Dr. Sarah's Statistics Review Sheet

One 8.5*11 sheet with writing on both sides allowed.
Calculator and straight edge/ruler are mandatory.
Some of the questions will be similar to problems you have seen before. There will also be some problems with new twists to test your understanding of the material. Partial credit will be granted so, for example, you can receive full credit for part b) even if it depends on part a) which you did incorrectly, as long as you communicate understanding of part b) on your test.

Creating various statistical representations of data: Aside from possibly asking you to calculate the mean and/or median, I will not give you any other problems where you must create statistical representations of data, but you do need to understand how to use, read off, or analyze other representations.

Analyzing and critiquing various statistical representations of data:

Make sure that you understand what kind of information you can get from statistical representations where you are not given the underlying data (like the ASULearn Material Review Questions for Test 3. ).
Make sure that you understand how to give various spins on data and statistical representations (as if you were in advertising and wanted to use the stats to say something positive or negative about the situation, like "Here's Good News... SAT scores are declining at a slower rate").
Make sure that you understand statistical common sense in the context of the real life problem that we are working on in order to critique statistical methodology of data collection, interpretations, conclusions and predictions
- problematic instructions like the MRT test may affect the results,
- it doesn't make sense to predict someone's ability when they haven't slept for 2000 hours because a human can't stay awake that long
- the stock market is based on emotion and thus not predictable. If the r² value was 100% in an increasing stock, we anticipate something fishy is going on, since our stocks should fluctuate instead of following a linear trend. So we might be just as safe shorting the stock (betting it will decline) as investing in it.
- It is problematic to use data to predict long in the future except in very specialized circumstances like the egg bungee where we had good reason to expect a linear trend to continue because the slope, the change in distance stretched per change in rubber bands, was approximately a constant since each rubber band stretched about the same amount...

mean and median (lab, Heart of Math reading)
boxplot (How Do You Know readings, and ASULearn Material Review Questions for Test 3 - be sure that you understand and could do similar problems-
linear regression, including what kind of predictor something is (see HDYK p. 179 and put this chart on your cheat sheet), what prediction the regression line gives for x-values not on the graph (see Example 4.4 on p. 179, and p. 187 #15 part b and c, and be able to do similar calculations using the line), and whether or not the prediction makes sense given the context of the problem (see also egg bungee and linear regression lab worksheets, class notes, ASULearn questions, Buchanan votes class analysis...).

Know big picture ideas, but it is NOT necessary to know the calculation details, ie I won't ask you to do a calculation, but I do expect you to be able to discuss the highlights and point of our homework readings and class discussions on

golden mean
census and sampling issues
stereotype vulnerability and statistics related to success in mathematics
stock market issues
HIV testing
election issues

The big picture as related to our mathematicians First review the top portion of the test 2 study guide for the themes. We employed the same methodology in the statistics segment. For this test you will be asked to look at examples from the statistics segment and discuss the similarities. Ideas from the rest of this study guide work well here. For example:

Impossibility of checking all the cases, but finding a solution by shifting our viewpoint.
It is impossible to conduct a census of everyone for most data collection situations, so we have to carefully shift our view to sampling issues (elaborate).

Viewing objects that are impossible to see by managing small pieces at a time.
When we examined the Vietnam Draft info, we obtained a scatterplot that looked random to the naked eye, but it was hard to tell because there were so many points. The regression line had a negative slope, indicating that as the birthday occurred later in the year, the draft number was lower, but the r² value was very small, indicating a very weak prediction. It was impossible to see any patterns via the complete picture, so instead we broke the data up into smaller pieces - by month, via 12 boxplots. Here it was easy to see the pattern. November and December birthdays had a 75% chance of being drafted because q₃ was under the 196 draft number, while earlier birthdays only had a 50% chance, since the median was near the 196 draft number.

Similarly, reflect on statistics examples that satisfy the following:

Impossibility of constructing a solution but finding a non-constructivist approach.

Reaching numerous conclusions from a complete set of measurements