1. Quantitative Methods in HPELS HPELS 6210
Central Tendency
Quantitative Methods in HPELS
HPELS 6210

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 Disadvantages 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
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 Disadvantages: 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 Advantages: Disadvantages:
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.