IB · Mathematics Applications & Interpretation (AI)
AISL 4.2.4 Outliers
Learn AISL 4.2.4 Outliers in this free IB Mathematics Applications & Interpretation (AI) video lesson for SL 4.2—Presentation of data.
Learn AISL 4.2.4 Outliers in this free IB Mathematics Applications & Interpretation (AI) video lesson for SL 4.2—Presentation of data.
Learn AISL 4.2.4 Outliers in this free IB Mathematics Applications & Interpretation (AI) video lesson for SL 4.2—Presentation of data.
The lesson focuses on understanding outliers in data analysis, referencing Malcolm Gladwell's book "Outliers" to illustrate exceptional individuals in various fields.
Key points include:
The lesson concludes with instructions on creating a box plot, highlighting how to represent outliers with an "X" and clarifying the distinction between the highest value and the highest non-outlier value.
00:00Hi guys, so in this
00:01lesson I want to look
00:02at outliers and whenever I
00:04teach this lesson I always
00:06mention the book outliers by
00:08Malcolm Gladwell and if you
00:09haven't read it I suggest
00:10you do so as excellent
00:11book, but it talks about
00:12people who are outliers like
00:15Mozart Bill Gates. I'll give
00:18you some examples like Messi
00:19and Ronaldo, football, Michael Jordan.
00:22These are people who, well
00:25the book is particularly looking
00:26at at six
00:28but there are people who
00:29are far, who have achieved
00:31far more than other people
00:34in their field. Now, what
00:37I want to do is
00:38come up with a, well,
00:39what we're gonna do here
00:40in this lesson is we're
00:41gonna come up with a
00:42way to define what an
00:43outlier is. Because, I mean,
00:47we could say, we could
00:48say Michael Jordan is an
00:49outlier, but where does it
00:52stop? Who isn't an outlier
00:54is Kobe Bryant an outlier?
00:56is LeBron James and Outlier
00:59is Zadana Outlier. We don't
01:03actually have a, well, until
01:06I show you this one
01:07here, we don't actually have
01:09a definition for what an
01:10Outlier is. Now, if you
01:11wanted to talk about Outliers
01:13in, say, football, you might
01:15come up with the average
01:17goals scored per season, and
01:22then look at Messi's average
01:23goals scored.
01:24or a procedure and you
01:25would quickly find out that
01:26he is certainly an outlier
01:28as his Michael Jordan. Anyway,
01:30let me explain with this
01:31more kind of simple example.
01:33So this is the same,
01:35it's actually not the same
01:36data, but it's the same
01:37example. So it's missed as
01:38I did for the box
01:39plot lesson. So it's 16
01:40of Mr. Flynn's students and
01:42how long they spend on
01:43the phone in hours. So
01:46yeah, just be careful. I've
01:49changed these numbers ever so
01:51slightly. So if you're doing
01:52this,
01:52Lesson again using the same
01:54numbers. They're slightly different so
01:56you have to put them
01:57in again. So what we're
02:00gonna do is we're gonna
02:02look at these. Now imagine
02:03these are these are your
02:04friends or whatever in the
02:05people in the class. You
02:06might look at them and
02:07say well hang on. This
02:08look at this person here.
02:10Here she is spending way
02:12too much time on their
02:12phone. They're an outlier. This
02:16guy here doesn't spend any
02:17time on his phone. He's
02:19an outlier.
02:20And I'm like, well, hang
02:21on, who else is? Is
02:23this guy an outlier? 18
02:24is three an outlier. We
02:27just don't know until I
02:28come up with a way
02:30of defining an outlier and
02:31the way we're gonna define
02:32it is using this formula.
02:35Now note, I've written it
02:36in red at the top
02:37of the lesson, which means
02:39it is not in the
02:40formula book, but so you
02:41need to remember this. It's
02:43fairly straightforward. It's 1 .5
02:45times the interquartile range above
02:47Q3
02:48or 1 .5 times the
02:49encore of range below Q1,
02:53at least that. So more
02:55than this would be an
02:59outlier. Okay, so this is
03:02kind of a typical exam
03:03question. It says calculate the
03:04boundaries that identify the outliers.
03:08So we need to find
03:08the boundaries. What is it?
03:11What is the kind of
03:12highest value that would not
03:16be an outlier?
03:16if you like. So let's
03:18do it. So we need,
03:20well, we need the interquartal
03:22range. So firstly, let's find
03:23the interquartal range. I'll define
03:25the interquartal range, any Q1,
03:28and I need Q3, and
03:30I can then find the
03:31interquartal range. So using our
03:34calculator, I've put in the
03:35data already to save us
03:37time, but this is a
03:38spreadsheet. Data is here. Then
03:43we go menu,
03:44Statistics, stack calculations, one variable
03:47statistics. Press OK, and change
03:51this to time just to
03:52be clear. This is all
03:53the same. Press OK, and
03:55I get this. So Q1
03:57is 10, Q3 is 15.
03:59Q1 is 10, Q3 is
04:0115, which means my interchora
04:03range is 5. Now, I
04:07need to do 1 .5
04:09times the interchora range. So
04:10I'm going to do interchora
04:12range.
04:12times 1 .5 and that
04:16equals 7 .5. That's pretty
04:19easy. Use your calculator if
04:22in doubt, but it's one
04:23and a half of these.
04:24Fine. Now I'm going to
04:25do Q3. Well I'll do
04:29Q1 minus 7 .5, which
04:33is 10 minus 7 .5,
04:35which is 2 .5 and
04:39then Q
04:403 plus 7 .5 which
04:45is 22 .5. Now look
04:48at it. This is 1
04:51.5 times the intercoronometer above
04:53Q3. So that's why I
04:55did Q3 plus 7 .5
04:57because this is above Q3
04:58and Q1 minus 7 .5
05:00would be 1 .5 times
05:02the intercoronometer below Q1. So
05:06minus a Q1 minus
05:08this and this so these
05:10are the boundaries lower lower
05:13boundary lower boundary is 2
05:19.5 and then upper boundary
05:23is 22 .5 and sometimes
05:32you might get asked the
05:33question what's the what's the
05:36the least amount of time
05:40that someone could spend on
05:41their phone and be an
05:43outlier to the nearest hour.
05:45And in that case, it
05:46would be 23, because 23
05:49would be an outlier and
05:5022 would not be an
05:52outlier, because it's less than
05:56this. So hope that makes
05:57sense. And this whole thing
06:01is to the nearest hour.
06:04So these
06:04are my boundaries. Now here
06:08it says draw a box
06:10plot of the data in
06:12the grid below. So what
06:15we need is we need
06:17our Q1, our Q2, and
06:18our Q3, let's fill in
06:19these first. This is 10,
06:21this is 15, and our
06:24Q2 is our median, which
06:27is 12. Okay, so this
06:29is 12.
06:33Okay, now our lowest value
06:35now we're going to put
06:37in our lowest value that's
06:38not an outlier. So here
06:40we say anything below two
06:42two point five is an
06:43outlier. So our lowest value
06:45that's not an outlier will
06:46be three. So he's at
06:48three and I'll put it.
06:51Let's put it here. Three.
06:56Let's write halfway between those
06:57two. Three is at the
06:59end of our whisker.
07:01you like. And then our
07:03highest value that's not an
07:04outlier will be 18. So
07:09he's the upper end of
07:11my of my whisker like
07:13this. And then my Q1
07:18Q2 and Q3 is the
07:19same as we've done before.
07:21So hopefully we know how
07:21to do this. 10, 12
07:22and 15. So this is
07:2510, 12,
07:29and 15 will be like
07:33here. Join this. Join this.
07:43That should be straight. Okay,
07:48so this is, and I'll
07:49write here. This is 3,
07:5110, 12, 15, and
07:5718 and now we put
08:00the outlier. So who were
08:02my outliers? Well, he's an
08:03outlier. This guy's an outlier
08:05and this guy's an outlier.
08:08The three is not an
08:09outlier. So these are my
08:11only two outliers. So if
08:12you were to guess which
08:13the outliers were at the
08:14beginning of the lesson, yeah,
08:16you probably definitely have said
08:1832. You probably would have
08:20said two and you might
08:20even have said three as
08:21well. Well, I don't know
08:22what you just said, but
08:24you might have
08:25But anyway, these are the
08:27two, these are your two
08:28outliers. Now we need to
08:29put these into the box
08:30plot the way we put
08:31them in is with a
08:32little x. So you're going
08:33to put an x there
08:34and an x at 32
08:38like that. So that's clear.
08:41This is my box plot
08:42and these are my outliers.
08:43Now, a common question I
08:44get asked here is, well,
08:47which is it? Is this
08:49the highest value or is
08:50it the highest value that's
08:52not an outlier? Well,
08:53It depends, it depends on
08:56the question. You can see
08:59it where they just put
09:00this as the highest value,
09:01where they don't even mention
09:02outliers. But if they're going
09:04to talk about outliers, they
09:07will indicate that they want,
09:11well, they will tell you
09:12to indicate the outliers. And
09:14once they do that, you
09:15have to, you have to
09:16work it out and then
09:17put the outliers in as
09:19an X. So it will
09:20be clear
09:21in an exam exactly what
09:25you need to do. Okay,
09:26hope that makes sense. I
09:27will see you in the
09:28next lesson.