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Multiple choice questions…grab handout!
Data Analysis: Displaying Quantitative Data
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In any graph, we look for the overall pattern and
for striking departures from that pattern. We
describe the overall pattern with shape, center,
and spread.
We describe departures from the pattern with
outliers, individuals that fall outside of the
overall pattern.
As a mnemonic device we sometime call
describing a distribution “checking our SOCS,” or
“remembering our SOCS.”
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A distribution is roughly symmetric if the right and left
sides of the graph are approximately mirror images of
each other.
A distribution is skewed to the right if the right side of
the graph (containing half of the observations with
larger values) is much longer than the left side.
Similarly to skewed to the right, a distribution is skewed
to the left if the left side of the graph (containing half
the observations with smaller values) is much longer
than the right side.
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Other common types of shape are: unimodal
or having a single peak, bimodal or having
two peaks, multimodal or having many peaks,
moundlike or resembling a single mound or
hill, and normal which we will define and
cover in detail later.
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The common measures of center we use are
mean, median, and mode.
◦ Mean is the average of a data set
◦ Median is the middle value of the data set
◦ Mode is the value that appears most often.
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Range is the numerical representation of the
distance between the largest and smallest value
in a data set.
Standard Deviation and Variance are also
measures of spread, these will be covered in
detail in the next section
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Shape?
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Center?
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Spread?
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Potential Outliers?
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How many pairs of shoes does a typical
teenager have? Here are the results from a
random sample:
50, 26, 26, 31, 57, 19, 24, 22, 23, 38, 13, 50, 13, 34,
23, 30, 49, 13, 15, 51
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Quantitative
Variables!
A bar graph with no
gaps in between.
The frequencies are
the heights of the
bars.
The x-axis is
divided into
“classes” or
intervals.
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75, 65, 121, 100, 101, 89, 114, 63, 123, 127, 100, 96, 116,
109, 92, 131, 134, 105, 108, 117, 90, 89, 101, 101, 89, 98,
104, 130, 128, 97, 113, 129, 106, 87, 107, 68
Class
Freq
60-69
70-79
80-89
90-99
100-109
110-119
120-129
130-139
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Shape determines the measure of center, and
center determines the measure of spread.
Outliers will always be calculated the same
way, independent of shape.
When graphing, don’t confuse histograms
(quantitative data) and bar graphs
(categorical data).
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Pg 42 (37, 39, 41-47, 50-52, 58-62, 64, 66-68)