So, in this example, we had, we
calculated the five-number summary. And when we were using the locator method
to find our quartiles, we looked the case where the locator comes out to be a
decimal value. In that case, we went up to the nearest
whole value and used that data value. So now, suppose that we had only eight
pieces of data so the minimum and the maximum are still very easy to find.
The median now remember, if it comes out to be a whole number, then we’re going to
find the mean of the fourth and fifth data values which is going to be 65, so
that’s our median. and now let’s see if we can find our
quartiles. So, we’re going to do this same thing,
we’re going to use the locator method, which means we’re going to find where 25%
of our data is, or for quartile 3, we’ll do 75%.
So here, if we do 25, that’s not a 5. If we do 25% of our 8 pieces of data, we
come up with 4, which is not a decimal value.
So, if this is if this is not decimal, then we’re going to basically run into
the same thing we did with our median, where we’re going to then find the mean,
of the Lth and the L plus first data values, which is a fancy way of saying
yeah, like if we come up with 4 here, then we’re going to use the fourth and
fifth. So, this value is going to give me the
first one to use, and then we also use the, the next one in the list.
And, wow, I did not calculate that right, I’m sorry.
25% of 8 is 2, not 4 [LAUGH] and so we’re going to use the, let me correct that
there, we’re going to use the 2nd and 3rd data values.
so, the 2nd and 3rd data values are here and here, so we’re going to find he mean
just to clarify, we’re going to to find the mean of the 2nd and 3rd data values
to the mean of 60 and 61, add them up, divide by 2, sorry, of 60 and 62 is 61.
For quartile 3, we’ll do the same thing. We’ll use the locator method.
so we’ll use 75% of n, of our data value, and that comes out to be 6.
again, that is a whole number, it’s not a decimal.
And so, we’re going to need to use the mean of the 6th, and next one, 7th data
values. So, let’s see here.
1, 2, 3, 4, 5, 6, and 7. So, 6th and 7th data values, we’ll find
the mean of those, is 68. So, our five-number summary here would be
59, that’s the minimum, 61 is quartile 1, 65 is the median, 68 is quartile 3, and
70 is the maximum. And that’s the five-number summary for