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Central Tendency

Central Tendency. 2011, 9, 27. Today’s Topics. What is central tendency? Three central tendency measures Mode Median ＊ Mean ＊. Central Tendency is a statistical measure to determine a single score that defines the center of a distribution. Mode. Median. Mean. Mode:.

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Central Tendency

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  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. Mode Median Mean

  4. Mode: The score or category that has the greatest frequency • 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. Median: 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

  7. Frequency Distribution Table

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

  9. In-Class Exercise 5 Mode Median Mean

  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

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