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Understanding Probability and Distribution in Statistics

Learn how to calculate probabilities, explore coin toss examples, and understand normal distributions. Discover skewed distributions, linear regression, and how to analyze data using Excel.

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Understanding Probability and Distribution in Statistics

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  1. Statistics Frequency and Distribution

  2. Calculating Probabilities

  3. Probability

  4. 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?

  5. 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%)

  6. 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).

  7. Normal Distribution

  8. Normal Distribution

  9. Normal Distribution - Higher Variance

  10. Student t 95%

  11. Distribution of Sample Means

  12. Uniform Distributions

  13. Distribution of Sample Means

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

  15. Skewed Descriptive Values

  16. Linear Regression

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

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

  19. Find out if relationship existsand how good the fit is • y = mx + b • In Excel…

  20. Problems with linear regression

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