Statistics and Probability Review

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.