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The
following standards outline the content
of a one-year course in Probability
and Statistics. If a one-semester
course is desired, the standards with
an asterisk (*) would apply. Students
enrolled in this course are assumed
to have mastered the concepts identified
in the Standards of Learning for Algebra
II. The purpose of the course is to
present basic concepts and techniques
for collecting and analyzing data,
drawing conclusions, and making predictions.
A graphing calculator
is essential for every student taking
the Probability and Statistics course
and is required for the Advanced
Placement Statistics Examination.
The calculator may not fully substitute
for a computer, however. In the
absence of a computer for student
use, teachers may provide students
with examples of computer output
generated by a statistical software
package.
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| *PS.1 |
The
student will analyze graphical
displays of data, including
dotplots, stemplots,
and histograms,
to identify and describe patterns
and departures from patterns,
using central tendency, spread,
clusters, gaps, and outliers. Appropriate
technology will be used to create
graphical displays. |
| *PS.2 |
The
student will analyze numerical
characteristics of univariate
data sets to describe patterns
and departure from patterns,
using mean, median, mode, variance, standard
deviation, interquartile
range, range,
and outliers. Appropriate technology
will be used to calculate statistics. |
| *PS.3 |
The
student will compare distributions
of two or more univariate data
sets, analyzing center and spread
(within group and between group
variations), clusters and gaps,
shapes, outliers, or other unusual
features. Appropriate technology
will be used to generate graphical
displays. |
| *PS.4 |
The
student will analyze scatterplots
to identify and describe the relationship
between two variables, using shape;
strength of relationship; clusters;
positive, negative, or no association;
outliers; and influential points. Appropriate
technology will be used to generate
scatterplots and identify outliers
and influential points. |
| PS.5 |
The
student will find and interpret
linear correlation, use the method
of least
squares regression to model
the linear relationship between
two variables, and use the residual
plots to assess linearity. Appropriate
technology will be used to compute
correlation coefficients and residual
plots. |
| PS.6 |
The
student will make logarithmic and
power transformations to achieve
linearity. Appropriate technology
will be used. |
| PS.7 |
The
student, using two-way
tables, will analyze categorical
data to describe patterns and
departure from patterns and to
find marginal
frequency and relative frequencies,
including conditional frequencies. |
| *PS.8 |
The
student will describe the methods
of data
collection in a census, sample
survey, experiment, and observational
study and identify an appropriate
method of solution for a given
problem setting. |
| *PS.9 |
The
student will plan and conduct
a survey. The plan will address
sampling techniques (e.g., simple
random and stratified) and methods
to reduce bias. |
| PS.10 |
The
student will plan and conduct
an experiment. The plan will
address control, randomization,
and measurement of experimental
error. |
| *PS.11 |
The
student will compute and distinguish
between permutations and combinations
and use technology for applications. |
| *PS.12 |
The
student will identify and describe
two or more events as complementary,
dependent, independent, and/or
mutually exclusive. |
| *PS.13 |
The
student will find probabilities
(relative frequency and theoretical),
including conditional probabilities
for events that are either dependent
or independent, by applying the “law
of large numbers” concept, the
addition rule, and the multiplication
rule. |
| *PS.14 |
The
student will develop, interpret,
and apply the binomial
probability distribution for
discrete random variables, including
computing the mean and standard
deviation for the binomial variable. |
| PS.15 |
The
student will simulate probability
distributions, including binomial
and geometric. |
| PS.16 |
The
student will identify random variables
as independent or dependent and
find the mean
and standard deviations for
sums and differences of independent
random variables. |
| *PS.17 |
The
student will identify properties
of a normal
distribution and apply the
normal distribution to determine
probabilities, using a table or graphing
calculator. |
| *PS.18 |
The
student, given data from a large
sample, will find and interpret
point estimates and confidence
intervals for parameters. The
parameters will include proportion
and mean, difference between
two proportions, and difference
between two means (independent
and paired). |
| PS.19 |
The
student will apply and interpret
the logic of a hypothesis-testing
procedure. Tests will include
large sample test for proportion,
mean, difference between two proportions,
and difference between two means
(independent and paired) and Chi-squared
test for goodness of fit, homogeneity
of proportions, and independence. |
| PS.20 |
The
student will identify the meaning
of sampling
distribution with reference
to random variable, sampling statistic,
and parameter and explain the Central
Limit Theorem. This will
include sampling distribution
of a sample proportion, a sample
mean, a difference between two
sample proportions, and a difference
between two sample means. |
| PS.21 |
The
student will identify properties
of a t-distribution and apply
t-distributions to single-sample
and two-sample (independent and
matched pairs) t-procedures, using
tables or graphing calculators. |
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Equipment
Available
Updated
Thursday, December 1, 2005