Instructor: Hello students.
Now we are going to solve problem one.
So this problem is asking us, which measure,
the mean or median is a better measure of a typical value
and we need to justify it.
So before I get started,
I'm going to read the problem again.
So the problem here states:
A study is run to estimate the mean total cholesterol level
in children 2 to 6 years of age.
A sample of nine participants is selected
and their total cholesterol levels are measured as follows:
185, 225, 240, 196, 175, 180, 194, 147 and 223.
Now to answer the question,
we need to determine if we have any outliers
and to identify if there are any outliers,
we first need to calculate the Tukey Fences
and basically the upper and lower limits
of the Tukey Fences.
So this is what we have to do here.
We have to calculate the Tukey Fences,
upper and lower limits.
So there is a formula to calculate these limits and that is
lower limit equal to Q.
So it's Q1 minus 1.5, multiplied by Q3 minus Q1.
Now Q3 minus Q1 has a name that is called IQR.
And then for the upper limit,
basically the formula is pretty much the same except
we will replace
Q1 with Q3
and instead of a subtraction
we are going to have an addition here.
And I'm just gonna call this IQR.
So now let's calculate the lower limit.
So what is our Q1?
We already calculated it before,
so it is 1-8-0 or 180, minus 1.5.
Our Q3 is 223, and our Q1 is 180.
Again, we have already calculated these things.
So what is our IQR?
When we do the subtraction, our IQR is 43
and when we do the multiplication,
what we get is 180 minus 64.5.
So that will be 115.5.
Now for the upper limit,
it's basically the same,
except some of these values will be replaced.
So our Q3 as we already know is 223.
And we already know the second part of the calculation
because we just performed it.
So no reason to do it again.
So it's going to be 223 plus 64.5.
So when we add them up,
what do we get?
We get 287.5.
Now as we look at our data set,
what do we see?
We do not see any value
that is less than 115.5,
or any value that is above 287.5.
Therefore, we do not have any outliers.
So because we do not have any outliers here,
mean will be
the better measure of a typical value.
Now what will happen if we have an outlier?
Well, we will discuss that in a later problem.