1. Statistics Frequency and Distribution

2. We interrupt this lecture for the following… Significant digits You should not report numbers with more significant digits than the contributing data Keep this in mind when doing homework assignments

3. Given data to the second decimal The mean calculated to be 168.2526667 Based on the precision of the original data, it should be reported as 168.25 Just because our calculators go to many decimals, they cannot create precision. You should round to a sensible number.

4. Calculating Probabilities

5. Probability Probability of an event happening = Number of ways it can happen Total number of outcomes

6. Coin Toss Example A balanced coin flipped in an unbiased way results in heads or tails (each with an equal 50% chance) Chance of heads = one/two possible outcomes What if the last 4 coin flips were heads, what is the chance of the next flip resulting in tails?

7. Probability of Failure Know the odds! Example when rolling a die, the chance of your number coming up equals 1/6 (or 16.6%) More importantly the chance of numbers that you didn’t pick to show up is 1 – 1/6 (or 83.3%)

8. Normal Distributions can be mathematically described with two parameters: a measure of central tendency, or mu (the mean symbolized as µ), and a measure of dispersion, or sigma (the standard deviation symbolized as σ).

9. Normal Distribution

10. Booooo!!!

11. Normal Distribution

12. Normal Distribution - Higher Variance

13. Student t 95%

14. Distribution of Sample Means

15. Uniform Distributions

16. Distribution of Sample Means

17. Skewed Distributions Often observed in nature – i.e. tree ages Inverse J shaped curve

18. Skewed Descriptive Values

19. Linear Regression

20. Parts of the regression equation Y = slope times X + intercept

21. Measure 2 variables, plot results Data for Scots Pine Force b to equal 0?

22. Find out if relationship exists and how good the fit is y = mx + b In Excel…

23. Problems with linear regression