00:01
In texas, water is extremely important.
00:03
So this data represents the ph levels in groundwater for a random sample of 102 west texas wells.
00:13
And the first thing we want to do is create a box and whisker plot to show the spread of this data.
00:20
So in order to do a box and whisker plot, we need a five number summary, which includes a minimum, quartile 1, the median quartile 3, and the maximum.
01:03
So our minimum value, these were arranged in order, and i kind of color -coded them this way you could see the groups of similar numbers.
01:12
So our minimum value was 7 .0.
01:16
Our maximum value was 8 .8.
01:22
Our median is the next thing.
01:25
There were 102 pieces of data.
01:31
Therefore, the median is the middle of that.
01:35
So if there's 102 pieces of data and you break it in half, that means there's 51 pieces of data in the front, and there's 51 pieces of data in the back.
01:49
So that means the median will be the average of the 51st and 52nd piece of data.
01:57
So therefore, when we locate our 51st and 52nd piece of data, here's the 51st piece of data, here's the 52nd piece of data, our median will be right in between, so that means we're going to average these two values together, and we get a median value of 7 .5.
02:23
Now our quartile 1 is the median of the first half.
02:29
So if you think about the first half of data, we just said that there's 51 pieces of data.
02:35
So if we find the middle of that, we'd have 25 pieces, then we'd have one piece of data, and then 25 more pieces of data.
02:46
So this one in the middle is going to be our quartile 1.
02:58
So that's is quartile one.
03:06
And then quartile three, we're going to think the same way.
03:10
There's 51 pieces of data in the second half of this list.
03:15
So if we think about 25, 1 in the middle, and 25, then the 26th piece of data from the end will be our quartile 3.
03:29
So we'll count backwards 26.
03:31
So 1, 2, 3.
03:32
So 1, 2, 3.
03:34
4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 25, 26.
03:49
So this will be quartile 3.
03:54
So now that we have our five number summary, we're ready to draw our box and whisker plot, and our box and whisker plot will be on a number line.
04:03
And our number line has to start at 7 .0 and count all the way up to 8 .8.
04:16
So here would be 7 .1, 7 .2, 7 .3, 7 .4, here's 7 .5, 7 .6, 7 .7, 7 .8 .8 .9, 7 .9, 8 .0.
04:34
8 .1, 8 .2, 8 .2, 8 .3, 8 .4, 8 .5, 8 .6, 8 .7, and 8 .8 .8 .8 .8 .8 .8 .8 .8 .8 .8 .8 .8 .8.
04:49
I'm just going to move.
04:50
These up a little bit so we can draw our box.
05:00
So now we're ready to plot our five number summary.
05:03
So we're going to plot our minimum piece of data, which was a 7 .0.
05:09
We're going to plot our quartile 1, which was a 7 .2.
05:13
Our quartile 2, or our median, which was a 7 .5.
05:19
Our quartile 3, which was a 7 .9.
05:22
And our maximum value, which was an 8 .8.
05:28
So our box and whisker, we're going to draw and connect all five of those, and we'll draw a box from quartile 1 up to quartile 3.
05:49
Move that a little bit.
05:55
And then we're going to close that box around, and then we'll separate our box at the median.
06:04
So there is your box and whisker plot.
06:06
So now we're ready to answer some questions...