Central Tendency

Quantitative Methods in HPELS

440:210

Agenda

Introduction Mode Median Mean Selection

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

Introduction

The Three M’s:ModeMedianMean

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 scalesOnly statistic appropriate for nominal data

On a frequency distribution:Tallest portion of graphCategory 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 interestOK

Agenda

Introduction Mode Median Mean Selection

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

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 dataEspecially 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.