1. Central Tendency 2011, 9, 27

2. Today’s Topics  What is central tendency?  Three central tendency measures –Mode –Median ＊ –Mean ＊

3. Central Tendency is a statistical measure to determine a single score that defines the center of a distribution. ModeMedianMean

4. The score or category that has the greatest frequency The score or category that has the greatest frequency Mode:  Set of n=20 scores was obtained from a 10-point quiz: 8, 9, 8, 7, 10, 5, 6, 4, 9, 8, 7, 8, 10, 9, 8, 6, 9, 7, 8, 8

5. Mode:

6. The score that divides a distribution exactly in half The score that divides a distribution exactly in half  Exactly 50% of the individuals in a distribution have scores at or below the median.  Distribution with odd numbers (n = 5): 11, 5, 10, 8, 3  Distribution w/ even numbers (n = 6): 4, 5, 7, 3, 3, 8  Using Frequency Distribution Table to find the median Median:

7. Frequency Distribution Table X, n=20 fP%c% 102.110100 94.202090 87.353570 73.151535 62.11020 51.05510 41.0555

8. Adding all observations and then dividing by the number of observation Adding all observations and then dividing by the number of observation  Mean = 7.7  Basic Notations for mean: Mean:  (mu): Population mean  Population parameter  (X-bar): Sample mean  Sample statistic

9. ModeMedianMean In-Class Exercise 5

10. Shape and Central Tendency Pos. Skewed Neg. Skewed

11. Characteristics of a Mean  Exam I: Mean = 88.5 –Change/add/delete a given score, then the mean will change –Add/subtract a constant to each score, then the mean will change by adding (or subtracting) that constant –Multiply (or divide) each score by a constant, then the mean will change by being multiplied by that constant

12. Lecture Recap  What are central tendency measures for a distribution? –Mode –Median –Mean  Central tendency measures and shape of a distribution –When to use mode, median, or mean?  Characteristics of a mean