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80 UNIT 1 Exploring One-Variable Data

UNIT 1, PART I REVIEW

SECTION 1A Statistics: The Language of Variation striking departures from that pattern (outliers). When com-
paring distributions of quantitative data, you should include
In this brief section, you learned how to identify the indi- explicit comparison words for center and variability such as “is
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viduals and variables in a data set. You also learned how to greater than” or “is approximately the same as.” When asked
distinguish between categorical variables and quantitative to compare distributions, a very common mistake on the AP
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variables, as well as how to summarize the distribution of a Statistics exam is describing the characteristics of each distri-
variable with a frequency table or relative frequency table.
bution separately without making these explicit comparisons.
SECTION 1B Displaying and Describing SECTION 1D Describing Quantitative Data
categorical Data
with Numbers
In this section, you learned how to display the distribution of a To measure the center of a distribution of quantitative data,
categorical variable with a bar graph or a pie chart, and what you learned how to calculate the median and the mean of
to look for when describing these graphs. Next, you learned a distribution. You also learned that the median is a resistant
how to compare the distribution of a categorical variable in measure of center, but the mean isn’t resistant because it can
two or more groups using side-by-side bar graphs. Remember be greatly affected by skewness or outliers.
to properly label your graphs! Poor labeling is an easy way to To measure the variability of a distribution of quanti-
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lose credit on the AP Statistics exam. You should also be able tative data, you learned how to calculate the range, stan-
to recognize misleading graphs and be careful to avoid making dard deviation, and interquartile range (IQR). The range
misleading graphs yourself.
measures the distance from the minimum value to the max-
imum value, while the standard deviation measures the
SECTION 1C Displaying Quantitative typical distance of values in the distribution from the mean.
Data with Graphs
The range and standard deviation are not resistant — both
In this section, you learned how to make three different types are heavily affected by extreme values. The interquartile
of graphs for displaying quantitative data: dotplots, stemplots, range (IQR) is a resistant measure of variability because it
and histograms. Each of the graphs has distinct benefits, but ignores the upper 25% and lower 25% of the distribution.
all of them are good tools for examining the distribution of a To identify outliers in a distribution of quantitative
quantitative variable. Dotplots and stemplots are handy for data, you learned the 1.5 × IQR rule and the less common
smaller sets of data. Histograms are the best choice when there 2 × SD rule. You also learned that boxplots are a great way
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are a large number of data values. On the AP Statistics exam, to visually summarize a distribution of quantitative data.
you will be expected to make, interpret, and describe each of Boxplots are helpful for comparing the center (median) and
these types of graphs. the variability (range, IQR) for multiple distributions. Box-
When you are describing the distribution of a quantita- plots aren’t as useful for identifying the shape of a distribu-
tive variable, you should look at a graph of the data to deter- tion because they do not display peaks, clusters, gaps, and
mine the overall pattern (shape, center, variability) and other interesting features.

What Did You Learn?

Related Example Relevant Review
Learning Target Section on Page(s) Exercise(s)
Identify the individuals and variables in a set of data, and classify the variables 1A 4 R1
as categorical or quantitative.
Make and interpret a frequency table or a relative frequency table for a distribu- 1A 6 R2
tion of data.
Make and interpret bar graphs of categorical data. 1B 12 R2
Compare distributions of categorical data. 1B 13 R4
Identify what makes some graphs of categorical data misleading. 1B 15 R3
Make and interpret dotplots of quantitative data. 1C 23 R5

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