Introduction to statistics

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