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Common Core Mapping for High School: Statistics & Probability




 

Statistics & Probability Overview

Interpreting Categorical and Quantitative Data

  • Summarize, represent, and interpret data on a single count or measurement variable
  • Summarize, represent, and interpret data on two categorical and quantitative variables
  • Interpret linear models
  • Making Inferences and Justifying Conclusions

  • Understand and evaluate random processes underlying statistical experiments
  • Make inferences and justify conclusions from sample surveys, experiments and observational studies
  • Conditional Probability and the Rules of Probability

  • Understand independence and conditional probability and use them to interpret data
  • Use the rules of probability to compute probabilities of compound events in a uniform probability model
  • Using Probability to Make Decisions

  • Calculate expected values and use them to solve problems
  • Use probability to evaluate outcomes of decisions

  • Related Topics:
    Common Core for Mathematics

    Common Core Mapping for High School: Statistics & Probability

    Interpreting Categorical and Quantitative Data

    Code

    Standard

    Lessons

    Worksheets

    HSS-ID.A.1

    Represent data with plots on the real number line (dot plots, histograms, and box plots).

    Represent Data

    Box and Whisker Plot

    Represent Data

    HSS-ID.A.2

    Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

    Center and Spread of Data

    Explore Mean and Median

    Explore Standard Deviation

    Standard Deviation of a population

    HSS-ID.A.3

    Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

    Interpret Center and Spread of Data

    Interpret and compare data distributions

    HSS-ID.A.4

    Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

    Normal Distribution

    Empirical rule

    Z scores 1

    Z scores 2

    Z scores 3

    HSS-ID.B.5

    Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

    Two-Way Frequency Tables

    Trends in categorical data

    Frequencies of Bivariate Data


    HSS-ID.B.6

    HSS-ID.B.6a

    HSS-ID.B.6b

    HSS-ID.B.6c

    Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

    Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

    Informally assess the fit of a function by plotting and analyzing residuals.

    Fit a linear function for a scatter plot that suggests a linear association.

    Scatter Plots

    Interpret Scatter Plots

    Estimate Line of Best Fit

    Linear models of bivariate data

    HSS-ID.C.7

    Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

    Slope and Intercept

    Slope of a line

    HSS-ID.C.8

    Compute (using technology) and interpret the correlation coefficient of a linear fit.

    Correlation Coefficient


    HSS-ID.C.9

    Distinguish between correlation and causation.

    Correlation vs Causation

    Types of Statistical Studies





    Making Inferences and Justifying Conclusions

    Code

    Standard

    Lessons

    Worksheets

    Games

    HSS-IC.A.1

    Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

    Understand Statistics

    Valid Claims

    Statistic Games

    HSS-IC.A.2

    Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

    Simple Hypothesis Testing Simple Hypothesis Testing

    HSS-IC.B.3

    Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

    Surveys, Experiments, and Observational Studies

    Types of Statistical Studies

    HSS-IC.B.4

    Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.


    HSS-IC.B.5

    Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

    Hypothesis Tesing in Experiments

    Hypothesis Testing in Experiments

    HSS-IC.B.6

    Evaluate reports based on data.

    Reports based on data

    Types of Statistical Studies



     

    Conditional Probability & the Rules of Probability

    Code

    Standard

    Lessons

    Worksheets

    Games

    HSS-CP.A.1

    Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (?or,? ?and,? ?not?).

    Sample Space

    Probability Space

    Describe subsets of sample spaces

    HSS-CP.A.2

    Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

    Independent Events

    Independent Probability

    Sample Space for Compound Events

    HSS-CP.A.3

    Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

    Conditional Probability

    Identify dependent and independent events

    HSS-CP.A.4

    Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

    Two-way Tables and Probabilities

    Trends in categorical data

    HSS-CP.A.5

    Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

    Conditional Probability and Tree Diagrams

    Trends in categorical data

    HSS-CP.B.6

    Find the conditional probability of A given B as the fraction of B?s outcomes that also belong to A, and interpret the answer in terms of the model.

    Compound and Conditional Probability

    Sample Space for Compound Events

    Dependent Probability

    HSS-CP.B.7

    Apply the Addition Rule, P(A or B) = P(A) + P(B) − P(A and B), and interpret the answer in terms of the model.

    Addition Rule for Probability

    Adding Probabilities

    HSS-CP.B.8

    (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.

    Multiplication Rule for Probability

    Multiplying dependent probabilities

    HSS-CP.B.9

    (+) Use permutations and combinations to compute probabilities of compound events and solve problems.

    Permutations and Combinations for Probability

    Combinations

    Permutations

    Permutations and Combinations

    Probability with Permutations and Combinations




    Using Probability to Make Decisions

    Code

    Standard

    Lessons

    Worksheets

    Games

    HSS-MD.A.1

    (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

    Random Variable

    Construct Probability Distributions

    HSS-MD.A.2

    (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

    Expected Value

    Expected value

     

    HSS-MD.A.3

    (+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.

    Probability Distribution

    Expected value with calculated probabilities

    HSS-MD.A.4

    (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?

    Probability Distribution

    Expected values with empirical probabilities

    HSS-MD.B.5

    HSS-MD.B.5a

    HSS-MD.B.5b

    (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.

    Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant.

    Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.

    Probability and Expected Values

    Expected value

    Make decisions with expected values

    HSS-MD.B.6

    (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

    Probability and Fair Decisions

    Use probability to make fair decisions

    HSS-MD.B.7

    (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

    Analyze decisions with expected values

    Make decisions with expected values





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