Instructional programs from prekindergarten through grade 12 should enable each and every student to— 

• Formulate questions  that can be addressed with data and collect, organize, and display relevant data to answer them
• Select and use  appropriate statistical methods to analyze data
• Develop and evaluate  inferences and predictions that are based on data
• Understand and apply  basic concepts of probability

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them  

Pre-K–2 Expectations: In pre-K through grade 2 each and every student should– 

• pose questions and gather data about themselves and their surroundings;
• sort and classify objects according to their attributes and organize data about the objects;
• represent data using concrete objects, pictures, and graphs.

Grades 3–5 Expectations: In grades 3–5 each and every student should– 

• design investigations to address a question and consider how data-collection methods affect the nature of the data set;
• collect data using observations, surveys, and experiments;
• represent data using tables and graphs such as line plots, bar graphs, and line graphs;
• recognize the differences in representing categorical and numerical data.

Grades 6–8 Expectations: In grades 6–8 each and every student should– 

• formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population;
• select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.

Grades 9–12 Expectations: In grades 9–12 each and every student should– 

• understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each;
• know the characteristics of well-designed studies, including the role of randomization in surveys and experiments;
• understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable;
• understand histograms, parallel box plots, and scatterplots and use them to display data;
• compute basic statistics and understand the distinction between a statistic and a parameter.

Select and use appropriate statistical methods to analyze data  

Pre-K–2 Expectations: In pre-K through grade 2 each and every student should– 

• describe parts of the data and the set of data as a whole to determine what the data show.

Grades 3–5 Expectations: In grades 3–5 each and every student should– 

• describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed;
• use measures of center, focusing on the median, and understand what each does and does not indicate about the data set;
• compare different representations of the same data and evaluate how well each representation shows important aspects of the data.

Grades 6–8 Expectations: In grades 6–8 each and every student should– 

• find, use, and interpret measures of center and spread, including mean and interquartile range;
• discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots.

Grades 9–12 Expectations: In grades 9–12 each and every student should– 

• for univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics;
• for bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools;
• display and discuss bivariate data where at least one variable is categorical;
• recognize how linear transformations of univariate data affect shape, center, and spread;
• identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled.

Develop and evaluate inferences and predictions that are based on data  

Pre-K–2 Expectations: In pre-K through grade 2 each and every student should– 

• discuss events related to students' experiences as likely or unlikely.

Grades 3–5 Expectations: In grades 3–5 each and every student should– 

• propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions.

Grades 6–8 Expectations: In grades 6–8 each and every student should– 

• use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken;
• make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit;
• use conjectures to formulate new questions and plan new studies to answer them.

Grades 9–12 Expectations: In grades 9–12 each and every student should– 

• use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions;
• understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference;
• evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions;
• understand how basic statistical techniques are used to monitor process characteristics in the workplace.

Understand and apply basic concepts of probability  

Grades 3–5 Expectations: In grades 3–5 each and every student should– 

• describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible;
• predict the probability of outcomes of simple experiments and test the predictions;
• understand that the measure of the likelihood of an event can be represented by a number from 0 to 1.

Grades 6–8 Expectations: In grades 6–8 each and every student should– 

• understand and use appropriate terminology to describe complementary and mutually exclusive events;
• use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations;
• compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models.

Grades 9–12 Expectations: In grades 9–12 each and every student should– 

• understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases;
• use simulations to construct empirical probability distributions;
• compute and interpret the expected value of random variables in simple cases;
• understand the concepts of conditional probability and independent events;
• understand how to compute the probability of a compound event.