Instructor: So hello, students.
We are now with problem 1d,
and here we are going to learn how to compute
the first and the third quartiles.
So we have already learned how to calculate the median,
and basically,
for the first quartile,
we tend to denote that with Q1.
And basically, that is the median of the upper half.
Okay, so it is the median
of the upper half,
and again, for the ordered set.
Okay, so here is our ordered set.
Our median, again, is 194
because we are using the same data set.
So we are looking at the upper half, which is this part.
So here we have four numbers above the median.
So basically, to find the physical midpoint here,
or the median,
we have to take an average of these two numbers, okay.
So it's going to be 175 and 180,
so our Q1 will be
177.5, okay.
So it's basically, again,
the physical midpoint of the ordered set,
but at the same time,
it is the median of the upper half of the ordered set.
And what I would like to mention here is
the method we are using in this class
is what we call more of an eyeball approach.
There are specific formulas to calculate
first and third quartiles,
but we are not using them in this class
because we are still kind of
in an introductory level bio statistics course.
But there are specific formulas for this.
So now, we are going to learn how to calculate Q3.
For that, I'm going to use a different color,
so it will be easier for us to see it.
So here, this is basically that lower half,
and we want to know the Q3 here.
And what is Q3?
Q three is our median
of the lower half
of the ordered set.
That is what Q3 is.
So Q3, here again,
we have two numbers that we have to average
to get our Q3.
So the Q3 will be
223 plus 225
divided by two,
and that will be 224.
So now we have both our Q3 and Q1,
and we are going to learn how to now calculate two events
by using all these things we have found so far
or we have calculated so far.
So again, I want to reiterate,
for Q3 and Q1,
there are specific formulas that can be used
to calculate these values.
We are not using them here in this class.
We are using more what we call an eyeball approach,
and that's why you have to make sure
that your data is an ordered set, smallest to largest.
And basically, we are going by the physical midpoints here
in terms of calculation.
So for an ordered data set,
your median is your physical midpoint.
Q1 is basically median of the upper half,
and Q3 is the median of the lower half.
And another name for median is actually Q2.
So we have Q1, Q2, and Q3.