0:00:00.000,0:00:00.550


0:00:00.550,0:00:02.900
We've seen in the last several[br]videos you start off with

0:00:02.900,0:00:05.410
any crazy distribution.

0:00:05.410,0:00:06.940
It doesn't have to be[br]crazy, it could be a nice

0:00:06.940,0:00:07.830
normal distribution.

0:00:07.830,0:00:10.380
But to really make the point[br]that you don't have to have

0:00:10.380,0:00:12.170
a normal distribution I[br]like to use crazy ones.

0:00:12.170,0:00:14.790
So let's say you have some kind[br]of crazy distribution that

0:00:14.790,0:00:15.790
looks something like that.

0:00:15.790,0:00:17.080
It could look like anything.

0:00:17.080,0:00:19.360
So we've seen multiple times[br]you take samples from

0:00:19.360,0:00:20.530
this crazy distribution.

0:00:20.530,0:00:27.890
So let's say you were to take[br]samples of n is equal to 10.

0:00:27.890,0:00:32.750
So we take 10 instances of this[br]random variable, average them

0:00:32.750,0:00:34.750
out, and then plot our average.

0:00:34.750,0:00:36.160
We plot our average.

0:00:36.160,0:00:37.590
We get 1 instance there.

0:00:37.590,0:00:38.680
We keep doing that.

0:00:38.680,0:00:39.280
We do that again.

0:00:39.280,0:00:42.650
We take 10 samples from this[br]random variable, average

0:00:42.650,0:00:43.430
them, plot them again.

0:00:43.430,0:00:47.360
You plot again and eventually[br]you do this a gazillion times--

0:00:47.360,0:00:50.230
in theory an infinite number of[br]times-- and you're going to

0:00:50.230,0:00:53.240
approach the sampling[br]distribution of the sample

0:00:53.240,0:00:56.290
mean. n equal 10 is not going[br]to be a perfect normal

0:00:56.290,0:00:58.900
distribution but it's[br]going to be close.

0:00:58.900,0:01:00.610
It'd be perfect only[br]if n was infinity.

0:01:00.610,0:01:05.680
But let's say we eventually--[br]all of our samples we get a lot

0:01:05.680,0:01:08.180
of averages that are there that[br]stacks up, that stacks up

0:01:08.180,0:01:10.290
there, and eventually will[br]approach something that

0:01:10.290,0:01:13.060
looks something like that.

0:01:13.060,0:01:16.190
And we've seen from the last[br]video that one-- if let's say

0:01:16.190,0:01:19.130
we were to do it again and this[br]time let's say that n is equal

0:01:19.130,0:01:23.200
to 20-- one, the distribution[br]that we get is going

0:01:23.200,0:01:24.990
to be more normal.

0:01:24.990,0:01:27.440
And maybe in future videos[br]we'll delve even deeper into

0:01:27.440,0:01:29.510
things like kurtosis and skew.

0:01:29.510,0:01:30.780
But it's going to[br]be more normal.

0:01:30.780,0:01:33.570
But even more important here or[br]I guess even more obviously

0:01:33.570,0:01:35.740
to us, we saw that in the[br]experiment it's going to have

0:01:35.740,0:01:37.420
a lower standard deviation.

0:01:37.420,0:01:38.680
So they're all going to[br]have the same mean.

0:01:38.680,0:01:41.800
Let's say the mean here is,[br]I don't know, let's say

0:01:41.800,0:01:43.410
the mean here is 5.

0:01:43.410,0:01:45.350
Then the mean here is[br]also going to be 5.

0:01:45.350,0:01:47.600
The mean of our sampling[br]distribution of the sample

0:01:47.600,0:01:48.960
mean is going to be 5.

0:01:48.960,0:01:50.260
It doesn't matter[br]what our n is.

0:01:50.260,0:01:52.250
If our n is 20 it's[br]still going to be 5.

0:01:52.250,0:01:54.140
But our standard deviation[br]is going to be less than

0:01:54.140,0:01:55.670
either of these scenarios.

0:01:55.670,0:01:57.260
And we saw that just[br]by experimenting.

0:01:57.260,0:01:58.015
It might look like this.

0:01:58.015,0:01:59.520
It's going to be more normal[br]but it's going to have a

0:01:59.520,0:02:01.350
tighter standard deviation.

0:02:01.350,0:02:03.160
So maybe it'll look like that.

0:02:03.160,0:02:06.810
And if we did it with an even[br]larger sample size-- let me do

0:02:06.810,0:02:09.770
that in a different color-- if[br]we did that with an even larger

0:02:09.770,0:02:13.430
sample size, n is equal to 100,[br]what we're going to get is

0:02:13.430,0:02:17.010
something that fits the normal[br]distribution even better.

0:02:17.010,0:02:19.820
We take a hundred instances[br]of this random variable,

0:02:19.820,0:02:21.230
average them, plot it.

0:02:21.230,0:02:22.730
A hundred instances of[br]this random variable,

0:02:22.730,0:02:23.600
average them, plot it.

0:02:23.600,0:02:25.230
And we just keep doing that.

0:02:25.230,0:02:27.510
If we keep doing that, what[br]we're going to have is

0:02:27.510,0:02:29.950
something that's even more[br]normal than either of these.

0:02:29.950,0:02:32.130
So it's going to be a much[br]closer fit to a true

0:02:32.130,0:02:33.480
normal distribution.

0:02:33.480,0:02:35.890
But even more obvious to[br]the human, it's going

0:02:35.890,0:02:37.650
to be even tighter.

0:02:37.650,0:02:40.640
So it's going to be a very[br]low standard deviation.

0:02:40.640,0:02:41.840
It's going to look[br]something like that.

0:02:41.840,0:02:46.760
And I'll show you on the[br]simulation app in the next or

0:02:46.760,0:02:48.710
probably later in this video.

0:02:48.710,0:02:49.680
So two things happen.

0:02:49.680,0:02:51.830
As you increase your sample[br]size for every time you

0:02:51.830,0:02:53.560
do the average, two[br]things are happening.

0:02:53.560,0:02:57.150
You're becoming more normal[br]and your standard deviation

0:02:57.150,0:02:57.970
is getting smaller.

0:02:57.970,0:03:00.810
So the question might[br]arise is there a formula?

0:03:00.810,0:03:04.680
So if I know the standard[br]deviation-- so this is my

0:03:04.680,0:03:07.990
standard deviation of just my[br]original probability density

0:03:07.990,0:03:10.910
function, this is the mean of[br]my original probability

0:03:10.910,0:03:11.800
density function.

0:03:11.800,0:03:15.320
So if I know the standard[br]deviation and I know n-- n is

0:03:15.320,0:03:17.330
going to change depending on[br]how many samples I'm taking

0:03:17.330,0:03:21.450
every time I do a sample mean--[br]if I know that my standard

0:03:21.450,0:03:23.870
deviation, or maybe if I[br]know my variance, right?

0:03:23.870,0:03:26.300
The variance to just the[br]standard deviation squared.

0:03:26.300,0:03:27.950
If you don't remember[br]that you might want to

0:03:27.950,0:03:29.640
review those videos.

0:03:29.640,0:03:34.450
But if I know the variance of[br]my original distribution and if

0:03:34.450,0:03:38.860
I know what my n is-- how many[br]samples I'm going to take every

0:03:38.860,0:03:41.620
time before I average them in[br]order to plot one thing in my

0:03:41.620,0:03:46.910
sampling distribution of my[br]sample mean-- is there a way to

0:03:46.910,0:03:50.700
predict what the mean of[br]these distributions are?

0:03:50.700,0:03:52.870
And so-- I'm sorry, the[br]standard deviation of

0:03:52.870,0:03:54.050
these distributions.

0:03:54.050,0:03:56.300
And so you don't get confused[br]between that and that,

0:03:56.300,0:03:57.190
let me say the variance.

0:03:57.190,0:03:58.560
If you know the variance[br]you can figure out the

0:03:58.560,0:03:59.570
standard deviation.

0:03:59.570,0:04:01.220
One is just the square[br]root of the other.

0:04:01.220,0:04:06.170
So this is the variance of[br]our original distribution.

0:04:06.170,0:04:09.300
Now to show that this is the[br]variance of our sampling

0:04:09.300,0:04:11.620
distribution of our sample mean[br]we'll write it right here.

0:04:11.620,0:04:16.430
This is the variance of our[br]mean of our sample mean.

0:04:16.430,0:04:19.470
Remember the sample--[br]our true mean is this.

0:04:19.470,0:04:22.100
The Greek letter Mu[br]is our true mean.

0:04:22.100,0:04:27.080
This is equal to the mean,[br]while an x a line over

0:04:27.080,0:04:28.350
it means sample mean.

0:04:28.350,0:04:31.300


0:04:31.300,0:04:34.110
So here what we're saying is[br]this is the variance of our

0:04:34.110,0:04:36.880
sample mean, that this is going[br]to be true distribution.

0:04:36.880,0:04:38.320
This isn't an estimate.

0:04:38.320,0:04:42.590
There's some-- you know, if we[br]magically knew distribution--

0:04:42.590,0:04:44.920
there's some true[br]variance here.

0:04:44.920,0:04:48.590
And of course the mean-- so[br]this has a mean-- this right

0:04:48.590,0:04:51.420
here, we can just get our[br]notation right, this is the

0:04:51.420,0:04:54.750
mean of the sampling[br]distribution of the

0:04:54.750,0:04:55.710
sampling mean.

0:04:55.710,0:04:57.870
So this is the mean[br]of our means.

0:04:57.870,0:04:59.830
It just happens to[br]be the same thing.

0:04:59.830,0:05:03.180
This is the mean of[br]our sample means.

0:05:03.180,0:05:05.410
It's going to be the same thing[br]as that, especially if we do

0:05:05.410,0:05:07.400
the trial over and over again.

0:05:07.400,0:05:09.490
But anyway, the point of this[br]video, is there any way to

0:05:09.490,0:05:13.600
figure out this variance given[br]the variance of the original

0:05:13.600,0:05:15.520
distribution and your n?

0:05:15.520,0:05:16.720
And it turns out there is.

0:05:16.720,0:05:18.230
And I'm not going to[br]do a proof here.

0:05:18.230,0:05:19.910
I really want to give you[br]the intuition of it.

0:05:19.910,0:05:22.830
I think you already do have the[br]sense that every trial you

0:05:22.830,0:05:26.010
take-- if you take a hundred,[br]you're much more likely when

0:05:26.010,0:05:29.140
you average those out, to get[br]close to the true mean than if

0:05:29.140,0:05:31.410
you took an n of[br]2 or an n of 5.

0:05:31.410,0:05:34.240
You're just very unlikely to be[br]far away, right, if you took

0:05:34.240,0:05:36.640
100 trials as opposed[br]to taking 5.

0:05:36.640,0:05:38.590
So I think you know that[br]in some way it should be

0:05:38.590,0:05:40.740
inversely proportional to n.

0:05:40.740,0:05:43.680
The larger your n the smaller[br]a standard deviation.

0:05:43.680,0:05:45.740
And actually it turns out it's[br]about as simple as possible.

0:05:45.740,0:05:47.740
It's one of those magical[br]things about mathematics.

0:05:47.740,0:05:50.110
And I'll prove it[br]to you one day.

0:05:50.110,0:05:51.690
I want to give you[br]working knowledge first.

0:05:51.690,0:05:54.390
In statistics, I'm always[br]struggling whether I should be

0:05:54.390,0:05:57.410
formal in giving you rigorous[br]proofs but I've kind of come to

0:05:57.410,0:05:59.220
the conclusion that it's more[br]important to get the working

0:05:59.220,0:06:02.010
knowledge first in statistics[br]and then later, once you've

0:06:02.010,0:06:05.010
gotten all of that down, we can[br]get into the real deep math

0:06:05.010,0:06:06.270
of it and prove it to you.

0:06:06.270,0:06:09.460
But I think experimental proofs[br]are kind of all you need for

0:06:09.460,0:06:11.110
right now, using those[br]simulations to show that

0:06:11.110,0:06:12.050
they're really true.

0:06:12.050,0:06:14.860
So it turns out that the[br]variance of your sampling

0:06:14.860,0:06:18.230
distribution of your sample[br]mean is equal to the

0:06:18.230,0:06:20.880
variance of your original[br]distribution-- that guy

0:06:20.880,0:06:23.310
right there-- divided by n.

0:06:23.310,0:06:24.300
That's all it is.

0:06:24.300,0:06:29.940
So if this up here has a[br]variance of-- let's say this up

0:06:29.940,0:06:33.640
here has a variance of 20-- I'm[br]just making that number up--

0:06:33.640,0:06:36.330
then let's say your n is 20.

0:06:36.330,0:06:38.850
Then the variance of your[br]sampling distribution of your

0:06:38.850,0:06:41.360
sample mean for an n of 20,[br]well you're just going to take

0:06:41.360,0:06:44.340
that, the variance up here--[br]your variance is 20--

0:06:44.340,0:06:45.840
divided by your n, 20.

0:06:45.840,0:06:49.780
So here your variance is[br]going to be 20 divided by

0:06:49.780,0:06:51.410
20 which is equal to 1.

0:06:51.410,0:06:53.230
This is the variance of[br]your original probability

0:06:53.230,0:06:55.860
distribution and[br]this is your n.

0:06:55.860,0:06:57.460
What's your standard[br]deviation going to be?

0:06:57.460,0:06:59.540
What's going to be the[br]square root of that, right?

0:06:59.540,0:07:00.870
Standard deviation is going[br]to be square root of 1.

0:07:00.870,0:07:02.410
Well that's also going to be 1.

0:07:02.410,0:07:04.090
So we could also write this.

0:07:04.090,0:07:07.040
We could take the square root[br]of both sides of this and say

0:07:07.040,0:07:10.830
the standard deviation of the[br]sampling distribution

0:07:10.830,0:07:13.800
standard-- the standard[br]deviation of the sampling

0:07:13.800,0:07:17.180
distribution of the sample mean[br]is often called the standard

0:07:17.180,0:07:18.550
deviation of the mean.

0:07:18.550,0:07:20.470
And it's also called-- I'm[br]going to write this down-- the

0:07:20.470,0:07:22.050
standard error of the mean.

0:07:22.050,0:07:27.810


0:07:27.810,0:07:30.230
All of these things that I just[br]mentioned, they all just mean

0:07:30.230,0:07:33.010
the standard deviation of the[br]sampling distribution

0:07:33.010,0:07:33.860
of the sample mean.

0:07:33.860,0:07:36.770
That's why this is confusing[br]because you use the word mean

0:07:36.770,0:07:38.080
and sample over and over again.

0:07:38.080,0:07:39.800
And if it confuses[br]you let me know.

0:07:39.800,0:07:42.030
I'll do another video or pause[br]and repeat or whatever.

0:07:42.030,0:07:44.000
But if we just take the square[br]root of both sides, the

0:07:44.000,0:07:46.770
standard error of the mean or[br]the standard deviation of the

0:07:46.770,0:07:50.300
sampling distribution of the[br]sample mean is equal to the

0:07:50.300,0:07:54.310
standard deviation of your[br]original function-- of your

0:07:54.310,0:07:56.580
original probability density[br]function-- which could be very

0:07:56.580,0:07:59.850
non-normal, divided by[br]the square root of n.

0:07:59.850,0:08:03.110
I just took the square root of[br]both sides of this equation.

0:08:03.110,0:08:07.090
I personally like to remember[br]this: that the variance is just

0:08:07.090,0:08:08.820
inversely proportional to n.

0:08:08.820,0:08:10.300
And then I like to[br]go back to this.

0:08:10.300,0:08:11.840
Because this is very[br]simple in my head.

0:08:11.840,0:08:13.790
You just take the[br]variance, divide it by n.

0:08:13.790,0:08:15.790
Oh and if I want the standard[br]deviation, I just take the

0:08:15.790,0:08:18.430
square roots of both sides[br]and I get this formula.

0:08:18.430,0:08:22.460
So here the standard[br]deviation-- when n is 20-- the

0:08:22.460,0:08:25.890
standard deviation of the[br]sampling distribution of the

0:08:25.890,0:08:27.210
sample mean is going to be 1.

0:08:27.210,0:08:31.530
Here when n is 100, our[br]variance here when

0:08:31.530,0:08:32.500
n is equal to 100.

0:08:32.500,0:08:35.230
So our variance of the sampling[br]mean of the sample distribution

0:08:35.230,0:08:37.580
or our variance of the mean--[br]of the sample mean, we

0:08:37.580,0:08:40.340
could say-- is going to be[br]equal to 20-- this guy's

0:08:40.340,0:08:43.290
variance-- divided by n.

0:08:43.290,0:08:46.950
So it equals-- n is[br]100-- so it equals 1/5.

0:08:46.950,0:08:50.730
Now this guy's standard[br]deviation or the standard

0:08:50.730,0:08:54.270
deviation of the sampling[br]distribution of the sample mean

0:08:54.270,0:08:55.760
or the standard error of the[br]mean is going to be the

0:08:55.760,0:08:56.480
square root of that.

0:08:56.480,0:08:58.780
So 1 over the square root of 5.

0:08:58.780,0:09:03.390
And so this guy's will be a[br]little bit under 1/2 the

0:09:03.390,0:09:05.060
standard deviation while[br]this guy had a standard

0:09:05.060,0:09:05.930
deviation of 1.

0:09:05.930,0:09:07.450
So you see, it's[br]definitely thinner.

0:09:07.450,0:09:08.140
Now I know what you're saying.

0:09:08.140,0:09:09.590
Well, Sal, you just gave[br]a formula, I don't

0:09:09.590,0:09:11.140
necessarily believe you.

0:09:11.140,0:09:13.610
Well let's see if we can[br]prove it to ourselves

0:09:13.610,0:09:15.960
using the simulation.

0:09:15.960,0:09:20.240
So just for fun let me make[br]a-- I'll just mess with this

0:09:20.240,0:09:21.670
distribution a little bit.

0:09:21.670,0:09:23.440
So that's my new distribution.

0:09:23.440,0:09:25.370
And let me take an n of-- let[br]me take two things that's easy

0:09:25.370,0:09:27.550
to take the square root of[br]because we're looking at

0:09:27.550,0:09:28.330
standard deviations.

0:09:28.330,0:09:33.830
So we take an n of[br]16 and an n of 25.

0:09:33.830,0:09:35.470
Let's do 10,000 trials.

0:09:35.470,0:09:37.490
So in this case every one of[br]the trials we're going to take

0:09:37.490,0:09:40.320
16 samples from here, average[br]them, plot it here, and

0:09:40.320,0:09:41.600
then do a frequency plot.

0:09:41.600,0:09:45.020
Here we're going to do 25 at a[br]time and then average them.

0:09:45.020,0:09:46.830
I'll do it once animated[br]just to remember.

0:09:46.830,0:09:50.620
So I'm taking 16[br]samples, plot it there.

0:09:50.620,0:09:53.500
I take 16 samples as described[br]by this probability density

0:09:53.500,0:09:56.960
function-- or 25 now,[br]plot it down here.

0:09:56.960,0:10:03.420
Now if I do that 10,000[br]times, what do I get?

0:10:03.420,0:10:06.710
All right, so here, just[br]visually you can tell just when

0:10:06.710,0:10:08.810
n was larger, the standard[br]deviation here is smaller.

0:10:08.810,0:10:10.020
This is more squeezed together.

0:10:10.020,0:10:12.490
But actually let's[br]write this stuff down.

0:10:12.490,0:10:14.420
Let's see if I can[br]remember it here.

0:10:14.420,0:10:17.370
So in this random distribution[br]I made my standard

0:10:17.370,0:10:19.160
deviation was 9.3.

0:10:19.160,0:10:20.460
I'm going to remember these.

0:10:20.460,0:10:24.470
Our standard deviation for[br]the original thing was 9.3.

0:10:24.470,0:10:27.980
And so standard deviation here[br]was 2.3 and the standard

0:10:27.980,0:10:29.590
deviation here is 1.87.

0:10:29.590,0:10:33.290
Let's see if it conforms[br]to our formula.

0:10:33.290,0:10:35.240
So I'm going to take this off[br]screen for a second and I'm

0:10:35.240,0:10:38.900
going to go back and[br]do some mathematics.

0:10:38.900,0:10:41.030
So I have this on my[br]other screen so I can

0:10:41.030,0:10:42.750
remember those numbers.

0:10:42.750,0:10:47.220
So in the trial we just did,[br]my wacky distribution had a

0:10:47.220,0:10:52.650
standard deviation of 9.3.

0:10:52.650,0:10:57.680
When n is equal to-- let me do[br]this in another color-- when n

0:10:57.680,0:11:01.900
was equal to 16, just doing the[br]experiment, doing a bunch of

0:11:01.900,0:11:04.460
trials and averaging and doing[br]all the things, we got the

0:11:04.460,0:11:08.070
standard deviation of the[br]sampling distribution of the

0:11:08.070,0:11:10.380
sample mean or the standard[br]error of the mean, we

0:11:10.380,0:11:15.570
experimentally determined[br]it to be 2.33.

0:11:15.570,0:11:21.500
And then when n is equal to 25[br]we got the standard error of

0:11:21.500,0:11:24.900
the mean being equal to 1.87.

0:11:24.900,0:11:28.330
Let's see if it conforms[br]to our formulas.

0:11:28.330,0:11:32.680
So we know that the variance or[br]we could almost say the

0:11:32.680,0:11:36.010
variance of the mean or the[br]standard error-- the variance

0:11:36.010,0:11:39.230
of the sampling distribution of[br]the sample mean is equal to the

0:11:39.230,0:11:42.050
variance of our original[br]distribution divided by n, take

0:11:42.050,0:11:45.490
the square roots of both sides,[br]and then you get the standard

0:11:45.490,0:11:48.770
error of the mean is equal to[br]the standard deviation of your

0:11:48.770,0:11:51.800
original distribution divided[br]by the square root of n.

0:11:51.800,0:11:54.350
So let's see if this works[br]out for these two things.

0:11:54.350,0:11:58.670
So if I were to take 9.3--[br]so let me do this case.

0:11:58.670,0:12:03.870
So 9.3 divided by the[br]square root of 16, right?

0:12:03.870,0:12:05.150
N is 16.

0:12:05.150,0:12:07.050
So divided by the square[br]root of 16, which is

0:12:07.050,0:12:09.300
4, what do I get?

0:12:09.300,0:12:11.566
So 9.3 divided by 4.

0:12:11.566,0:12:14.840
Let me get a little[br]calculator out here.

0:12:14.840,0:12:15.550
Let's see.

0:12:15.550,0:12:18.720
We have-- let me clear it[br]out-- we want to divide

0:12:18.720,0:12:21.000
9.3 divided by 4.

0:12:21.000,0:12:24.930
9.3 three divided by our[br]square root of n. n was 16.

0:12:24.930,0:12:32.060
So divided by 4 is[br]equal to 2.32.

0:12:32.060,0:12:41.540
So this is equal to 2.32 which[br]is pretty darn close to 2.33.

0:12:41.540,0:12:43.160
This was after 10,000 trials.

0:12:43.160,0:12:45.780
Maybe right after this I'll see[br]what happens if we did 20,000

0:12:45.780,0:12:48.960
or 30,000 trials where we take[br]samples of 16 and average them.

0:12:48.960,0:12:50.340
Now let's look at this.

0:12:50.340,0:12:55.400
Here we would take 9.3-- so let[br]me draw a little line here.

0:12:55.400,0:12:57.300
Let me scroll over,[br]that might be better.

0:12:57.300,0:13:00.340
So we take our standard[br]deviation of our

0:13:00.340,0:13:01.790
original distribution.

0:13:01.790,0:13:05.280
So just that formula that we've[br]derived right here would tell

0:13:05.280,0:13:09.180
us that our standard error[br]should be equal to the standard

0:13:09.180,0:13:13.350
deviation of our original[br]distribution, 9.3, divided by

0:13:13.350,0:13:15.400
the square root of n, divided[br]by the square root

0:13:15.400,0:13:16.380
of 25, right?

0:13:16.380,0:13:18.410
4 was just the[br]square root of 16.

0:13:18.410,0:13:21.860
So this is equal to[br]9.3 divided by 5.

0:13:21.860,0:13:23.820
And let's see if it's 1.87.

0:13:23.820,0:13:28.320
So let me get my[br]calculator back.

0:13:28.320,0:13:36.410
So if I take 9.3 divided[br]by 5, what do I get?

0:13:36.410,0:13:41.720
1.86 which is very[br]close to 1.87.

0:13:41.720,0:13:49.480
So we got in this case 1.86.

0:13:49.480,0:13:53.150
So as you can see what we got[br]experimentally was almost

0:13:53.150,0:13:56.010
exactly-- and this was after[br]10,000 trials-- of what

0:13:56.010,0:13:56.600
you would expect.

0:13:56.600,0:13:58.690
Let's do another 10,000.

0:13:58.690,0:14:00.220
So you've got another[br]10,000 trials.

0:14:00.220,0:14:01.550
Well we're still[br]in the ballpark.

0:14:01.550,0:14:04.920
We're not going to-- maybe I[br]can't hope to get the exact

0:14:04.920,0:14:07.350
number rounded or whatever.

0:14:07.350,0:14:10.690
But as you can see, hopefully[br]that'll be pretty satisfying to

0:14:10.690,0:14:14.410
you, that the variance of the[br]sampling distribution of the

0:14:14.410,0:14:21.500
sample mean is just going to be[br]equal to the variance of your

0:14:21.500,0:14:23.790
original distribution, no[br]matter how wacky that

0:14:23.790,0:14:27.370
distribution might be, divided[br]by your sample size-- by the

0:14:27.370,0:14:33.530
number of samples you take for[br]every basket that you average I

0:14:33.530,0:14:35.220
guess is the best way[br]to think about it.

0:14:35.220,0:14:37.710
You know, sometimes this can[br]get confusing because you are

0:14:37.710,0:14:40.275
taking samples of averages[br]based on samples.

0:14:40.275,0:14:43.300
So when someone says sample[br]size, you're like, is sample

0:14:43.300,0:14:46.510
size the number of times I[br]took averages or the number

0:14:46.510,0:14:48.780
of things I'm taking[br]averages of each time?

0:14:48.780,0:14:51.160
And you know, it doesn't[br]hurt to clarify that.

0:14:51.160,0:14:52.790
Normally when they talk[br]about sample size

0:14:52.790,0:14:54.220
they're talking about n.

0:14:54.220,0:14:57.570
And, at least in my head, when[br]I think of the trials as you

0:14:57.570,0:15:00.700
take a sample size of 16, you[br]average it, that's the one

0:15:00.700,0:15:01.990
trial, and then you plot it.

0:15:01.990,0:15:03.680
Then you do it again and[br]you do another trial.

0:15:03.680,0:15:04.980
And you do it over[br]and over again.

0:15:04.980,0:15:06.930
But anyway, hopefully this[br]makes everything clear and then

0:15:06.930,0:15:11.340
you now also understand how to[br]get to the standard

0:15:11.340,0:15:13.750
error of the mean.

0:15:13.750,0:15:14.848