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Chapter 1:
Looking at Data--Distributions
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, back-to-back, split), histograms, and boxplots
(regular, modified, side-by-side).
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, 5-number 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.