Page 32 - Statistics for Dummies

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Part I: Vital Statistics about Statistics
✓ Some of the basic graphs used for categorical data include pie charts
and bar graphs, which break down variables, such as gender or which
applications are used on teens’ cellphones. A bar graph, for example,
may display opinions on an issue using five bars labeled in order from
“Strongly Disagree” up through “Strongly Agree.” Chapter 6 gives you all
the important info on making, interpreting, and, most importantly, evalu-
ating these charts and graphs for fairness. You may be surprised to see
how much can go wrong with a simple bar chart.
✓ For numerical data such as height, weight, time, or amount, a different
type of graph is needed. Graphs called histograms and boxplots are
used to summarize numerical data, and they can be very informative,
providing excellent on-the-spot information about a data set. But of
course they also can be misleading, either by chance or even by design.
(See Chapter 7 for the scoop.)
You’re going to run across charts and graphs every day — you can open
a newspaper and probably find several graphs without even looking hard.
Having a statistician’s magnifying glass to help you interpret the information
is critical so that you can spot misleading graphs before you draw the wrong
conclusions and possibly act on them. All the tools you need are ready for you
in Chapter 6 (for categorical data) and Chapter 7 (for numerical data).
Determining Distributions
A variable is a characteristic that’s being counted, measured, or categorized.
Examples include gender, age, height, weight, or number of pets you own.
A distribution is a listing of the possible values of a variable (or intervals of
values), and how often (or at what density) they occur. For example, the dis-
tribution of gender at birth in the United States has been estimated at 52.4%
male and 47.6% female.
Different types of distributions exist for different variables. The following
three distributions are the most commonly occurring distributions in an intro-
ductory statistics course, and they have many applications in the real world:
✓ If a variable is counting the number of successes in a certain number
of trials (such as the number of people who got well by taking a certain
drug), it has a binomial distribution.
✓ If the variable takes on values that occur according to a “bell-shaped
curve,” such as national achievement test scores, then that variable has
a normal distribution.
✓ If the variable is based on sample averages and you have limited data,
such as in a test of only ten subjects to see if a weight-loss program
works, the t-distribution may be in order.

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