Data Analysis and Probability Standard for Grades 912
Instructional programs from
prekindergarten through grade 12 should enable all students to— 
In grades 9–12 all students
should— 
Formulate questions that can be addressed
with data and collect, organize, and display relevant data to answer them 
 understand the differences among various kinds of studies and which types of
inferences can legitimately be drawn from each;
 know the characteristics of welldesigned 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 
 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 
 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 
 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.


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