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Chapter 21
Describing Data Through Statistics
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Types of Statistics
Descriptive statistics
Used to describe and synthesize data
Inferential statistics
Used to make inferences about the population
based on sample data
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Frequency Distributions
• A systematic arrangement of numeric values on a
variable from lowest to highest, and a count of the
number of times each value was obtained
• Frequency distributions can be described in terms
of:
– Shape
– Central tendency
– Variability
Copyright © 2008 Wolters Kluwer Health | Lippincott Williams & Wilkins
Construction of Frequency Distributions
• Can be presented in tabular form (counts
and percentages)
• Can be presented graphically
– Histograms
– Frequency polygons
Copyright © 2008 Wolters Kluwer Health | Lippincott Williams & Wilkins
Shapes of Distributions
1. Symmetry
• Symmetric
• Skewed (asymmetric)
 Positive skew (long tail points to the
right)
 Negative skew (long tail points to the
left)
Copyright © 2008 Wolters Kluwer Health | Lippincott Williams & Wilkins
Examples of Symmetric Distributions
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Examples of Skewed Distributions
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Shapes of Distributions (cont.)
2. Peakedness (how sharp the peak is)
3. Modality (number of peaks)
 Unimodal (1 peak)
 Bimodal (2 peaks)
 Multimodal (2+ peaks)
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Modality
• Symmetric
• Unimodal
• Not too peaked, not too flat
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Distribution of Values: Central Tendency
Index of “typicalness” of set of scores
that comes from center of the
distribution
Mode—the most frequently occurring
score in a distribution
2
3
3
3
4
5
6
7
8
9
Mode = 3
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Distribution of Values: Central Tendency
(cont.)
• Median—the point in a distribution
above which and below which 50% of
cases fall
2
3
3
3
4
5
6
7
8
9
Median = 4.5
• Mean—equals the sum of all scores
divided by the total number of scores
2
3
3
3
4
5
6
7
8
9
Mean = 5.0
Copyright © 2008 Wolters Kluwer Health | Lippincott Williams & Wilkins
Indexes of Central Tendency
• Mode, useful mainly as gross descriptor,
especially of nominal measures
• Median, useful mainly as descriptor of
typical value when distribution is skewed
• Mean, most stable and widely used
indicator of central tendency
Copyright © 2008 Wolters Kluwer Health | Lippincott Williams & Wilkins
Variability of Distributions
The degree to which scores in a distribution
are spread out or dispersed
• Homogeneity—little variability
• Heterogeneity—great variability
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Two Distributions of Different Variability
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Indexes of Variability
• Range: highest value minus lowest value
• Standard deviation (SD): average deviation
of scores in a distribution
• Variance: a standard deviation, squared
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Standard Deviations in a
Normal Distribution
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Contingency Table (or Crosstab)
• A two-dimensional frequency distribution;
frequencies of two variables are crosstabulated
• “Cells” at intersection of rows and columns
display counts and percentages
• Variables must be nominal or ordinal
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Contingency Table for Gender and
Smoking Status Relationship
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Correlation Procedures
• Indicate direction and magnitude of relationship
between two variables
• Used with ordinal, interval, or ratio measures
• Can be shown graphically (scatter plot)
• Correlation coefficient (usually Pearson’s r) can
be computed
• With multiple variables, a correlation matrix can
be displayed
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Various Relationships Graphed
on Scatter Plots
Copyright © 2008 Wolters Kluwer Health | Lippincott Williams & Wilkins