| 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 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 |
| • |
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. |
|
