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Lecture

# Lecture #4: Mean, Median, Mode.doc

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McMaster University

Economics

ECON 2B03

Jeff Racine

Fall

Description

Lecture #4 (Chap 1 & 2 Continued)
-With categorical data, you’re either in a category or not (unlike numerical where
you have a chance of being in a category).
Summary Statistics: Symbolic Expression
• Population Parameters (typically unknown)
I.e.: what is the true height of everyone living on earth right now
-Summary statistics based on population data
-Designated by Greek letters (eg: sigma, mew)
• Sample Statistics (computed from sample)
-Summary statistics based on sample data
-Designated by Roman letters (eg: X bar, s)
• Observed values
-Traditionally represented by x or X
-Different values indicated by subscripts 1,2,3 etc… (eg: X , X ,1X ,2…)3
• Observation Totals
-Population total = N
-Sample Total= n
• In statistics, we often need to “accumulate” or “sum” some variable of
interest
• For example, A might denote, income, with A being the income of the first
1
person in our sample, A tha2 for the second and so on.
• It Is supremely convenient to avoid having to write things like
A 1 A +2A + 3 +A4+A +A +A 6 7 8
(A 1B) + (A 2B) + (A -3) + (A -4)
2 2
(A 1B) + (A -2)
• One convenient operator that we shall use heavily is the “summation”
(sigma) operator
• The sum of a variable X can be written as
Note: are often interchanged • Care must be taken when expanding sums. For instance,
But note that,
• Some useful manipulations involving the summation operator follow from the
definition of the arithmetic function.
• Common ones you may find useful are: Summary Measure Types
• Central Tendency Measures
-Locate a data set’

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