Now, you might think it doesn't look that good, actually, [LAUGH] right?

So what's wrong with this picture?

Well, you got this huge spike in the histogram at around $10, okay?

That's not predicted by the volume,

the normal distribution doesn't have a huge spike right there, and furthermore,

there are no values that are either close to zero or negative, whereas the normal

distribution has all these negative values in its functional form.

So it doesn't look like the histogram really fits that well.

So what are we going to do about that?

So there may be multiple problems.

There may be multiple explanations for why the histogram from the data

doesn't look like what we'd expect from a normal distribution.

For starters, the data may not even be representative of the population.

This is just a website that was up there and anyone who just happened to come by

could fill in their name and say what price they'd be willing to pay.

Who knows who these people were, who knows if they were even prospective customers,

people who would actually buy the product?

So that the data collection process might have been very skewed.

We have no real way of knowing that.

But on the other hand it could be that the model clearly just does not fit well and

we may need to revise the model too.

It may be easier in some circumstances to revise the model than to revise the data,

especially at the data collection process.

Is very expensive, okay?

So one of the things we can do is let's try the gamma distribution.

Okay, so the gamma distribution is another model and

one of its key features is that it only allows for positive values.

So unlike the normal which has negative and positive values.

The gamma distribution only allows positive values.

So then we can just repeat all the steps that we just went right through.

We can set expectations.

We can draw a fake picture and then we can compare our expectations to the data.

Okay.

So, I'll skip the first two steps there, and I'll just show you,

here's what the picture looks like with the data,

and the gamma distribution that's fitted on top of it, okay?

So you can see from this picture that the fit's not perfect either, okay?

Maybe, you could argue it's a little bit better,

you've got a little hump wherever that spike at ten is.

But it's not, it doesnt exactly fit it perfectly, and still you have a bunch of,

the curve, is kind of covering values where there's no data between the zero and

five range.

And now, but the important thing is that we have a different model, and so

a different model is gonna yield different predictions.

So this model is telling us something completely different about the population

than the normal model was, right?

So the normal model told us there was gonna be a big hump kind of around 20.

But this model tells us that the hump's more like around seven and ten.

Okay?

So the model is telling us something very different about what the population is

willing to pay for this product.

Okay?

For example,

before we said that 11% of people would be willing to pay more than $30.

However, if we use the gamma model

we find that only 7% of people would be willing to pay more than $30.

So the importance of using models, different types of models is that

they tell you very different things about the population, and

they result in very different predictions.

And so, if you're interested in making these predictions and

being accurate about them, you want to make sure you have a model that's

reasonably a reasonable approximation of the population.

And you can use the data to help you see if that fits well.

Now we have looked at two different types of models

to tell us about our data and to tell us about the population, okay?

So now you may want to keep, continue to refine this, think about different models.

Obviously this last one didn't really fit perfectly, so you might wanna

either refine your model or you might want to do another survey to get more data,

to get a better sense and so you kind of think about where you go from here.

The point of this whole exercise is that you get a little sketch

of where you're gonna go and kinda what your solution's gonna be.

If your question was originally, how much are people willing to pay for

this product, you have a better sense now in terms of

what the shape of that distribution might look like.

And what the population might be willing to do.

From here where you go, it depends.

You may have enough information as it is to kind of set prices or

to figure out how your marketing campaign's gonna go.

Or you might want to go into more formal modeling.

So you can test the sensitivity of your assumptions,

of your expectations to various features.

So that's what we'll talk about more when we talk about formal modeling.