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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

Common Core for Mathematics

**Interpreting Categorical and Quantitative Data**

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

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. |

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). |

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. |

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. |

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. |

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. |

HSS-ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. |

HSS-ID.C.9 Distinguish between correlation and causation. |

**Making Inferences and Justifying Conclusions**

HSS-IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. |

HSS-IC.A.2 Decide if a specified model is consistent with results
from a given data-generating process, e.g., using
simulation. |

HSS-IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. |

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. |

HSS-IC.B.6 Evaluate reports based on data. |

**Conditional Probability & the Rules of Probability**

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). |

HSS-CP.A.2 Understand that two events |

HSS-CP.A.3 Understand the conditional probability of |

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. |

HSS-CP.A.5 Recognize and explain the concepts of conditional
probability and independence in everyday language and
everyday situations. |

HSS-CP.B.6 Find the conditional probability of |

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. |

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. |

HSS-CP.B.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. |

**Using Probability to Make Decisions**

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. |

HSS-MD.A.2 (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. |

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. |

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. |

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. |

HSS-MD.B.6 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). |

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). |

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