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 video, explore the characteristics of that distribution and learn you how to use it in Excel.
- [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. My sample file is the Poisson workbook and you can find it in the chapter four folder of your exercise files collection. The Poisson distribution which is named after a French mathematician allows you to estimate the number of customers who will come into a store during a given time period such as a 10-minute segment.
You can also use it for other purposes such as the number of cars arriving at a tollbooth within a specific time frame. Again, it can be 10 minutes, every minute, and so on. The only parameter of the Poisson distribution that you need to know to do your calculations is the average time or the average number of occurrences. The mean that I have in cell B1 is three. So let's assume that means that in the three o'clock hour at a sandwich shop that approximately three customers will arrive within a 10 minute segment.
What I want to do is to calculate the probability of a specific number of customers coming in and then also the total probability which would be the cumulative probability of a specific number of customers or less. We'll start out by calculating the probability that we will see zero customers in our 10-minute segment. So in cell B3, I'll type an equal sign, and the function we'll use is Poisson.DIST.
Now I can input my arguments. The first is x and that is the number that we are inquiring about. That's zero, that's in cell A3 so I'll type that reference. And I will leave it as a relative reference so it will change when copied. Then a comma. The mean is in cell B1 so I'll type B1 and I will press F4 to make the reference absolute, unchanging. Then a comma. Now I indicate whether I want the cumulative probability that is a specific number or less or the specific probability also called the probability mass function.
For this formula, I want the specific probability so I will highlight false, press tab. Type a right parentheses and enter. And I see that the probability is right at 5%, just under. To copy my formula down, I can click cell B3 and double click the Fill handle. I know my mouse pointer's in the right place when it changes to a black crosshair. Double click and we get the specific probabilities and you can see the probability of getting 12 customers is extremely small, almost zero.
Now we can do the same thing for the total or cumulative probability. The formula will be almost exactly the same. The only difference is that we'll set the last argument to true. So in cell C3, I'll type an equal sign, POISSON.DIST, the value's in A3, comma. The mean is still in B1 so I'll type B1 then press F4 to make it absolute, comma, and then make sure true for the cumulative probability. Distribution is highlighted, press tab.
Right parentheses and enter. And when I do, I see a value that is very similar to the value in B3. It is actually the same value. It's just rounded to one less place to the right of the decimal because column C is narrower than column B. They are actually the same value. Now as before I can double click the Fill handle, this time at the bottom right corner of cell c3 and fill in the values. So you see that we have about a 5% probability of getting zero customers.
20% approximately of getting zero or one. 42% of up to two. 64.7% of up to three, and so on. The Poisson distribution is extremely useful. If you perform simulations and you need to know the number of arrivals within a specific period of time, this is what you'll use.
- Distinguish between the mean, median, and mode.
- Describe the relationship between variance and standard deviation.
- Identify a nondirectional hypothesis.
- Point out the difference between COVARIANCE.P and COVARIANCE.S.
- Explain correlation.
- Analyze Bayes’ rule.