbers,
so Q3 is 10 plus 12
divided by two.
So, that will be what?
That will be 11.
Okay, so now what is our next step?
Our next step is to calculate the IQR.
So, what is going to be our IQR?
Our IQR is going to be the difference between
Q3 and Q1.
So, IQR will be Q3 minus Q1,
and that is going to be what?
11 minus six, that is five.
Correct. Okay, great.
So, now what we need to do is calculate
the lower limit and the upper limit.
So, again, the lower limit,
I'm going to again write the formulas.
So, that will be Q1
minus 1.5 multiplied by IQR.
So, what is our Q1?
We just calculated it.
Q1 is 6,
so it's going to be 6 minus 1.5
multiplied by 5.
So, it's going to be what?
6 minus 7.5.
So, what's gonna happen here?
We're gonna have a negative number.
-: 1.5, correct?
Yes, so now we are going to go to the upper limit.
So, the upper limit, again, it seems like repetitive,
but it's always a good idea to write the formula again.
It always is. I love doing it, okay?
So, Q3 plus 1.5
multiplied by IQR.
Okay, oops, that got a little, little.
Okay, let me make sure it fits here.
Okay, so I'm going to just erase this
and write this whole thing so everything fits nicely.
Okay, upper limit
is formula is Q3
plus 1.5 multiplied by IQR.
Okay, so, again, remember from before.
I'm going to again use a different color,
maybe purple this time.
This is going to be the same, right?
So, this is going to be still 7.5
so we don't need to do that calculation again,
all we need to do is take that and add it to Q3.
And this is how you can save time
when you are taking the test
by not repeating the calculations.
Okay, that really saves time.
So, what is our Q3?
Q3 is 11.
So, 11 plus now 7.5.
Okay, so 11 plus 7.5 is going to be what?
18.5.
So, are there outliers?
That's the question.
Yes, there are, right?
We do have outliers.
How do we know that?
Because 35 is bigger than 18.5.
We don't have any outliers in terms of the lower limit
because we don't have any value less than -1.5,
but we do have a value that is greater than our upper limit,
which is 18.5.
So, again, we have an outlier.
Let me use another nice color,
let's use green this time.
Okay, so 35 is actually,
as we know, bigger than 18.5
so yes, we have an outlier.
Yes, outlier exists, okay?
Because 35 is greater than 18.5,
so that is our outlier.
Okay, let me write it clearly.
Okay, so 18.5.
Okay, so we have done
this calculation now a few times
and I really, really encourage students
to go through the calculations multiple times.
The magic number for me has been three.
If I go through a calculation three times,
go through a problem three times
even when I know the answer, I know the process,
even then when I repeat that
it really helps me because you know why?
When you take a test, you are what?
You have a time constraint
so you have to go a little faster
and that really is very helpful
when you have solved a problem a few times
then that process naturally gets speeded
or sped up in your mind,
you can do it much faster.
You can think faster
because you have gone through the process a few times.
So, again, I very much encourage you
to go through these problems a couple of times.
Again, I'm showing you a number of problems,
I'm putting a lot more examples this time
because I think it's important to go through these examples
so that will clear the understanding in your mind
and you will also be able to solve the problems
much faster when you take the test.