Central Tendency Quantitative Methods in HPELS 440:210

Agenda Introduction Mode Median Mean Selection

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

Introduction The Three M’s:  Mode  Median  Mean Each statistic has its advantages and disadvantages

Agenda Introduction Mode Median Mean Selection

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

Central Tendency: Mode Example: 2, 3, 4, 6, 7, 8, 8, 8, 9, 9, 10, 10, 10, 10 Mode?

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

Calculation of the Mode  Instat Statistics tab Summary tab Group tab  Select “group”  Select column of interest  OK

Agenda Introduction Mode Median Mean Selection

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

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

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

Calculation of the Median  Instat Statistics tab Summary tab Describe tab  Choose “additional statistics”  Choose “median”  OK

Agenda Introduction Mode Median Mean Selection

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

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

Calculation of the Mean  Instat Same as median Mean is calculated automatically

Agenda Introduction Mode Median Mean Selection

When to Use the Mode Appropriate for all scales of measurement Use the mode with nominal data

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

When to Use the Median Use the median with undetermined values

When to Use the Median Use the median with open-ended distributions

When to Use the Mean Use the mean with interval or ratio data Use the mean when the distribution is normal or near normal

Textbook Problem Assignment Problems: 2, 4, 6, 8, 12, 16, 22.