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Chapter 1:
Looking at DataDistributions
Section 1.1:
Introduction, Displaying Distributions with Graphs
Section 1.2:
Describing Distributions with Numbers
Learning goals for this chapter:
Identify categorical and quantitative variables.
Interpret, create (by hand and with SPSS), and know when to use:
bar graphs, pie
charts, stemplots (standard, backtoback, split), histograms, and boxplots
(regular, modified, sidebyside).
Describe the shape, center, and spread of data distributions.
Define, calculate (by hand and with SPSS), and know when to use measures of
center (mean vs. median) and spread (range, 5number summary, IQR, variance,
standard deviation).
Understand what a resistant measure of center and spread is and when this is
important.
Use the 1.5IQR rule to look for outliers.
Draw a Normal curve in correct proportions and identify the mean/median,
standard deviation, middle 68%, middle 95%, and middle 99.7%.
Perform calculations with the empirical rule, both backwards and forwards.
Understand the need for standardization.
Big picture:
what do we learn in this chapter?
Individuals
vs.
Variables
Categorical
vs.
Quantitative
Variables
Graphs:
Bar graphs
and
pie charts
(categorical variables)
Histograms
and
stemplots
(quantitative variables—good for checking for
symmetry and skewness)
Boxplots
(quantitative variables—graphical display of the 5 # summary, modified
boxplots show outliers)
Describing distributions
Shape
(symmetric/skewed, unimodal/bimodal/multimodal)
Center
(mean or median)
Spread
(usually standard deviation/variance or IQR from the 5 # summary)
Outliers
If you have a symmetric distribution with no outliers, use the mean and standard
deviation.
If you have a skewed distribution and/or you have outliers, use the 5 # summary
instead.
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2 components in describing data or information:
Individuals
:
objects being described by a set of data (people, households, cars,
animals, corn, etc.)
Variables
:
characteristics of individuals (height, yield, length, age, eye color,
etc.)
Categorical
:
places an individual into one of several groups (gender, eye
color, college major, hometown, etc.)
Quantitative
:
Attaches a numerical value to a variable so that adding or
averaging the values makes sense (height, weight, age, income, yield, etc.)
Distribution of a variable
:
describes what values a variables takes and how often it
takes those values
If you have more than one variable in your problem, you should look at each variable by
itself before you look at relationships between the variables.
Example:
Identify whether the following questions would give you categorical or
quantitative data.
a)
What letter grade did you get in your Calculus class last semester?
b)
What was your score on the last exam?
c)
Who will you vote for in the next election?
d)
How many votes did George W. Bush get?
e)
How many red M&Ms are in this bag?
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 Spring '08
 Staff

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