Central Tendency
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Transcript of Central Tendency
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Central Tendency
Quantitative Methods in HPELS
440:210
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Agenda
Introduction Mode Median Mean Selection
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Introduction Statistics of central tendency:
Describe typical value within the distributionDescribe the middle of the distributionDescribe how values cluster around the
middle of the distribution Several statistics Appropriate
measurement depends on:Scale of measurementDistribution
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Introduction
The Three M’s:ModeMedianMean
Each statistic has its advantages and disadvantages
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Agenda
Introduction Mode Median Mean Selection
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Mode
Definition: The score that occurs most frequently
Scale of measurement: Appropriate for all scalesOnly statistic appropriate for nominal data
On a frequency distribution:Tallest portion of graphCategory with greatest frequency
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Central Tendency: Mode
Example:
2, 3, 4, 6, 7, 8, 8, 8, 9, 9, 10, 10, 10, 10
Mode?
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Mode
Advantages Ease of determination Only statistic appropriate for nominal data
Disadvantages Unstable Terminal statistic Disregards majority of data Lack of precision (no decimals) There maybe more than one mode
Bimodal two Multimodal > 2
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Calculation of the Mode Instat
Statistics tab Summary tab Group tab
Select “group”Select column of interestOK
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Agenda
Introduction Mode Median Mean Selection
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Median Definition:The score associated with the 50th
percentile Scale of measurement:
Ordinal, interval or ratio Methods of determination:
N = even List scores from low to high Median is the middle score
N = odd List scores from low to high Median = sum of two middle numbers / 2
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Central Tendency: Median
Example 1:
1, 2, 3, 4, 5
Example 2:
1, 2, 3, 4
Odd #:
Median = middle number
Even #:
Median = middle two numbers / 2
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Median Advantages
Ease of determination Effective with ordinal data Effective with skewed data
Not sensitive to extreme outliers Examples: Housing costs
Disadvantages: Terminal statistic Not appropriate for nominal data Disregards majority of data Lack of precision
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Calculation of the Median Instat
Statistics tab Summary tab Describe tab
Choose “additional statistics”Choose “median”OK
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Agenda
Introduction Mode Median Mean Selection
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Mean
Definition: Arithmetic average Most common measure of central
tendency Scale of measurement:
Interval or ratio Statistical notation:
Population: “myoo” Sample: x-bar or M
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Mean Method of determination:
= ΣX/N X-bar or M = ΣX/n
Advantages: Sensitive to all values Considers all data Not a terminal statistic Precision (decimals)
Disadvantages: Not appropriate with nominal or ordinal data Sensitive to extreme outliers
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Calculation of the Mean Instat
Same as median Mean is calculated automatically
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Agenda
Introduction Mode Median Mean Selection
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When to Use the Mode Appropriate for all scales of measurement Use the mode with nominal data
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When to Use the Median
Appropriate with ordinal, interval and ratio dataEspecially effective with ordinal data
DO NOT use with nominal data Use the median with skewed data
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When to Use the Median
Use the median with undetermined values
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When to Use the Median
Use the median with open-ended distributions
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When to Use the Mean
Use the mean with interval or ratio data Use the mean when the distribution is
normal or near normal
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Textbook Problem Assignment
Problems: 2, 4, 6, 8, 12, 16, 22.