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Lecture

# Lecture #2: Distributions.doc

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McMaster University

Economics

ECON 2B03

Jeff Racine

Fall

Description

Lecture #2 (Chap 1 & 2 continued…)
Presenting Data: Tables and Graphs
• When presenting data either in the form of tables or graphs, it is often
desirable to first split the data into groups/classes
• How we split the data often depends on the data type (ie. Numeric or
Quantative)
Data types:
-Categorical (nominal or ordinal)
-Quantitative (discrete or continuous)
• Regardless of the data type, data should be:
-Collectively exhaustive: (must exhaust all logical possibilities for
classifying available data)
-Mutually exclusive: (must not overlap or have data in common)
One immediately confronts the issue of how many classes to create
Desirable class number:
-Should fit the data type
-Often recommended: between 5 and 20 classes
-Sturgess’s rule: If you don’t know how many classes to use; use this rule.
Desirable number of classes=k, where k is the integer closest to (use standard rules
for rounding)
1+ 3.3 log 10n, where n is the sample size, and where log 10n is
the power to which the
base (10) is raised to yield n
Ex: If n=1,000 than log 101000=3, so 1+3.3 log 101000=10.9 and therefore k=11
so by Sturgess’s rule you would use 11 classes when n=1,000
Data Classes
Desirable class widths:
-Class width: the difference between the lower and the upper limits of a class
-To achieve uniform class widths in a table, divide the data set width by desirable
class number
Approximate class width:
Largest value- smallest value
Desirable class number Tabular Components
• We first consider creating effective tabular summaries
• An effective table includes:
-Number (often based on chapter or page numbers)
-Title (focus on what, where and when)
-Caption (brief verbal summary)
-Footnotes (eg: size of sampling error, likely extent of systematic error, etc..)
-Decimals (consistent number or decimals)
-Rounding (consistent rounding rules)
-Class sums (sum of data pertaining to each class; crucial for open-ended
classes)
Frequency Distributions
• Frequency distributions are an effective way to summarize data
• Absolute Frequency Distributions
-Absolute class frequency:
-Absolute number of observations that fall into a given class (Total number
of observations
lying in each cla

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