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Data Analysis and Probability

Instructional programs from prekindergarten through grade 12 should enable all students to—

Pre-K–2 Expectations: In pre-K through grade 2 all students 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.

• 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.

• 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.

• 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.

Pre-K–2 Expectations: In pre-K through grade 2 all students should–

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

• 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.

• 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.

• 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.

Pre-K–2 Expectations: In pre-K through grade 2 all students should–

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

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

• 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.

• 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.

Pre-K–2 Expectations: In pre-K through grade 2 all students 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.

• 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.