Statistics

Frequency and Distribution

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

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.

Calculating Probabilities

Probability

Probability of an event happening =Number of ways it can happen

Total number of outcomes

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?

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%)

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).

Normal Distribution

Booooo!!!

Normal Distribution

Normal Distribution - Higher Variance

Student t 95%

Distribution of Sample Means

Uniform Distributions

Distribution of Sample Means

Skewed Distributions

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

Skewed Descriptive Values

Linear Regression

Parts of the regression equation

• Y = slope times X + intercept

Measure 2 variables, plot results

• Data for Scots Pine

• Force b to equal 0?

Find out if relationship existsand how good the fit is

• y = mx + b• In Excel…

Problems with linear regression