1. Click to edit Master title style Today’s Lecture Descriptive Statistics: Measures of Central Tendency And Measures of Variability

2. Click to edit Master title style Studies show that the more beautiful faces are the more average faces. So variability is ugly…

3. Click to edit Master title style The “Average” Score and Measures of Central Tendency A measure of central tendency ‘locates’ the distribution or histogram on the X axis. Remember: We are taking the average value of a variable, so the variable must be quantitative. Measure #1 (of 3): The “Mean” is the sum of the scores divided by number of scores in the set (n).

4. Click to edit Master title style SummationSummation NotationNotation  (Capital Sigma) https://www.khanacademy.org/math/trigonometry/seq_inducti on/geometric-sequence-series/v/sigma-notation-sum

5. Click to edit Master title style Formula for the Mean

6. Click to edit Master title style Formula for the Mean

7. Click to edit Master title style Formula for the Mean

8. Click to edit Master title style Formula for the Mean

9. Click to edit Master title style What if we had…

10. Click to edit Master title style Formula for the Mean

11. Click to edit Master title style Formula for the Mean

12. Click to edit Master title style Other Measures of Central Tendency

13. Click to edit Master title style Summarizing a Distribution: “ Measures of Central Tendency ” The Median = score that divides the set of scores into two halves, "smaller" & "larger". 4, 6, 9, 3, 5, 11, 2 Median: 2 3 4 5 6 9 11 "Median Position": 12345671234567

14. Click to edit Master title style Summarizing a Distribution: “ Measures of Central Tendency ” The Median = score that divides the set of scores into two halves, "smaller" & "larger". 4, 6, 9, 3, 5, 11, 2 Median: 2 3 4 5 6 9 11 "Median Position": 12345671234567

15. Click to edit Master title style Summarizing a Distribution: “ Measures of Central Tendency ” The Median = score that divides the set of scores into two halves, "smaller" & "larger". 4, 6, 9, 3, 11, 2 Median: 2 3 4 6 9 11 "Median Position": 123456123456 So, take the average of the third and fourth scores in the set.

16. Click to edit Master title style Summarizing a Distribution: “ Measures of Central Tendency ” One number to represent the entire population The Mode = the most frequent score 4, 6, 4, 3, 11, 4, 3 Mode:

17. Click to edit Master title style Summarizing a Distribution: “ Measures of Central Tendency ” One number to represent the entire population The Mode = the most frequent score 4, 6, 4, 3, 11, 4, 3 Mode:

18. Click to edit Master title style Dependent Variable: Number of Legs What’s the mode?

19. Click to edit Master title style Mode? Frequency

20. Click to edit Master title style Why 3 Different Measures of Central Tendency? Each has it’s advantages and disadvantages. The mean or median values might be rare or not even exist (so beautiful faces can be rare). The mode might be an ‘extreme’ on the edge of the distribution.

21. Click to edit Master title style Misleading Properties of the Mean What is the mean income of Survivor participants? What would the distribution look like? Mean = $1,506, 000

22. Click to edit Master title style Misleading Properties of the Mean Median = $50,000

23. Click to edit Master title style Misleading Properties of the Mean Mode = $40,000 Positive Skew: Mean > Median > Mode Negative Skew: Mean < Median < Mode

24. Click to edit Master title style Variability (Quantitative Variables)

25. Click to edit Master title style Variety: the Spice of Life? Variability in your population  Unreliability in your sample.

26. Click to edit Master title style Demo 4…Again