WEBVTT

00:00:00.000 --> 00:00:02.775
- [Instructor] We have a
list of 15 numbers here,

00:00:02.775 --> 00:00:05.634
and what I want to do is
think about the outliers.

00:00:05.634 --> 00:00:09.502
And to help us with that,
let's actually visualize this,

00:00:09.502 --> 00:00:12.318
the distribution of actual numbers.

00:00:12.318 --> 00:00:13.818
So let us do that.

00:00:14.887 --> 00:00:16.242
So here, on a number line,

00:00:16.242 --> 00:00:19.409
I have all the numbers from one to 19.

00:00:20.494 --> 00:00:23.540
And let's see, we have two ones.

00:00:23.540 --> 00:00:27.666
So I could say that's one
one and then two ones.

00:00:27.666 --> 00:00:29.403
We have one six.

00:00:29.403 --> 00:00:31.681
So let's put that six there.

00:00:31.681 --> 00:00:33.098
We have got a 13,

00:00:34.531 --> 00:00:36.009
or we have two 13s.

00:00:36.009 --> 00:00:39.842
So we're gonna go up
here, one 13 and two 13s.

00:00:41.367 --> 00:00:43.784
Let's see, we have three 14s.

00:00:45.105 --> 00:00:45.938
So 14,

00:00:46.962 --> 00:00:48.258
14,

00:00:48.258 --> 00:00:49.091
and 14.

00:00:50.153 --> 00:00:53.050
We have a couple of 15s, 15, 15.

00:00:53.050 --> 00:00:53.883
So 15,

00:00:55.148 --> 00:00:56.444
15.

00:00:56.444 --> 00:00:58.471
We have one 16.

00:00:58.471 --> 00:01:01.103
So that's our 16 there.

00:01:01.103 --> 00:01:03.128
We have three 18s.

00:01:03.128 --> 00:01:04.725
One, two, three.

00:01:04.725 --> 00:01:05.558
So one,

00:01:06.680 --> 00:01:08.085
two,

00:01:08.085 --> 00:01:09.996
and then three.

00:01:09.996 --> 00:01:12.575
And then we have a 19.

00:01:12.575 --> 00:01:14.590
Then we have a 19.

00:01:14.590 --> 00:01:15.667
So when you look,

00:01:15.667 --> 00:01:17.819
when you look visually at
the distribution of numbers,

00:01:17.819 --> 00:01:20.824
it looks like the meat of the
distribution, so to speak,

00:01:20.824 --> 00:01:23.757
is in this area, right over here.

00:01:23.757 --> 00:01:25.012
And so some people might say,

00:01:25.012 --> 00:01:26.610
"Okay, we have three outliers.

00:01:26.610 --> 00:01:28.411
"There are these two ones and the six."

00:01:28.411 --> 00:01:29.244
Some people might say,

00:01:29.244 --> 00:01:31.333
"Well, the six is kinda close enough.

00:01:31.333 --> 00:01:33.889
"Maybe only these two ones are outliers."

00:01:33.889 --> 00:01:37.758
And those would actually be
both reasonable things to say.

00:01:37.758 --> 00:01:40.849
Now to get on the same page,

00:01:40.849 --> 00:01:44.829
statisticians will use a rule sometimes.

00:01:44.829 --> 00:01:46.991
We say, well, anything that is more than

00:01:46.991 --> 00:01:49.440
one and a half times
the interquartile range

00:01:49.440 --> 00:01:52.483
from below Q-one or above Q-three,

00:01:52.483 --> 00:01:54.602
well, those are going to be outliers.

00:01:54.602 --> 00:01:56.325
Well, what am I talking about?

00:01:56.325 --> 00:01:58.021
Well, let's actually, let's
figure out the median,

00:01:58.021 --> 00:01:59.686
Q-one and Q-three here.

00:01:59.686 --> 00:02:01.715
Then we can figure out
the interquartile range.

00:02:01.715 --> 00:02:03.741
And then we can figure
out by that definition,

00:02:03.741 --> 00:02:05.950
what is going to be an outlier?

00:02:05.950 --> 00:02:07.563
And if that all made sense to you so far,

00:02:07.563 --> 00:02:08.863
I encourage you to pause this video

00:02:08.863 --> 00:02:10.372
and try to work through it on your own,

00:02:10.372 --> 00:02:13.176
or I'll do it for you right now.

00:02:13.176 --> 00:02:16.350
All right, so what's the median here?

00:02:16.350 --> 00:02:17.551
Well, the median is the middle number.

00:02:17.551 --> 00:02:20.626
We have 15 numbers, so the
middle number is going to be

00:02:20.626 --> 00:02:22.698
whatever number has seven on either side.

00:02:22.698 --> 00:02:24.307
So it's gonna be the eighth number.

00:02:24.307 --> 00:02:27.980
One, two, three, four, five, six, seven.

00:02:27.980 --> 00:02:29.013
Is that right?

00:02:29.013 --> 00:02:32.900
Yep, six, seven, so that's the median.

00:02:32.900 --> 00:02:35.619
And then you have one, two,
three, four, five, six, seven

00:02:35.619 --> 00:02:36.836
numbers on the right side too.

00:02:36.836 --> 00:02:41.064
So that is the median,
sometimes called Q-two.

00:02:41.064 --> 00:02:43.297
That is our median.

00:02:43.297 --> 00:02:44.928
Now what is Q-one?

00:02:44.928 --> 00:02:47.927
Well, Q-one is going to be the
middle of this first group.

00:02:47.927 --> 00:02:50.347
This first group has seven numbers in it.

00:02:50.347 --> 00:02:53.163
And so the middle is going
to be the fourth number.

00:02:53.163 --> 00:02:54.850
It has three and three,

00:02:54.850 --> 00:02:56.649
three to the left, three to the right.

00:02:56.649 --> 00:02:58.066
So that is Q-one.

00:02:59.507 --> 00:03:00.710
And then Q-three is going

00:03:00.710 --> 00:03:02.674
to be the middle of this upper group.

00:03:02.674 --> 00:03:04.178
Well, that also has seven numbers in it.

00:03:04.178 --> 00:03:06.267
So the middle is going
to be right over there.

00:03:06.267 --> 00:03:08.340
It has three on either side.

00:03:08.340 --> 00:03:09.923
So that is Q-three.

00:03:11.670 --> 00:03:14.239
Now what is the interquartile
range going to be?

00:03:14.239 --> 00:03:15.822
Interquartile range

00:03:16.911 --> 00:03:19.377
is going to be equal to

00:03:19.377 --> 00:03:20.661
Q-three

00:03:20.661 --> 00:03:21.661
minus Q-one,

00:03:22.631 --> 00:03:24.610
the difference between 18 and 13.

00:03:24.610 --> 00:03:26.110
Between 18 and 13,

00:03:26.991 --> 00:03:30.055
well, that is going to be 18 minus 13,

00:03:30.055 --> 00:03:32.085
which is equal to five.

00:03:32.085 --> 00:03:33.996
Now to figure out outliers,

00:03:33.996 --> 00:03:36.415
well, outliers are gonna
be anything that is below.

00:03:36.415 --> 00:03:37.415
So outliers,

00:03:38.579 --> 00:03:39.996
outliers,

00:03:39.996 --> 00:03:42.453
are going to be less than

00:03:42.453 --> 00:03:43.286
our Q-one

00:03:44.554 --> 00:03:45.387
minus 1.5,

00:03:46.620 --> 00:03:49.120
times our interquartile range.

00:03:50.593 --> 00:03:53.048
And this, once again, this
isn't some rule of the universe.

00:03:53.048 --> 00:03:54.246
This is something that statisticians

00:03:54.246 --> 00:03:55.346
have kind of said, well,

00:03:55.346 --> 00:03:57.489
if we want to have a better
definition for outliers,

00:03:57.489 --> 00:03:59.143
let's just agree that
it's something that's

00:03:59.143 --> 00:04:00.408
more than one and half times

00:04:00.408 --> 00:04:02.662
the interquartile range below Q-one.

00:04:02.662 --> 00:04:03.926
Or,

00:04:03.926 --> 00:04:07.751
or an outlier could be
greater than Q-three

00:04:07.751 --> 00:04:11.629
plus one and half times
the interquartile range,

00:04:11.629 --> 00:04:13.730
interquartile range.

00:04:13.730 --> 00:04:15.102
And once again, this is somewhat,

00:04:15.102 --> 00:04:16.929
you know, people just
decided it felt right.

00:04:16.929 --> 00:04:18.488
One could argue it should be 1.6.

00:04:18.488 --> 00:04:22.353
Or one could argue it should
be one, or two, or whatever.

00:04:22.353 --> 00:04:25.040
But this is what people
have tended to agree on.

00:04:25.040 --> 00:04:26.888
So let's think about
what these numbers are.

00:04:26.888 --> 00:04:27.973
Q-one we already know.

00:04:27.973 --> 00:04:30.058
So this is going to be 13

00:04:30.058 --> 00:04:33.927
minus 1.5 times our interquartile range.

00:04:33.927 --> 00:04:36.517
Our interquartile range here is five.

00:04:36.517 --> 00:04:39.600
So it's 1.5 times five, which is 7.5.

00:04:43.020 --> 00:04:44.270
So this is 7.5.

00:04:45.966 --> 00:04:47.716
13 minus 7.5 is what?

00:04:48.891 --> 00:04:50.592
13 minus seven is six,

00:04:50.592 --> 00:04:53.566
and then you subtract another .5, is 5.5.

00:04:53.566 --> 00:04:55.766
So we have outliers,

00:04:55.766 --> 00:04:57.262
outliers.

00:04:57.262 --> 00:04:58.095
Outliers

00:04:59.135 --> 00:05:01.052
would be less than 5.5.

00:05:02.617 --> 00:05:03.868
Or

00:05:03.868 --> 00:05:06.028
the Q-three is 18,

00:05:06.028 --> 00:05:08.111
this is, once again, 7.5.

00:05:09.726 --> 00:05:10.643
18 plus 7.5

00:05:12.118 --> 00:05:12.951
is 25.5,

00:05:14.287 --> 00:05:15.287
or outliers,

00:05:16.855 --> 00:05:18.938
outliers greater than 25,

00:05:20.698 --> 00:05:21.531
25.5.

00:05:22.507 --> 00:05:24.331
So based on this, we have a,

00:05:24.331 --> 00:05:26.436
kind of a numerical definition
for what's an outlier.

00:05:26.436 --> 00:05:28.373
We're not just subjectively saying,

00:05:28.373 --> 00:05:29.854
well, this feels right
or that feels right.

00:05:29.854 --> 00:05:32.595
And based on this, we
only have two outliers,

00:05:32.595 --> 00:05:36.795
that only these two
ones are less than 5.5.

00:05:36.795 --> 00:05:40.008
Only these two ones are less than 5.5.

00:05:40.008 --> 00:05:42.595
This is the cutoff, right over here.

00:05:42.595 --> 00:05:45.070
So this dot just happened to make it.

00:05:45.070 --> 00:05:48.013
And we don't have any
outliers on the high side.

00:05:48.013 --> 00:05:49.722
Now another thing to think about

00:05:49.722 --> 00:05:51.998
is drawing box-and-whiskers plots

00:05:51.998 --> 00:05:54.353
based on Q-one, our median, our range,

00:05:54.353 --> 00:05:55.567
all the range of numbers.

00:05:55.567 --> 00:05:56.650
And you could do it either

00:05:56.650 --> 00:05:58.351
taking in consideration your outliers

00:05:58.351 --> 00:06:02.370
or not taking into
consideration your outliers.

00:06:02.370 --> 00:06:05.267
So there's a couple of
ways that we can do it.

00:06:05.267 --> 00:06:08.909
So let me actually clear,
let me clear all of this.

00:06:08.909 --> 00:06:11.645
We've figured out all of this stuff.

00:06:11.645 --> 00:06:14.187
So let me clear all of that out.

00:06:14.187 --> 00:06:17.587
And let's actually draw
a box-and-whiskers plot.

00:06:17.587 --> 00:06:19.254
So I'll put another,

00:06:22.335 --> 00:06:24.305
another, actually let me do two here.

00:06:24.305 --> 00:06:25.222
That's one,

00:06:26.259 --> 00:06:28.852
and then let me put
another one down there.

00:06:28.852 --> 00:06:30.779
And then this is another.

00:06:30.779 --> 00:06:32.077
Now if we were to just draw

00:06:32.077 --> 00:06:35.307
a classic box-and-whiskers plot here,

00:06:35.307 --> 00:06:37.745
we would say, all right,
our median's at 14.

00:06:37.745 --> 00:06:39.207
And actually, I'll do it both ways.

00:06:39.207 --> 00:06:40.468
Our median's at 14.

00:06:40.468 --> 00:06:42.073
Median's at 14.

00:06:42.073 --> 00:06:43.631
Q-one's at 13.

00:06:43.631 --> 00:06:45.224
Q-one's at 13,

00:06:45.224 --> 00:06:46.905
and Q-one's at 13.

00:06:46.905 --> 00:06:48.453
Q-three is at 18.

00:06:48.453 --> 00:06:50.015
Q-three is at 18,

00:06:50.015 --> 00:06:51.042
Q-three is 18.

00:06:51.042 --> 00:06:52.729
So that's the box part.

00:06:52.729 --> 00:06:55.151
Now let me draw that as an actual,

00:06:55.151 --> 00:06:57.886
let me actually draw that as a box.

00:06:57.886 --> 00:06:59.469
So my best attempt,

00:07:00.655 --> 00:07:01.651
there you go.

00:07:01.651 --> 00:07:03.146
That's the box.

00:07:03.146 --> 00:07:05.753
And this is also a box.

00:07:05.753 --> 00:07:08.049
So far, I'm doing the exact same thing.

00:07:08.049 --> 00:07:09.607
Now if we don't want to consider outliers,

00:07:09.607 --> 00:07:11.373
we would say, well, what's
the entire range here?

00:07:11.373 --> 00:07:14.430
Well, we have things that go
from one all the way to 19.

00:07:14.430 --> 00:07:15.955
So one way to do it is to, hey,

00:07:15.955 --> 00:07:17.661
we start at one.

00:07:17.661 --> 00:07:19.940
And so our entire range, we go,

00:07:19.940 --> 00:07:22.471
actually let me draw it a
little bit better than that.

00:07:22.471 --> 00:07:24.691
We're going all the way,

00:07:24.691 --> 00:07:26.358
all the way from one

00:07:27.974 --> 00:07:28.807
to 19.

00:07:30.128 --> 00:07:32.256
Now in this one, we're
including everything.

00:07:32.256 --> 00:07:35.046
We're including even these two outliers.

00:07:35.046 --> 00:07:37.003
But if we don't want to
include those outliers,

00:07:37.003 --> 00:07:38.918
we want to make it clear
that they're outliers,

00:07:38.918 --> 00:07:40.454
well, let's not include them.

00:07:40.454 --> 00:07:42.671
And what we can do instead is say,

00:07:42.671 --> 00:07:45.978
all right, including
(chuckles) our non-outliers,

00:07:45.978 --> 00:07:47.843
we would start at six

00:07:47.843 --> 00:07:50.268
'cause six we're saying
is in our data set,

00:07:50.268 --> 00:07:52.069
but it is not an outlier.

00:07:52.069 --> 00:07:54.156
Let me make this look better.

00:07:54.156 --> 00:07:55.893
So we're gonna,

00:07:55.893 --> 00:07:57.143
we are going to

00:07:59.285 --> 00:08:02.452
start at six and go all the way to 19.

00:08:04.053 --> 00:08:05.689
And then to say that
we have these outliers,

00:08:05.689 --> 00:08:09.453
we would put this, we
have outliers over there.

00:08:09.453 --> 00:08:11.586
So once again, this is
a box-and-whiskers plot

00:08:11.586 --> 00:08:14.167
of the same data set without outliers.

00:08:14.167 --> 00:08:15.875
And this is one where we make specific,

00:08:15.875 --> 00:08:19.875
we make it clear where
the outliers actually are.