# Academic standards list

### Statistics — Mathematics

### Introduction

Academic standards define the expectations for knowledge and skills that students are to learn in a subject by a certain age or at the end of a school grade level. This page contains a list of standards for a specific content area, grade level, and/or course. The list of standards may be structured using categories and sub-categories.

### Interpreting Categorical and Quantitative Data

TSS.Math.S.S.ID — Conceptual Category: Statistics and Probability

Understand, represent, and use univariate data.

Understand the term 'variable' and differentiate between the data types: measurement, categorical, univariate, and bivariate.

Understand histograms, parallel box plots, and scatterplots, and use them to display and compare data.

For univariate measurement data, be able to display the distribution and describe its shape; select and calculate summary statistics.

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…

Understand, represent, and use bivariate data.

For bivariate measurement data, be able to display a scatterplot and describe its shape; use technological tools to determineregression equations and…

Identify trends in bivariate data; find functions that model the data and that transform the data so that they can be modeled.

### Conditional Probability and the Rule of Probability.

TSS.Math.S.S.CP — Conceptual Category: Statistics and Probability

Understand and apply basic concepts of probability.

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or…

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

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Demonstrate an understanding of the addition rule, the multiplication rule, conditional probability, and independence.

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.

### Using Probability to Make Decisions

TSS.Math.S.S.MD — Conceptual Category: Statistics and Probability

Understand and use discrete probability distributions.

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…

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

Design a simulation of random behavior and probability distributions (e.g., drawing by lots, using a random number generator, and using the results to make…

Analyze discrete random variables and their probability distributions, including binomial and geometric.

Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected…

Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected…

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

*There are 2 components within this standard*.Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Understand the normal probability distribution.

Calculate the mean (expected value) and standard deviation of both a random variable and a linear transformation of a randomvariable.

### Making Inferences and Justify Conclusions

TSS.Math.S.S.IC — Conceptual Category: Statistics and Probability

Know the characteristics of well-designed studies.

Understand the differences among various kinds of studies and which types of inferences can be legitimately drawn from each.

Design and conduct a statistical experiment to study a problem, then interpret and communicate the outcomes.

Compare and use sampling methods, including simple random sampling, stratified random sampling, and cluster sampling.

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

Make inferences about population parameters based on a random sample from that population.

Understand and use confidence intervals.

Understand the meaning of confidence level, of confidence intervals, and the properties of confidence intervals.

Construct and interpret a large sample confidence interval for a proportion and for a difference between two proportions.

Use distributions to make inferences about a data set.

Apply the properties of a Chi-square distribution in appropriate situations in order to make inferences about a data set.

Apply the properties of the normal distribution in appropriate situations in order to make inferences about a data set.

♦ Academic Standards marked with a diamond are "

*Supporting Content*" within the grade level or course.

**This website provides a reference tool for browsing academic standards and locating associated resources. We are not the originator of these academic standards. Although we strive to maintain accuracy, there may be revisions, updates, or errors within the text and structure of the information displayed. In case of any discrepancy, please respect the originator's published version (https://www.tn.gov/content/dam/tn/stateboardofeducation/documents/massivemeetingsfolder/meetingfiles4/10-20-17_III_J_Non-Substantive_Chanages_to_Math_ELA__Science_Standards_Attachment_1_-_Math.pdf) as the definitive record.**

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