PROBABILITY AND STATISTICS
CURRICULUM GUIDE
2012-2013
Loudoun County Public Schools
INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE
This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun
County Public Schools. The CURRICULUM GUIDE includes excerpts from documents published by the Virginia Department of Education. Other
statements, such as suggestions on the incorporation of technology and essential questions, represent the professional consensus of Loudoun’s teachers
concerning the implementation of these standards. In many instances the local expectations for achievement exceed state requirements. The GUIDE is the
lead document for planning, assessment and curriculum work. It is a summarized reference to the entire program. Other documents, called
RESOURCES, are updated more frequently. These are published separately but teachers can combine them with the GUIDE for ease in lesson planning.
Mathematics Internet Safety Procedures
1. Teachers should review all Internet sites and links prior to using it in the classroom.
During this review, teachers need to ensure the appropriateness of the content on the site, checking for
broken links, and paying attention to any
inappropriate pop-ups or solicitation of information.
2. Teachers should circulate throughout the classroom while students are on the
internet checking to make sure the students are on the appropriate site and
are not minimizing other inappropriate sites.
Teachers should periodically check and update any web addresses that they have on their LCPS web
pages.
3. Teachers should assure that the use of websites correlate with the objectives of
lesson and provide students with the appropriate challenge.
4. Teachers should assure that the use of websites correlate with the objectives
of the lesson and provide students with the appropriate challenge.
The students will use problem solving, mathematical communication, mathematical reasoning, connections, and
representations as they engage in mathematics activities throughout the year.
Quarter 1
Number
Of Blocks
Topics and Essential Questions
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.
OBJECTIVES: The student will be able to:
1. Define Simpson’s paradox in reference to the fact that
aggregate proportions can reverse the direction of the
relationship seen in the individual parts
2. Understand that two categorical variables are independent
if the conditional frequencies of one variable are the same
for every category of the other variable
3. Produce a two-way table as a summary of the information
obtained from two categorical variables
4. Calculate marginal, relative, and conditional frequencies
in a two-way table
5. Use marginal, relative, and conditional frequencies to
analyze data in two-way tables within the context of the
data.
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.
OBJECTIVES: The student will be able to:
1. Collect data for a purpose and provide context
2. Compare and contrast two or more univariate data sets by
analyzing measures of center and spread within the
contextual framework
3. Describe any unusual features of the data, such as clusters,
gaps or outliers, within the context of the data
4. Analyze in context kurtosis and skewness in conjunction
with other descriptive measures
Optional Instructional Resources

Conduct a poll to determine
the political preferences that
exist in the classroom.
Create a two-way table that
breaks down political
preference based on gender.
Have the students calculate
the relative, conditional,
marginal frequencies and
determine if there the two
variables are independent of
each other.

Workshop Statistics
o Topic 7 –
“Comparing
Distributions:
Categorical
Variables”

Workshop Statistics
o “Features of
Distributions”
o Topic 3: Displaying
and Describing
Distributions
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.
OBJECTIVES: The student will be able to:
1. Analyze descriptive statistical information that is
generated by a univariate data set that includes the
interplay between central tendency and dispersion
2. Interpret mean, median, mode, range, interquartile range,
variance, and standard deviation of a univariate data set in
terms of the problem’s context.
3. Identify possible outliers, using an algorithm.
4. Explain the influence of outliers on a univariate data set.
5. Explain ways in which standard deviation addresses
dispersion by examining the formula for standard
deviation.
PS.16 The student will identify properties of normal
distribution and apply the normal distribution to determine
probabilities, using a table or graphing calculator.
OBJECTIVES: The student will be able to:
1. Associate the normal distribution curve as a family of
symmetrical curves defined by the mean and the standard
deviation
2. Identify the properties of a normal probability distribution
3. Label the normal distribution curve given the mean and
the standard deviation using the Empirical rule
4. Understand that the total area under the curve is one
5. Describe how the standard deviation and the mean affect
the graph of the normal distribution
6. Describe the probability of a given event, using the normal
distribution
7. Calculate the data point that is associated with a certain
percentile

Each student will receive a
bag of M&M’s or Skittles to
determine the color
distribution that exists. The
different descriptive
characteristics will be
calculated by hand and will
be interpreted.

Workshop Statistics
o Topic 6: Comparing
Distributions
o Topic 5: Measures of
Spread

Activity-Based Statistics
o “Matching Plots to
Variables”
o “Matching Statistics
to Plots”
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.
OBJECTIVES: The student will be able to:
1. Use scatterlots to determine if there is a useful relationship
between two variables and determine the family of
equations that describes the relationship
2. Examine scatterplots of data, and describe skewness,
kurtosis, and correlation within the context of the data
3. Consider both the direction and strength of the association
between two variables.
4. Understand that the strength of an association between two
variables reflects how accurately the value of one variable
can be predicted based on the value of the other variable
5. Describe and explain any unusual features of the data,
such as clusters, gaps, or outliers, within the context of the
data.
6. Identify influential data points (observations that have
great effect on a line of best fit because of extreme xvalues) and describe the effect of the 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.
OBJECTIVES: The student will be able to:
1. Measure the degree of association between two variables
that are related linearly using the correlation coefficient.
2. Calculate a correlation coefficient
3. Explain how the correlation coefficient, r, measures
association by looking at is formula.
4. Generate the least squares regression line that minimizes
the sum of the squared distances from the data points.
5. Use residual plots to determine if a linear model is
satisfactory for describing the relationship between two

Collect data on heights and
weights and use the data to
create scatterplots.

Present the students with
different scenarios to
determine if there is a
relationship between the two
variables being studied

Have students be able to
describe a scatterplot based
on its strength, direction, and
shape when given multiple
graphs

Workshop Statistics
o Topic 8: Graphical
Displays of
Association
o Topic 9: Correlation
Coefficient
o Topic 10: Least
Squares Regression
o Topic 11: Least
Squares Regression II

ActivStats
o Lesson 7:
“Scatterplots”
o Lesson 8: “Least
Squares Regression”
variables
6. Describe the errors inherent in extrapolation beyond the
range of the data.
7. Use least squares regression to find the equation of the line
of best fit for a set of data
8. Explain how least squares regression generates the
equation of the line of best fit by examining the formulas
used in computation
Quarter 2
Number
Of Blocks
Topics and Essential Questions
PS.12 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.
OBJECTIVES: The student will be able to:
1. Understand that data is collected for a purpose and has
meaning in a context.
2. Calculate relative frequency and expected frequency.
3. Find conditional probabilities for dependent, independent,
and mutually exclusive events.
PS.11 The student will identify and describe two or more
events as complementary, dependent, independent, and/or
mutually exclusive.
Optional Instructional Resources

Students will play the game
War with a partner to
determine what it takes for a
card to win war. The
students will make
interpretations about the
data.

ActivStats
o Lesson 14

ActivStats
o Lesson 15 –
“Conditional
Probability and
Independence”

Have students design their
own games of chance where
OBJECTIVES: The student will be able to:
1. Define and give contextual examples of complementary,
dependent, independent, and mutually exclusive events.
2. Given two or more events in a problem setting, determine
if the events are complementary, dependent, independent,
and/or mutually exclusive.
PS.13 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.
they come up with their own
rules
OBJECTIVES: The student will be able to:
1. Develop the binomial probability distribution within a
real-world context
2. Calculate the mean and standard deviation for the binomial
variable
3. Use the binomial distribution to calculate probabilities
associated with experiments for which there are only two
possible outcomes.
PS.9 The student will plan and conduct a survey. The plan
will address sampling techniques (e.g., simple random,
stratified) and methods to reduce bias

OBJECTIVES: The student will be able to:
1. Understand the purpose sampling is to provide sufficient
information so that population characteristics may be
inferred
2. Investigate and describe sampling techniques, such as
simple random sampling, stratified sampling, and cluster
sampling.
3. Determine which sampling technique is best, given a
particular context.
4. Plan a survey to answer a question or address an issue.
5. Given a plan for a survey, identify possible sources of
bias, and describe ways to reduce bias.
6. Design a survey instrument.
7. Conduct a survey.
PS.8 The student will describe the methods of data
collection in a census, sample survey, experiment, and


Students will conduct a
survey that is approved by
the teacher. A proposal will
be written that contains the
methodology of how the
survey will be conducted and
the questions that will be
asked. Once the survey is
conducted, the data will be
analyzed and a report will be
written.
Workshop Statistics
o Topic 12: Sampling
ActivStats
o Lesson 12: “Sample
Surveys”
observational study and identify an appropriate solution for
a given problem setting.
OBJECTIVES: The student will be able to:
1. Compare and contrast controlled experiments and
observational studies and the conclusions one can draw
from each.
2. Compare and contrast population and sample and
parameter and statistic
3. Understand that the value of sample statistics varies from
sample to sample if the simple random samples are taken
repeatedly from the population of interest
4. Identify biased sampling methods
5. Describe simple random sampling
PS.10 The student will plan and conduct an experiment.
The plan will address control, randomization, and
measurement of experimental error.
OBJECTIVES: The student will be able to:
1. Plan and conduct an experiment that is carefully designed
in order to detect a cause-and-effect relationship between
variables.
2. Design an experiment that addresses control,
randomization, and minimization of experimental control.
3. Compare an experimental group with a control group.

Students will work together
with a partner to create an
approved experiment. A
formal report must be
handed

Workshop Statistics
o Topic 13: Designing
Studies

ActivStats
o Lesson 13:
“Designed
Experiments”
PS.17 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).
OBJECTIVES: The student will be able to:
1. Comprehend that the primary goal of sampling is to
estimate the value of a parameter based on a statistic
2. Construct confidence intervals to estimate a population
parameter, such as a proportion or the difference between
two proportions; or a mean or the difference between two
means
3. Select a value for alpha (Type I error) for a confidence
interval
4. Interpret confidence intervals in the context of the data
5. Explain the importance of a random sampling for
confidence intervals
Calculate point estimates for parameters and discuss the
limitations of point estimates
If time permits:
PS.15 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.
OBJECTIVES: The student will be able to:
1. Define that a random variable is a variable that has a
single numerical value, determined by chance, for each
outcome of a procedure
2. Compare and contrast independent and dependent random
variables
3. Find the standard deviation or sums and differences of
independent random variables.
PS.18 The student will apply and interpret the logic of a
hypothesis-testing procedure. Tests will include larges
sample test for proportion, mean, difference between two
proportions, and difference between two means
(independent and paired) and Chi-squared tests for
goodness of fit, homogeneity of proportions, and
independence.
OBJECTIVES: The student will be able to:
1. Use the Chi-squared test for goodness of fit to decide if the
population being analyzed fits a particular distribution
pattern.
2. Use hypothesis-testing procedures to determine whether or
not to reject the null hypothesis. The null hypothesis may
address proportion, mean, difference between two
proportions or two means, goodness of fit, homogeneity of
proportions, and independence.
3. Compare and contrast Type I and Type II errors.
4. Explain how and why the hypothesis-testing procedure
allows one to reach a statistical decision
PS.19 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.
OBJECTIVES: The student will be able to:
1. Describe the use of the Central Limit Theorem for drawing
inferences about a population parameter based on a sample
statistic.
2. Describe the effect of sample size on the sampling
distribution and on related probabilities
3. Use the normal approximation to calculate probabilities of
sample statistic falling within a given interval.
4. Identify and describe the characteristics of a sampling
distribution of a sample proportion, mean, difference
between two sample proportions, or difference between
two sample means.
PS.20 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.
OBJECTIVES: The student will be able to:
1. Identify the properties of a t-distribution
2. Compare and contrast a t-distribution and a normal
distribution
3. Use a t-test for single-sample and two-sample data