Review Sheet for Test I, Fall 2016
Colorado State University, Pueblo
Math 156 — Introduction to Statistics

Definitions

Terms you should know -- be able to state clearly what they mean, recognize them in examples, and create your own examples of them
  1. individuals, sample, and population
  2. parameter and statistic
  3. variables/measurements, being categorical/qualitative or quantitative
  4. pie chart
  5. bar graph
  6. stem[-and-leaf] plot
  7. histogram
  8. symmetric, skew
  9. quantitative measures of center and spread:
    1. mean $\bar{x}$ and median (and mode)
      • using mean and median to determine right or left skew
    2. quartiles $Q_1$ and $Q_3$
    3. variance $s^2$, standard deviation $s$, IQR, and range
    4. sensitivity of the above to outliers
  10. the five number summary
  11. boxplots (=box-and-whisker plots)
  12. outliers, the 1.5 IQR rule
  13. the $z$-score of a data value
  14. the Empirical or 68-95-99.7 Rule
  15. probability: the idea, also sample space, outcomes, events, fair coins and dice
  16. Venn diagrams
  17. operations on sets
  18. mutually exclusive events
  19. conditional probability
  20. [in]dependent events
  21. random variables [RVs], being discrete or continuous
  22. [probability] distribution of a discrete RV
  23. mean/expectation/expected value of a discrete RV
  24. density function of a continuous RV
  25. the Normal distribution
  26. the standard Normal distribution

Things to know how to do

  1. given some data:
    1. make any of the graphs mentioned above, by hand or with help from an electronic tool
    2. compute any of the quantitative statistical measures above, by hand or with help from an electronic tool
    3. interpret/apply any of the above qualitative terms for the given data
    4. determine if there are any outliers and, if so, what they are
  2. know the strengths and weaknesses of the various graphical and quantitative statistical measures above, and chose the appropriate one in a particular situation
  3. determine probabilities for events described in words
  4. know when to use conditional probability
  5. know how to compute a probability from a continuous RV density function
  6. making a Venn diagram
  7. writing down the distribution of a discrete RV and computing its expectation
  8. tell if two events are dependent or independent
  9. take some text describing a statistical situation and do an ASE-type analysis: name individuals, sample, population, variables and their types, statistical methods used, give a critique.
  10. do not confuse mean and median or independent and mutually exclusive
  11. use the Empirical rule and the table or an electronic tool to find normal probabilities
  12. always, always, always, explaining your work clearly and completely, mixing explanation with calculation, and justifying each step of your work

Format of the test

Problems will be of a level of difficulty and wording similar to those on homework and quizzes. There will also be one problem with some information to interpret as if for an ASE. The total points for the test will be well more than 100, you can choose which 100 points you want to do out of the available problems. This means you should definitely choose to do first the problems about which you are the most confident, only coming back for the rest after finishing your first pass through the entire test.

Don't forget your calculator or whatever electronic tool[s] you like and notes or books to consult. While you can consult notes, you should always do so simply to make certain you have the right formula or you are checking all of the appropriate conditions — you should know the general shape of all the formulæ, results, and definitions.

How to Study

It might be a good idea to put together all of your Big Ideas, review them, and make sure you know all of the things they describe. Make sure you can make a Venn diagram, the distribution of a discrete RV, and do probability computations. Make sure you can make histograms and boxplots, find outliers, and talk about skew. Make sure you can tell if events are mutually exclusive or independent, or use the fact that one of those is true, if you are told it is.

Go over your quizzes and HW problems and make sure you know how to do those kinds of things, and that you could do them again and get perfect scores on them now. If you want more problems, try doing other problems in the books which are near and similar to the ones which were assigned. If you do odd problems, you can check the answer is correct — but remember that the answer is not the important part, it is the explanation which is important. Maybe practice writing good solutions with complete explanations and justifications of every step.

Look at your ASEs and make sure you know how you could change them so that you would get a better score (if that is possible).