# Common Core Mapping for High School: Statistics & Probability

Related Topics:
Common Core for Mathematics

## 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

• ### Common Core Mapping for High School: Statistics & Probability

Interpreting Categorical and Quantitative Data

 Standard Lessons Worksheets HSS-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). 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 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 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 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 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 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

 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

 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 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 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. 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 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

 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

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.