00:00Hi everybody. In this lesson
00:02we're going to look at
00:03box and whisker diagrams. Sometimes
00:05called box plots or box
00:06and whisker plots. They're the
00:08same thing. And what it
00:10does is it gives you
00:10a nice visualization of a
00:13set of data. It's sometimes
00:16called the five number summary
00:19where it'll show you the
00:21minimum, the first quarter, second
00:23quarter of the median, the
00:24third quarter, and the maximum.
00:26And you'll get to see
00:27how spread out
00:28It's a nice little chart
00:30once I've drawn it, I'll
00:31explain a bit more about
00:34its uses. I've created an
00:36example here. This is the
00:39data that shows the amount
00:40of time in our 16
00:41students in Mr. Flint's class
00:43spend on their phone per
00:45week on the grid below,
00:47construct a box and whisker
00:48diagram to display the data.
00:51Okay, so this is how
00:52long each student spend on
00:54their phone.
00:56I certainly get to feeling
00:58some people have lied here.
00:59In fact, possibly everyone because
01:01I would imagine people spend
01:03more than 10 hours on
01:05their phone per week. Anyway,
01:07let's do it. So what
01:09I'm going to do is
01:09I'm going to put these
01:10numbers into my calculator and
01:12I actually have already done
01:15it. So if I click
01:18on this spreadsheet in here,
01:20I've already put in the
01:21numbers. So here are the
01:22numbers.
01:24Now, let's call this something
01:30I'll call this ours, just
01:32to be sure, I know
01:33what's happening. Then what I'm
01:35going to do is I've
01:36done this in the previous
01:37lesson. Press menu, statistics, stack
01:42calculations, one variable statistics, this,
01:47yes, click ours here. Frequency,
01:50this is all fine, press
01:51OK. And I
01:52Get this. Now, what this
01:56tells me is, well, these
01:59are the five numbers I'm
02:02after. Look, two, nine, 11,
02:0416, and 21. So let's
02:06write that down. Two, nine,
02:0911, 16, and 21. So
02:14the minimum value is two,
02:16the maximum value is 21,
02:17and these are the three
02:19quartiles.
02:20What we do is we
02:22draw a box and whiskers.
02:24That's why I call it
02:25a box and we're screwed
02:25around. And the box looks
02:27like this. I'm going to
02:28get my, and I start
02:29with my median, 11. So
02:32I go to 11 and
02:33I'm going to draw this
02:34box. Now exactly where to
02:36draw it. The height of
02:38it doesn't actually matter. All
02:41that matters is I'm on
02:42the 11 here. Now let's
02:43make a big enough so
02:44I can actually, let's make
02:46a big enough so I
02:47can read it.
02:48I'm doing is I'm just
02:50going to go three boxes
02:50there. Well actually, why don't
02:53I just draw the whole,
02:55why don't I just draw
02:56this whole thing here? Okay,
03:00so that's right. Should have
03:02been right on 11. That
03:04is the median. The Q1
03:08is at nine. So I'm
03:09going to draw this right
03:11on nine. And then Q3
03:14is 16.
03:16There. So this is Q1,
03:22Q2, Q3. How high did
03:23I put those lines? It
03:24really didn't matter. I could
03:25have put them up to
03:26here. I could have put
03:27them small. Let's certainly make
03:29them big enough so that
03:29we can see them. And
03:31then we're going to put
03:32a straight line across. And
03:34this is my box. Now,
03:39what we already have here
03:40is this is the
03:44half of the data is
03:48in this box. So half
03:49of the people are between
03:509 and 16 and this
03:51is kind of the the
03:53the middle of the data
03:54or the well the interquartile
03:56range would be 16 minus
03:589. So between 9 and
04:0016 the middle half of
04:02the people. So yeah, this
04:07so this tells us this
04:08tells us 25 25 %
04:10of people are between 9
04:11and 11. So even
04:12this is quite short. There's
04:15only two hours between 9
04:16and 11. 25 % of
04:17the people are in here.
04:1925 % of the people
04:21are also in here. Now,
04:23my max is a 21.
04:24So I'm going to go
04:25to 21. I'm not going
04:27to draw a line as
04:28high. I'm just going to
04:29draw a line like that.
04:33Again, it doesn't matter exactly
04:35how high it is, but
04:36it definitely shorter than the
04:38box. And then I'm going
04:40to
04:40join this like so and
04:43here I have my whisker
04:44and that's the maximum and
04:46then my minimum is at
04:492 so I'm gonna draw
04:50that here draw this along
04:56and here I have my
04:58minimum now this is my
05:00box and whisker box and
05:03whisker diagram this shows me
05:05the minimum the min this
05:08is my key
05:08Q1, this is my Q2,
05:11or the median, this is
05:12my Q3, and this is
05:15my Q4. You can see
05:20from the diagram how spread
05:22out the data is. So
05:23immediately you can see the
05:24lowest is two, you can
05:26see the biggest is 21.
05:27You can see that's 25
05:29% of people are between
05:30two and nine, 25 %
05:32of people are between nine
05:33and 11, 25 %
05:36are between 11 and 16
05:39and 25 percent of people
05:40are between 16 and 21.
05:46You may be asked to
05:48draw a box, a box
05:49and a screw diagram, or
05:50you may be asked to
05:53interpret it, which means they'll
05:54give you the box and
05:55a screw diagram and say,
05:57what's the inter -cordal range?
05:58So they give you that
05:59and say, what's the inter
06:00-cordal range? You need to
06:01know, well that's the upper
06:03cordal, 16. That's the lower
06:04or quartile nine. So the
06:07interquartile range is 16 minus
06:09nine equals eight. Okay, that's
06:14my, that is the lesson
06:16on box and risk of
06:17diagram. I'm going to do
06:18another lesson, another video that
06:21kind of shows us how
06:23we can get more of
06:26an interpretation from it and
06:27look at the skewness, which
06:29is a word I'll explain
06:30in the next video, how
06:31we can read
06:33The skewness from a box
06:34and whisker diagram.