III. Summarizing Distributions


  1. Central Tendency
    1. What is Central Tendency
    2. Measures of Central Tendency
    3. Balance Scale Simulation
    4. Absolute Difference Simulation
    5. Squared Differences Simulation
    6. Median and Mean
    7. Mean and Median Simulation
    8. Additional Measures
    9. Comparing measures
  2. Variability
    1. Measures of Variability
    2. Variability Demo
    3. Estimating Variance Simulation
  3. Shape
  4. Comparing Distributions Demo
  5. Effects of Transformations
  6. Variance Sum Law I
  7. Exercises
  8. PDF Files (in .zip archive)

Descriptive statistics often involves using a few numbers to summarize a distribution. One important aspect of a distribution is where its center is located. Measures of central tendency are discussed first. A second aspect of a distribution is how spread out it is. In other words, how much the numbers in the distribution vary from one another. The second section describes measures of variability. Distributions can differ in shape. Some distributions are symmetric whereas others have long tails in just one direction. The third section describes measures of the shape of distributions. The final two sections concern (1) how transformations affect measures summarizing distributions and (2) the variance sum law, an important relationship involving a measure of variability.