Statistics and Probability Review

Study Notes

Statistics and Probability Review

Discrete vs. Continuous Variables: Discrete variables have countable outcomes (e.g., number of voters, calculators used). Continuous variables have outcomes on a continuous scale (e.g., height, weight).
Discrete Variable Examples: Number of students present, red marbles, coin flips, grade levels.
Continuous Variable Examples: Height of students, weight of students, time to get to school, distance between classes, amount of solution.
Rolling Two Dice Outcomes: There are 36 possible outcomes when rolling two dice.
Area Under Standard Normal Curve: The total area under the standard normal curve is 1.
Half of a Normal Curve: Half of the area under a normal curve is 0.5.
Descriptive Measures from Population: Parameters describe the entire population (e.g., population mean).
Descriptive Measures from Sample: Statistics describe a sample from a population (e.g., sample mean).
Normal Distribution Properties: The normal distribution is bell-shaped, the mean, median, and mode coincide, the area under the curve equals 1, and the length is determined by the standard deviation.
Probability of an Event in Normal Distribution The area under the curve corresponds to the probability of an event within a range.
Finding Probabilities from Z-score: Specific values of X on a normal distribution transformed into standardized Z-scores to find areas under the curve.
Finding Z-Score: Calculate using the formula Z = (X - μ) / σ. Knowing z tells whether the score is above or below the mean.
Combinations: Calculation of combinations (n choose k) is important.
Percentile Ranks and Z-scores: Z-scores associated with percentiles allow for conversions and understanding of ranks relating to the standard normal distribution.
Properties of Discrete Probability Distributions: Probabilities are between 0 and 1 with their sum equal to 1, not 100%.
Discrete vs. Continuous Probability Distributions: Certain distributions are specific to each.
Sampling Distributions: The probability distribution of a sample statistic (e.g. mean) constructed from many samples of a population.
Mean, Variance, and Standard Deviation of Sampling Distribution: Essential for understanding sample means.
Probability of Events in a Normal Distribution The area under a curve can be used to get probabilities for various events when considering the distribution of data.