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CHAPTER 7:
Exploring Data: Part I Review
Exploring One Variable
2
Exploring Data – Two Variables
3
Chapters 1-6
4
A: Data
Identify the individuals and variables in a set of data.
 Identify each variable as categorical or quantitative.
 Identify the explanatory and response variables in
situations where one variable explains or influences
another.

Chapters 1-6
5
B: Displaying Distributions
Recognize when a pie chart can and cannot be used.
 Make a bar graph of the distribution of a categorical
variable or, in general, to compare related quantities.
 Interpret pie charts and bar graphs.
 Make a histogram of the distribution of a quantitative
variable.
 Make a stemplot of the distribution of a small set of
observations.
 Make a time plot of a quantitative variable over time.
Recognize patterns such as trends and cycles in time
plots.

Chapters 1-6
6
C: Describing Distributions (Quantitative)
Look for the overall pattern and for major deviations
from the pattern.
 Assess the shape of a distribution from a histogram or
stemplot.
 Describe the overall pattern by giving numerical
measures of center and spread in addition to a verbal
description of shape.
 Decide which measures of center and spread are more
appropriate.
 Recognize outliers and give plausible explanations for
them.

Chapters 1-6
7
D: Numerical Summaries of Distributions
Find the median and quartiles for a set of observations.
 Find the five-number summary and draw a boxplot.
 Find the mean and standard deviation for a set of
observations.
 Understand that the median is more resistant than the
mean. Recognize that skewness in a distribution moves
the mean away from the median toward the long tail.
 Know the basic properties of the standard deviation.

Chapters 1-6
8
E: Density Curves and Normal Distributions
Know that areas under a density curve represent
proportions of all observations and that the total area
under a density curve is 1.
 Approximate the median and mean on a density curve.
 Know that the mean and median both lie at the center
of a symmetric density curve and that the mean moves
toward the long tail of a skewed curve.
 Recognize the shape of Normal curves and estimate by
eye both the mean and standard deviation from such a
curve.

Chapters 1-6
9
E: Density Curves and Normal Distributions (con’t)
Use the 68-95-99.7 rule and symmetry to state what
percent of the observations from a Normal distribution fall
between two points when both lie at one, two, or three
standard deviations from the mean.
 Find the z-score of an observation. Interpret z-scores.
 Given that a variable has a Normal distribution, calculate
the proportion of values above, below, and between
stated values.
 Given that a variable has a Normal distribution, calculate
the point having a stated proportion of values above or
below it.

Chapters 1-6
10
F: Scatterplots and Correlation
Make a scatterplot to display the relationship between
two quantitative variables.
 Add a categorical variable to a scatterplot.
 Describe the direction, form, and strength of the overall
pattern of a scatterplot. Recognize outliers.
 Judge whether it is appropriate to use correlation to
describe the relationship between two quantitative
variables. Find the correlation r.
 Know the basic properties of correlation r.

Chapters 1-6
11
G: Regression Lines
Understand that regression requires an explanatory and
a response variable. Use a calculator or software to find
the least-squares regression line.
 Explain what the slope and intercept mean in the
equation of a regression line.
 Draw the graph of a regression line when given an
equation.
 Find the slope and intercept of the least-squares
regression line from the means and standard deviations
of x and y and their correlation.

Chapters 1-6
12
G: Regression Lines (con’t)
Use r2 to describe how much of the variation in one
variable can be accounted for by a straight-line
relationship with another variable.
 Recognize outliers and potentially influential observations
from a scatterplot with the regression line drawn on it.
 Calculate the residuals and plot them against the
explanatory variable.

Chapters 1-6
13
H: Cautions about Correlation and Regression
Understand that both r and the least-squares regression
line can be strongly influenced by a few extreme
observations.
 Recognize possible lurking variables that may explain the
observed association between two variables.
 Understand that even a strong correlation does not mean
there is a cause-and-effect relationship between x and y.
 Give plausible explanations for an observed association
between two variables.

Chapters 1-6
14
I: Categorical Data
Find the marginal distributions from a two-way table.
 Express any distribution in percents.
 Describe the relationship between two categorical
variables by comparing the conditional distributions of
one variable for the different categories of the other
variable.
 Recognize Simpson’s paradox and be able to explain it.
