AISL 4.2.4 Outliers | Free Mathematics Applications & Interpretation (AI) Video | RevisionDojo
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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.
About this video 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:
Defining an outlier using the formula: 1.5 × IQR 1.5 \times \text{IQR} 1.5 × IQR Q3 or below Q1 , where IQR is the interquartile range.
An example is provided using a dataset of students' phone usage to calculate boundaries for identifying outliers, resulting in lower and upper boundaries of 2.5 and 22.5 , respectively.
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.
Video transcript 00:00 Hi guys, so in this
00:01 lesson I want to look
00:02
at outliers and whenever I
00:04 teach this lesson I always
00:06 mention the book outliers by
00:08 Malcolm Gladwell and if you
00:09 haven't read it I suggest
00:10 you do so as excellent
00:11 book, but it talks about
00:12 people who are outliers like
00:15 Mozart Bill Gates. I'll give
00:18 you some examples like Messi
00:19 and Ronaldo, football, Michael Jordan.
00:22 These are people who, well
00:25 the book is particularly looking
00:28 but there are people who
00:29 are far, who have achieved
00:31 far more than other people
00:34 in their field. Now, what
00:38 come up with a, well,
00:39 what we're gonna do here
00:40 in this lesson is we're
00:41 gonna come up with a
00:42 way to define what an
00:43 outlier is. Because, I mean,
00:47 we could say, we could
00:48 say Michael Jordan is an
00:49 outlier, but where does it
00:52 stop? Who isn't an outlier
00:54 is Kobe Bryant an outlier?
00:56 is LeBron James and Outlier
00:59 is Zadana Outlier. We don't
01:03 actually have a, well, until
01:07 here, we don't actually have
01:09 a definition for what an
01:10 Outlier is. Now, if you
01:11 wanted to talk about Outliers
01:13 in, say, football, you might
01:15 come up with the average
01:17 goals scored per season, and
01:22 then look at Messi's average
01:24 or a procedure and you
01:25 would quickly find out that
01:26 he is certainly an outlier
01:28 as his Michael Jordan. Anyway,
01:30 let me explain with this
01:31 more kind of simple example.
01:33 So this is the same,
01:35 it's actually not the same
01:36 data, but it's the same
01:37 example. So it's missed as
01:39 plot lesson. So it's 16
01:40 of Mr. Flynn's students and
01:42 how long they spend on
01:43 the phone in hours. So
01:46 yeah, just be careful. I've
01:49 changed these numbers ever so
01:51 slightly. So if you're doing
01:52 Lesson again using the same
01:54 numbers. They're slightly different so
01:56 you have to put them
01:57 in again. So what we're
02:00 gonna do is we're gonna
02:02 look at these. Now imagine
02:03 these are these are your
02:04 friends or whatever in the
02:05 people in the class. You
02:06 might look at them and
02:07 say well hang on. This
02:08 look at this person here.
02:10 Here she is spending way
02:12 too much time on their
02:12 phone. They're an outlier. This
02:16 guy here doesn't spend any
02:17 time on his phone. He's
02:20 And I'm like, well, hang
02:23 this guy an outlier? 18
02:24 is three an outlier. We
02:27 just don't know until I
02:30 of defining an outlier and
02:31 the way we're gonna define
02:32 it is using this formula.
02:35 Now note, I've written it
02:37 of the lesson, which means
02:40 formula book, but so you
02:41 need to remember this. It's
02:43 fairly straightforward. It's 1 .5
02:45 times the interquartile range above
02:49 encore of range below Q1,
02:53 at least that. So more
02:55 than this would be an
02:59 outlier. Okay, so this is
03:02 kind of a typical exam
03:03 question. It says calculate the
03:04 boundaries that identify the outliers.
03:08 the boundaries. What is it?
03:12 highest value that would not
03:16 if you like. So let's
03:20 well, we need the interquartal
03:22 range. So firstly, let's find
03:23 the interquartal range. I'll define
03:25 the interquartal range, any Q1,
03:31 interquartal range. So using our
03:34 calculator, I've put in the
03:35 data already to save us
03:38 spreadsheet. Data is here. Then
03:44 Statistics, stack calculations, one variable
03:47 statistics. Press OK, and change
03:51 this to time just to
03:52 be clear. This is all
03:53 the same. Press OK, and
04:01 15, which means my interchora
04:09 times the interchora range. So
04:10 I'm going to do interchora
04:16 equals 7 .5. That's pretty
04:19 easy. Use your calculator if
04:22 in doubt, but it's one
04:23 and a half of these.
04:24 Fine. Now I'm going to
04:29 Q1 minus 7 .5, which
04:51 .5 times the intercoronometer above
04:57 because this is above Q3
05:02 the intercoronometer below Q1. So
05:08 this and this so these
05:10 are the boundaries lower lower
05:13 boundary lower boundary is 2
05:19 .5 and then upper boundary
05:23 is 22 .5 and sometimes
05:32 you might get asked the
05:33 question what's the what's the
05:36 the least amount of time
05:40 that someone could spend on
05:41 their phone and be an
05:43 outlier to the nearest hour.
05:45 And in that case, it
05:46 would be 23, because 23
05:49 would be an outlier and
05:52 outlier, because it's less than
05:56 this. So hope that makes
05:57 sense. And this whole thing
06:01 is to the nearest hour.
06:04 are my boundaries. Now here
06:12 the grid below. So what
06:18 our Q3, let's fill in
06:19 these first. This is 10,
06:24 Q2 is our median, which
06:27 is 12. Okay, so this
06:33 Okay, now our lowest value
06:35 now we're going to put
06:37 in our lowest value that's
06:38 not an outlier. So here
06:40 we say anything below two
06:42 two point five is an
06:43 outlier. So our lowest value
06:45 that's not an outlier will
06:46 be three. So he's at
06:48 three and I'll put it.
06:51 Let's put it here. Three.
06:56 Let's write halfway between those
06:57 two. Three is at the
07:01 you like. And then our
07:03 highest value that's not an
07:04 outlier will be 18. So
07:09 he's the upper end of
07:11 my of my whisker like
07:13 this. And then my Q1
07:19 same as we've done before.
07:21 So hopefully we know how
07:33 here. Join this. Join this.
07:43 That should be straight. Okay,
07:48 so this is, and I'll
07:49 write here. This is 3,
08:00 the outlier. So who were
08:02 my outliers? Well, he's an
08:03 outlier. This guy's an outlier
08:05 and this guy's an outlier.
08:09 outlier. So these are my
08:11 only two outliers. So if
08:12 you were to guess which
08:13 the outliers were at the
08:14 beginning of the lesson, yeah,
08:16 you probably definitely have said
08:18 32. You probably would have
08:20 said two and you might
08:20 even have said three as
08:21 well. Well, I don't know
08:22 what you just said, but
08:25 But anyway, these are the
08:27 two, these are your two
08:28 outliers. Now we need to
08:29 put these into the box
08:32 little x. So you're going
08:38 like that. So that's clear.
08:42 and these are my outliers.
08:43 Now, a common question I
08:44 get asked here is, well,
08:47 which is it? Is this
08:49 the highest value or is
08:50 it the highest value that's
08:52 not an outlier? Well,
08:53 It depends, it depends on
08:56 the question. You can see
08:59 it where they just put
09:00 this as the highest value,
09:01 where they don't even mention
09:02 outliers. But if they're going
09:04 to talk about outliers, they
09:07 will indicate that they want,
09:11 well, they will tell you
09:12 to indicate the outliers. And
09:14 once they do that, you
09:15 have to, you have to
09:16 work it out and then
09:17 put the outliers in as
09:21 in an exam exactly what
09:25 you need to do. Okay,
09:26 hope that makes sense. I