Instructor: Hello, students.
Welcome to problem 1d.
In this problem, we are going to learn
how to calculate the first and third quartiles.
Now, before we start it,
we have to arrange the numbers lowest to highest,
so let's do that.
That would be 147,
175,
180,
185,
194,
196,
223,
225,
and 240.
Now, as I mentioned previously,
very easily we can do this sorting using Excel.
and I have actually video at the end
which will show you how to do that.
So now once sorted,
we will use the formula we learned previously,
which is L equal to
K divided by 100 multiplied by n.
Now n here is the sample size,
and K is the percentile that we are trying to calculate.
So for the 25th percentile,
it's going to be L equal to 25
divided by 100 multiplied by n.
And the n here is of course nine.
So when we do the algebra here, what we get is 2.25.
Now as we know, 2.25 is not a whole number.
So when we convert it to the next whole number,
that will be three.
So now the question is,
what is the third number in our ordered set?
So that is going to be one, two, three, 180,
so 180 is our Q1.
Now we have to calculate Q3, which is the 75th percentile.
So again, here we are going to replace the K
with the percentile we are trying to calculate
multiplied by the sample size, which is nine.
And what do we get this time?
We get 6.75.
Again, we are going to convert 6.75
to the next whole number, and that will be seven.
So again, we are going to go back to our ordered data set
to find out which one is the seventh number in our set.
So here again, one, two, three, four, five, six, seven.
So the seventh number in the ordered set is 223.
So our Q1 is 180, and our Q3 is 223.
Q1 again is our 25th percentile,
and Q3 is our 75th percentile.
Thank you for your attention.
I will see you in the next video.