Central Tendency

1. Central Tendency Quantitative Methods in HPELS 440:210

2. Agenda • Introduction • Mode • Median • Mean • Selection

3. 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

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

6. Agenda • Introduction • Mode • Median • Mean • Selection

7. 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

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

9. 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

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

12. Agenda • Introduction • Mode • Median • Mean • Selection

13. 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

14. 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

15. 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

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

17. Agenda • Introduction • Mode • Median • Mean • Selection

18. 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

19. 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

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

21. Agenda • Introduction • Mode • Median • Mean • Selection

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

23. 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

25. When to Use the Median • Use the median with undetermined values

26. When to Use the Median • Use the median with open-ended distributions

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

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