All language subtitles for 04 - Use the Poisson distribution

- [Instructor] If you analyze business data,

and especially if you perform any kind of simulation,

it's useful to know about the Poisson Distribution.

In this movie,

I will describe the characteristics of that distribution

and also show you how to use it in Excel.

The Poisson Distribution uses an average called Lambda

and it determines the amount of time

between events occurring.

So for example, if you have customers

that arrive on average every seven minutes,

then this is what the curve would look like

given that your data is distributed

according to the Poisson Distribution.

To show what that looks like in Excel,

I will switch over to our workbook.

I've switched over to Excel

and my sample file is 04_04_Poisson

and you can find that in the Chapter Four folder

of the Exercise Files collection.

And this distribution is called the Poisson Distribution

because it was created, or at least discovered,

by a French mathematician by the name of Poisson.

The idea is that you want to calculate

the probability of specific gaps between events,

such as customers arriving.

I've already set up a worksheet with a number of values

and also my mean, or Lambda, which is seven.

You can see that in cell E1.

So, now I can calculate the probabilities

of each of these gaps between events.

So, I'll click in cell B2 and type an equal sign.

And as you might guess,

based on the way that functions are named,

we'll use Poisson, P-O-I-S-S-O-N dot D-I-S-T.

We need three pieces of information.

The first is our X value that we're comparing. That's in A2.

Then a comma. The mean is in cell E1.

And I don't want that reference to change,

so I will press F4, that's on Windows.

If you're on a Mac it's command T.

Then a comma,

and we want the probability mass function

or point probability.

So we want to know the probability

of an exact value occurring.

So I will use the down arrow key to highlight false.

Press tab, right parentheses, and enter.

So we can see that the probability of a customer

arriving at the same time as another customer is very low.

So it's less than 1/100 of a percent.

We can now create the same calculation

for the other values in my list.

So, I will click cell B2

and then move my mouse pointer

over the bottom right corner of the cell

and double click the fill handle.

And there we see the probability.

So, we have our mean of seven,

which occurs here at the top

and will happen about 15% of the time.

It's the same for six minutes between occurrences

in this case.

And you can see the other probabilities

according to this curve.

You can also determine the likelihood

of a specific gap between customers or less occurring.

And to do that, all you need to do

is change the last argument from false,

which will give you the point probability,

to true, which gives you the cumulative probability.

So if I make sure that B2 is selected,

I can double click it,

and then I will edit the last value

or the last argument from false to true, enter.

I get the same value because I'm only looking at zero.

And then, I will click cell B2,

double click the fill handle,

and there we see the probability.

So as you can see, it's rare that we will get values

between zero and five.

Those will happen about a quarter of the time.

And then up to 10, because remember our average is seven.

We have a probability cumulatively of 0.9

and then as we get further out,

the values get closer and closer to one.

Two final things to note about the Poisson Distribution.

The first is that it only deals with whole numbers,

so you won't get any decimals in there.

And secondly, you can think of it

as the inverse of the exponential function.

Remember when we used the exponential function

we needed to divide one by Lambda.

In the Poisson Distribution, we use Lambda by itself.