Review Sheet for Test I, Spring 2017
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
- individuals, population, and sample
- variable, being categorical or quantitative
- bar graph [ or bar chart]
- pie chart
- stem[-and-leaf] plot
- histogram
- frequency and relative frequency
- shape, center, and spread
- symmetric and [right or left] skew
- unimodal, bimodal, and multimodal
- quantitative measures of central tendency and of spread:
- sample mean $\bar{x}$, population mean $\mu$,
median, and mode
- using mean and median to determine right or left skew
- quartiles $Q_1$ and $Q_3$
- sample variance $s^2$, population variance $\sigma^2$,
sample standard deviation $s$,
population standard deviation $\sigma$, IQR, and
range
- sensitivity of the above to outliers
- outliers, the 1.5 IQR rule
- the five number summary
- boxplots (=box-and-whisker plots)
- independent/explanatory and dependent/response variables
- deterministic and non-deterministic relationships between
variables
- scatterplots; their shape, strength, and
direction
- [Pearson] correlation coefficient $r$, meaning of $r^2$
- residuals, the total square error
- the least squares regression line [LSRL]
- the slope and $y$-intercept of a line
- interpolation
- bivariate outliers
- extrapolation
- correlation is not causation, but it sure is a hint
- Simpson's Paradox
Things to know how to do
- given some data:
- make any of the graphs mentioned above, by hand or with help from
an electronic tool
- compute any of the quantitative statistical measures above, by hand
or with help from an electronic tool
- interpret/apply any of the above qualitative terms for the given data
- determine if there are any outliers and, if so, what they are
- know the strengths and weaknesses of the various graphical and
quantitative statistical measures above, and chose the appropriate one in
a particular situation
- create examples of both uni- and bivariate data with any desired
graphical representation or numerical measure [of central tendency,
etc.]
- choose the right statistical computation, graphical representation, or
interpretation for a particular situation
- analyze, interpret, and critique someone else's statistical computation,
graphical representation, or other method
- interpolate, extrapolate, make predications and critiques of associations
in bivariate data
- 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.
Go over your quizzes, HW problems, and quizzes, 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. 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).