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Introduction to Statistics: Averages, Variances, and Statistical Independence

Learn about averages, variances, and statistical independence in statistics. Explore frequency distributions, central tendency, and identities involving averages. Understand dispersion, deviation, and covariance. Discover how statistical independence affects functions and variables. Dive into formulas and practical applications.

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Introduction to Statistics: Averages, Variances, and Statistical Independence

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  1. Introduction to statistics Averages and variances Statistical independence Frequency P 1 2 3 4 5 6 x (# dots)

  2. Distributions 25 23 22 15 0.25 Frequency P 0.23 0.22 8 5 0.15 0.08 1 2 3 4 5 6 0.05 x (# dots)

  3. Statistics 0.25 Frequency P 0.23 0.22 0.15 0.08 1 2 3 4 5 6 0.05 x (# dots)

  4. Central tendency Average 0.25 Frequency P 0.23 0.22 0.15 0.08 1 2 3 4 5 6 0.05 x (# dots)

  5. Identities involving averages Average Average of sum 0.25 Frequency P 0.23 0.22 0.15 0.08 1 2 3 4 5 6 0.05 x (# dots)

  6. Identities involving averages Average Average of sum 0.25 Frequency P 0.23 0.22 0.15 0.08 1 2 3 4 5 6 0.05 x (# dots)

  7. Identities involving averages Average Average of sum 0.25 Frequency P 0.23 0.22 0.15 0.08 1 2 3 4 5 6 0.05 x (# dots)

  8. Identities involving averages Average Average of sum 0.25 Frequency P 0.23 0.22 0.15 0.08 1 2 3 4 5 6 0.05 x (# dots)

  9. Identities involving averages Average Average of sum 0.25 Frequency P 0.23 0.22 Average of constant times function 0.15 0.08 1 2 3 4 5 6 0.05 x (# dots) Average of constant

  10. Dispersion Average Deviation (from average) 0.25 Frequency P 0.23 0.22 0.15 Cancellation can happen between positive and negative deviations 0.08 1 2 3 4 5 6 0.05 Variance x (# dots) Squared deviations are never negative, so no cancellation “Computing formula”

  11. Introduction to statistics Averages and variances Statistical independence Frequency P 1 2 3 4 5 6 x (# dots)

  12. Statistical independence # of instances Frequency P (# dots on 2nd die) 1 2 3 4 5 6 x (# dots) (# dots on 1st die) Simple: Variation with y independent of x

  13. Statistical independence (# dots on 2nd die) (# dots on 1st die) Simple: Variation with y independent of x

  14. Identities following from statistical independence Average of function of a single variable 1

  15. Identities following from statistical independence Average of function of a single variable Covariance of independent functions

  16. Identities following from statistical independence 0

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