# Probability and Statistics

### Topics

Bivariate data is data where two values are recorded for each observation (as opposed to univariate data). We could look at a bunch of cars in a parking lot, write down both their manufacturers and colors, and come up with data like this:

Toyota, red

Honda, blue

Honda, black

Ferrari, red

Ford, grey

Ford, white

Honda, blue

Honda, black

Most likely, we are writing down this information because several people parked like idiots and we want to report them. But we may also simply be solving an algebra problem. As in this case.

We can organize this data by sticking it into a table. The table can go either this way:

or that way:

Just depends on whether you're in more of a horizontal or vertical mood. If you're in a vertical mood, you probably still haven't gotten out of bed.

In the car example, both variables were qualitative and categorical. We could have one variable be qualitative and the other be quantitative. We could also have both variables be quantitative. Our head is swimming from having so many options.

### Sample Problem

If we record the heights and weights of a bunch of people we get bivariate data where both variables are quantitative:

No comment about the last guy.