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.

Test your understanding of key concepts in Algebra 2, Chapter 11, focusing on Probability and Statistics. This quiz covers essential terms such as the Fundamental Counting Principle, permutations, combinations, and factorials. Perfect for reinforcing your knowledge of these foundational statistical concepts.