Algebra 2 Chapter 11 Probability and Statistics
50 Questions
100 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What does the Fundamental Counting Principle describe?

  • A method of using addition to count
  • A method of using subtraction to count
  • A method of using division to count
  • A method of using multiplication to count (correct)

    • What is a permutation?

    An arrangement of items in a particular order.

    What is n factorial (n!)?

    n!=n(n-1)(n-2)...32*1. 0!=1

    What is a combination?

    <p>A selection in which order does not matter.</p> Signup and view all the answers

    What is the experimental probability of an event?

    <p>P(event)=number of times the event occurs ÷ number of trials</p> Signup and view all the answers

    What is a simulation?

    <p>A model of the event.</p> Signup and view all the answers

    What is the sample space?

    <p>The set of all possible outcomes to an experiment or activity.</p> Signup and view all the answers

    What are equally likely outcomes?

    <p>When each outcome in a sample space has the same chance of occurring.</p> Signup and view all the answers

    What is theoretical probability?

    <p>P(A)=m/n</p> Signup and view all the answers

    What are dependent events?

    <p>When the occurrence of one event affects how a second event can occur.</p> Signup and view all the answers

    What are independent events?

    <p>When the occurrence of one event does not affect how a second event can occur.</p> Signup and view all the answers

    What is a probability distribution?

    <p>A function that gives the probability of each outcome in a sample space.</p> Signup and view all the answers

    What is uniform distribution?

    <p>The theoretical probability of rolling each number on a standard number cube is the same.</p> Signup and view all the answers

    What is cumulative frequency?

    <p>When you can assign numerical values to events.</p> Signup and view all the answers

    What is cumulative probability?

    <p>The probability of events occurring with values that are less than or equal to a given value.</p> Signup and view all the answers

    What is conditional probability?

    <p>The probability that an event, B, will occur given that another event, A, has already occurred.</p> Signup and view all the answers

    What is a contingency table?

    <p>A two-way frequency table that contains data from two different categories.</p> Signup and view all the answers

    What is a probability model?

    <p>A model used to assign probabilities to outcomes of a chance process.</p> Signup and view all the answers

    What is the measure of central tendency?

    <p>Indicates the middle of the data set; the mean, median, and mode are the most common measures.</p> Signup and view all the answers

    What is the mean?

    <p>Sum of the data values ÷ number of data values.</p> Signup and view all the answers

    What is the median?

    <p>The middle value for an odd number of data values; the mean of the two middle values for an even number of data values.</p> Signup and view all the answers

    What is the mode?

    <p>The most frequently occurring value.</p> Signup and view all the answers

    What is bimodal?

    <p>Two modes in a data set, in which case the modes are probably not statistically useful.</p> Signup and view all the answers

    What is an outlier?

    <p>A value that is substantially different from the rest of the data in a set.</p> Signup and view all the answers

    What is the range of a set of data?

    <p>The difference between the greatest and least values.</p> Signup and view all the answers

    What are quartiles?

    <p>The values that are separated into four parts.</p> Signup and view all the answers

    What is a box-and-whisker plot?

    <p>A way to display data that uses quartiles to bound the center box and the minimum and maximum values to form the whiskers.</p> Signup and view all the answers

    What is a percentile?

    <p>A number from 0 to 100 that you can associate with a value x from a data set.</p> Signup and view all the answers

    What is the measure of variation?

    <p>Describes how the data in a data set are spread out.</p> Signup and view all the answers

    What is variance?

    <p>In a data set, sum of the differences between each value x and the mean divided by the n values in the data set.</p> Signup and view all the answers

    What is standard deviation?

    <p>In a data set, the square root of the sum of the differences between each value x and the mean divided by the n values in the data set.</p> Signup and view all the answers

    What is a convenience sample?

    <p>Select any members of the population who are conveniently and readily available.</p> Signup and view all the answers

    What is a self-selected sample?

    <p>Select only members of the population who volunteer for the sample.</p> Signup and view all the answers

    What is a systematic sample?

    <p>Order the population in some way, and then select from it at regular intervals.</p> Signup and view all the answers

    What is a random sample?

    <p>All members of the population are equally likely to be chosen.</p> Signup and view all the answers

    What is bias?

    <p>A systematic error introduced by the sampling method.</p> Signup and view all the answers

    What is an observational study?

    <p>You measure or observe members of a sample in such a way that they are not affected by the study.</p> Signup and view all the answers

    What is a controlled experiment?

    <p>You divide the sample into two groups, imposing a treatment on one group and not the other group.</p> Signup and view all the answers

    What is a survey?

    <p>You ask every member of the sample a set of questions.</p> Signup and view all the answers

    What is a binomial experiment?

    <p>An experiment that has a fixed number of trials, each trial has two possible outcomes, the trials are independent, and the probability of each outcome is constant throughout the trials.</p> Signup and view all the answers

    What is binomial probability?

    <p>With n repeated independent trials (p+q=1), the probability of x successes in the n trials can be found by a specific formula.</p> Signup and view all the answers

    What is a discrete probability distribution?

    <p>A finite number of possible events or values.</p> Signup and view all the answers

    What is a continuous probability distribution?

    <p>The events can be any value in an interval of real numbers.</p> Signup and view all the answers

    What is a normal distribution?

    <p>Data that vary randomly from the mean.</p> Signup and view all the answers

    What is margin of error?

    <p>Helps you find the interval in which the mean of the population is likely to be.</p> Signup and view all the answers

    What is confidence interval?

    <p>A range of values so defined that there is a specified probability that the value of a parameter lies within it.</p> Signup and view all the answers

    What is a z-score?

    <p>An important measure for normally distributed data which indicates the number of standard deviations a value lies above or below the mean of a population.</p> Signup and view all the answers

    What is the interquartile range?

    <p>The difference between the third and first quartiles.</p> Signup and view all the answers

    What are mutually exclusive events?

    <p>Two events that cannot happen at the same time where P(A and B)=0.</p> Signup and view all the answers

    What is a sample?

    <p>A part of a population.</p> Signup and view all the answers

    Study Notes

    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.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    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.

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser