00:01
All right, so we're given some data here.
00:02
Here's our data.
00:04
And we are told to find the mean, standard deviation, and standard deviation of the mean.
00:10
All right, so let's go ahead and do this.
00:11
So the mean is given as the sum of all the x values.
00:21
And you might see it as this.
00:24
I going from 1 up to n all over the sample size.
00:27
This is the notation that says add them all up and divide by how many there are.
00:32
And when we do that, i let me do that.
00:35
My spreadsheet do the work for us.
00:37
So that's what it is right here.
00:39
So the sum is 63 .15.
00:42
The mean then is 3 .1575.
00:46
And then we're going to find the standard deviation of the data set.
00:50
So the standard deviation is equal to the square root of the sum of all these squared deviations about the mean.
01:01
And this would go from minus one up to n all over n minus one because we're going to assume this is a sample.
01:09
So there's that.
01:11
And then when we do that, we end up with following calculations here.
01:20
So there we go.
01:21
So this is, these are all those squared deviations.
01:25
So it's 3 .16 minus 3 .1575.
01:29
That different squared is right here.
01:31
And do that for all 20 data points.
01:33
Boom, boom, you sum them together, and that's this number.
01:36
022975.
01:38
Divide that by, it says 20, but it's actually 19.
01:42
So please be aware of that.
01:44
It's actually 19 down there.
01:52
I know because i know it says divide by 20, but that's for the mean.
01:56
This is actually divided by 19.
01:58
So just be aware of that.
02:01
Good.
02:01
So that's our standard deviation right here.
02:05
Oh, and then the square of that is the standard deviation here.
02:07
0 .0377.
02:09
And that's our standard deviation.
02:11
And then the standard deviation about the mean, i'm going to write it as this as s.
02:19
Subx bar.
02:20
You might even see it as standard error.
02:23
That's another way to talk about it.
02:25
And what you do is you take that sample standard deviation divided by the square root of the sample size.
02:31
And that, my friends, is right here.
02:35
Again, using your spreadsheet to do, your calculations is going to help you a lot.
02:38
So there, 0 .00 followed by 3 -7s.
02:42
Good.
02:43
So the mean is used to figure out where the center of the data is.
02:47
That's what it's useful for...