All language subtitles for 04 - Introduce the central limit theorem

- [Instructor] One of the dangers of business data analysis

is making decisions too soon.

The reason is that short-term results can be deceiving.

But you should start to see patterns

as you gather more data.

One reliable principle of data analysis

is the central limit theorem, which says that as the number

of measurements increases, the more likely it is

that your data will be distributed as you expect.

As an example, let's say that your data

is normally distributed.

And a normal distribution has an average

and also a standard deviation.

In this case, we're looking at a so-called normal curve

with a mu or average value of 100

and a standard deviation of 20.

And you can see a curve of values on this graph.

And on the left, in the vertical axis,

there is the probability of a specific value occurring.

So you can see that the chance of getting exactly 100 is 2%.

That's pretty low but there are a lot

of values clustered around it.

And that is where the power of the normal curve

and normal distribution comes into play.

If your data is normally distributed, and a lot of it is,

then you should expect to see about 68% of your values

in your data set within one standard deviation

plus or minus of the mean.

In this case, that would mean that 68% of your values

would be between 80 and 120.

So again, that's the average or mean of 100 minus 20 for 80

and plus 20 for 120.

You can also expect to see about 95% of your values

within two standard deviations plus or minus,

between 60 and 140, and approximately 99.7% of values

within three standard deviations plus or minus.

And of course the probabilities of seeing other values

get smaller as you go further away from the average.

It doesn't mean they never occur but it does mean

that they are very rare.

To show you how this data works in practice,

I will switch to an Excel workbook, which you can find

in the exercise files collection, to use a macro

to generate random values and show you

what it looks like in practice.

The workbook I'm using is 01_04 Central Limit Theorem.

And as I said, it is available

in the exercise files collection.

This workbook uses macros so I'm going to go ahead

and enable that content.

If you're not able to run macros on your own system,

then you probably won't be able

to interact with this workbook.

But if you can, go ahead and click Enable Content

and we're ready to go.

So what just happened was that Excel recalculated

my workbook and I have a new set of random values.

I have 30 values and again it's within plus or minus

three standard deviations from the mean.

Currently I have 30 values selected.

And if I click the 30 button and you'll see

that I have four values that are one standard deviation

above the mean and I have one that is three

standard deviations below and so on.

But also note that the values are distributed

in what appears to be a flat pattern.

You don't see the curve that we saw in the graphic earlier.

Now let's go up to 100 values. So I click 100.

And you can see we're starting to get something

that looks a little bit more like a curve.

We're seeing more clustering toward the middle.

So I'll click 100 again. 100 again.

And we're seeing patterns but it's not

what we looked at before.

So now click 1,000.

And here the pattern really does start to develop

because we have created or randomized more values

and we're seeing a bit more of a hump in the middle.

And if I click there again.

And you can see that the pattern

is much more like what we expected.

Now click 10,000.

And here the curve really starts to look like

what we saw in the graphic earlier.

So you have 10,000.

And it's still a little bit lumpy in the sense

that some bars are larger than others toward the middle.

But it looks very much like the curve we saw.

And finally, if I click 100,000,

then the curve looks almost perfect.

Because we're taking so many values,

we've had the opportunity to smooth out random chance

and our values look very much like the normal curve

that we saw before.

So keep measuring, keep analyzing, and keep an open mind

as to what your data tells you.