00:01
We have some data here, and we want to make a box plot.
00:03
So to make a box plot, we need the five -number summary.
00:06
That's the minimum, the first quartile, the second quartile, or median, third quartile, and the maximum.
00:13
So the minimum and maximum are easy enough, they're just the smallest and largest values.
00:19
Smallest here is 0, largest is 25.
00:22
For the others, we have to do a little bit more work.
00:25
The first quartile is the 25th percentile.
00:29
A quarter of the data is below it, 75 % above.
00:32
You find it at the n plus 1 over 4th piece of data in ascending order.
00:38
We have 20 pieces of data here, so we are looking for the 5 .25th piece.
00:44
Now of course that doesn't exist, so we're going to get the 5th and the 6th, and we might have to take a weighted average.
00:51
So the fifth is 7, the sixth is an 8.
00:56
I want a value that's mostly this one, but 25 % of the way up to the sixth.
01:02
So to get that, i multiply this by 0 .75, this by 0 .25, and that will give me what i'm looking for.
01:09
So that would be 7 .25.
01:16
The median is the 50th percentile, the halfway point, is at the n plus one over two -th piece, so the 10 .5th.
01:24
Similarly the third quartile, the 75th percentile, is at the three, n plus one over fourth piece of data to round this out, and that is the 15 .75th.
01:36
So i need the 10th and the 11th, let's see what those are.
01:41
10th is a 9, 11th is a 10, we want halfway between those, so add not divide by 2, let's get 9 .5.
01:50
For the third quartile, i need the 15th and the 16th.
01:55
Let's see what those are.
01:56
Both of those are a 12, so no fancy stuff here.
02:01
It's just 12.
02:02
There we go.
02:03
So now we have the five number summary.
02:05
I can go ahead and make my box plot.
02:09
So i'll have an axis down here.
02:10
We're going to go from 0 up to 25...