Study Guide

Probability and Statistics

Probability and Statistics Introduction


This unit is all about statistics and probability. Although the two are often confused, they're different areas of mathematics. Covering them both here in one unit probably isn't helping. Ah well, it'll keep you on your toes.

Statistics is about data (observations). In statistics we organize and analyze data. We come up with statements that somehow summarize what the data looks like all together, like "the average score on the test was 81." That statement doesn't reveal anything about anyone's individual test scores, but it still tells something about how the class did as a whole. The kid who got a 47 can run home to mom and dad and brag that his class averaged an 81, and they might be so proud they take him out for ice cream. His parents are apparently not statistics experts.

Here's another definition of statistics by people who do it for a living. Statistics is where we find the words "average,'' "mean," "median," and "mode.'' They can also be found in a dictionary, but they're slightly trickier to track down. Someone really should arrange all those words into alphabetical order.

Probability is about planning experiments and comparing the number of possible outcomes to the number of outcomes you want. If we roll a die and want to roll either a 1 or a 6, there are 6 possible outcomes (any of the 6 faces of the die could land facing up), but only 2 that we actually want to happen (either the 1 or the 6 facing up). Of course, if you have money on it your odds decrease substantially, as you'll then have some anti-gambling karma working against you.

Probability and Statistics Resources

Websites

Qualitative v. Quantitative Data
Do you still get these two mixed up? We don't blame you; the names are pretty similar. This site will help you distinguish between "qualitative" and "quantitative" descriptions, if you have qualms about being in a quandary. Ooh, we just made it worse, didn't we?

Math is Fun: Quartiles
Lists of numbers can sometimes get long and unwieldy, so quartiles help break them up into sections and make them more…wieldy. Check out this handy-dandy refresher; just be careful when making your cuts. Your scissors may be imaginary, but that doesn't mean they're not dangerous. (Actually, it does.)

Connexions: Introduction to Bivariate Data
Don't let the fact that this website spelled the word "Connections" wrong bother you. They know what they're talking about. See how to display bivariate data in histogram or scatter plot form, and how to interpret what you see in those graphs. Be careful while browsing: you break-variate, you bi-variate.

Video

Schooltube.com: Discrete v. Continuous Data
This video puts an interesting spin on discrete and continuous data, asking you to look at the two in a new light. Then, if that helps, try looking at them under fluorescents without getting a headache.

5min.com: How to Construct a Box and Whisker Plot
A box and whisker plot may sound like an evil scheme to pack up and ship kittens on the black market (or we have an overactive imagination, which is definitely possible), but it really just helps us organize lists of numbers and make sense of data. Even if our data relates to the salability of rare cat breeds.

Ten Marks: Histograms
Not quite sure what the difference is between a bar graph and a histogram? Make your confusion history with this helpful, step-by-step video tutorial on building histograms.

Onlinemathlearning.com: Scatter Plot and Line of Best Fit Videos
Why give you just one video when we can give you four? This page has links to four videos that will make you less scatterbrained about scatter plots. If four isn't enough for you, we believe there are even more videos out there on this thing called "the Internet."

Games and Tools

Quia.com: Mean, Median, Mode and Range
Play this "Who Wants to Be a Millionaire"-style game and try to answer all of the questions about mean, median, mode, and range correctly to move up the money list and win the big prize! Unfortunately, the fake money is awarded in pounds rather than dollars, so you'll need to factor in the exchange rate.

Math-play.com: Probability Game
See how well you do on these probability problems. If you do poorly, this obnoxious parrot will let you know about it. If you do well, you'll be able to rub it in his beak.

Math-play.com: Permutations Millionaire
Answer these permutation questions correctly and you can win a million "dollars!" Okay, so we already had a millionaire game above, but what—you couldn't use two million?