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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 distribution Describe the middle of the distribution Describe how values cluster around the middle of the distribution Several statistics Appropriate measurement depends on: Scale of measurement Distribution
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Introduction The Three M’s: Mode Median Mean 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 scales Only statistic appropriate for nominal data On a frequency distribution: Tallest portion of graph Category 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 interest OK
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Agenda Introduction Mode Median Mean Selection
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Median Definition:The score associated with the 50 th 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 data Especially 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.
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