Algebra 2 Chapter 11 Probability and Statistics

Probability and Statistics Terms

• Fundamental Counting Principle: Utilizes multiplication for counting outcomes in a scenario with multiple choices.

• Permutation: Refers to the specific arrangement of items where the order is crucial.

• Factorial Notation (n!): Represents the product of all positive integers up to n; notably, 0! equals 1.

• Combination: Represents selections where order does not play a critical role.

• Experimental Probability: Calculated as P(event) = (number of times the event occurs) ÷ (total number of trials).

• Simulation: A technique that models a real-life event to understand its probabilities better.

• Sample Space: The comprehensive set of all outcomes resulting from an experiment or activity.

• Equally Likely Outcomes: States that each outcome in a sample space has the same probability of occurring.

• Theoretical Probability: For n equally likely outcomes in a sample space, if event A occurs m times, then P(A) = m/n.

• Dependent Events: Events where the outcome of one event influences the outcome of another.

• Independent Events: Events where the outcome of one event has no effect on the outcome of another.

• Probability Distribution: A function that specifies the probability for each possible outcome in a sample space.

• Uniform Distribution: Each outcome on a classic number cube has an equal chance of occurring.

• Cumulative Frequency: Assigns a numerical value to events based on frequency.

• Cumulative Probability: Involves the probability of events occurring that are less than or equal to a specific value.

• Conditional Probability: The probability of event B occurring given that event A has already occurred.

• Contingency Table: A two-way frequency table displaying data across two distinct categories.

• Probability Model: A framework used to assign probabilities to various outcomes in a stochastic process.

Measures of Central Tendency

• Measure of Central Tendency: Describes the central point of a data set, with mean, median, and mode being the primary measures.

• Mean: The average calculated by summing data values and dividing by the count of values.

• Median: The middle number in a sorted data set, or the average of the two middle values for an even set.

• Mode: The most frequently occurring value(s) within a data set.

• Bimodal: Indicates the presence of two modes in a data set, which may not be statistically significant.

• Outlier: A value that markedly differs from the other values in a data set.

• Range: The difference between the maximum and minimum values in a dataset.

• Quartiles: Divides ordered data into four parts, with the median separating the data into lower and upper halves.

• Box-and-Whisker Plot: A graphical representation of data using quartiles to form a box and the minimum/maximum values as whiskers.

• Percentile: A value that ranks the position of a specific number within a data set, on a scale of 0 to 100.

Measures of Variation

• Measure of Variation: Assesses how spread out the data points are in a dataset.

• Variance: Calculated by averaging the squared differences of each value from the mean.

• Standard Deviation: The square root of the variance, indicating average distance from the mean.

Sampling Methods and Bias

• Convenience Sample: Involves choosing individuals who are easiest to reach, which may introduce bias.

• Self-Selected Sample: Comprises only those who choose to participate or volunteer, often leading to biased results.

• Systematic Sample: Involves selecting individuals at regular intervals from a population.

• Random Sample: Ensures every member of the population has an equal chance of being selected.

• Bias: Systematic error introduced by the sampling method, affecting the representativeness of data.

Studies and Experiments

• Observational Study: Researchers observe and measure without affecting the sample, maintaining natural conditions.

• Controlled Experiment: Divides a sample into two groups, applies treatment to one, and compares outcomes.

• Survey: Involves querying each member of a sample using a set list of questions.

• Binomial Experiment: A fixed number of trials, each with two outcomes, independent trials, and consistent probabilities.

• Binomial Probability: Determines the likelihood of achieving x successes within n independent trials using a specific formula.

Distributions and Intervals

• Discrete Probability Distribution: Represents experiments with a finite number of outcomes.

• Continuous Probability Distribution: Covers outcomes that can take any value in a given interval.

• Normal Distribution: Displays data that varies randomly around a mean value.

• Margin of Error: Indicates the range in which the population mean is likely to fall, influenced by sample size and confidence level.

• Confidence Interval: A set of values within which a certain parameter is expected to lie with a specified probability.

• Z-Score: A measure indicating how many standard deviations a value is from the mean in a normally distributed dataset.

• Interquartile Range (IQR): The difference between the third and first quartiles, reflecting the range of the middle 50% of data.

• Mutually Exclusive Events: Two events cannot occur simultaneously, leading to P(A and B) = 0.

• Sample: A segment of a population used for analysis and inference.