PROBABILITY & STATISTICS
CURRICULUM GUIDE
Overview
Loudoun County Public Schools
2015-2016
(Additional curriculum information and resources for teachers can be accessed through CMS and VISION)
Probability and Statistics Overview
Quarter 1
PS.7
PS.3
PS.2
PS.16
PS.4
PS.5
PS.12
PS.11
21 blocks
Semester Overview
Quarter 2
PS.13
PS.9
PS.8
PS.10
PS.17
PS.15
PS.18
PS.19
PS.20
24 blocks
Probability and Statistics – Scope and Sequence
Number
Of Blocks
2
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.
2
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
Number
Of Blocks
5
Optional Instructional
Resources
Topics and Essential Questions
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.

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
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 Empircal 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
Activity-Based Statistics
o “Matching Plots to
Variables”
o “Matching Statistics
to Plots”
Number
Of Blocks
4
Topics and Essential Questions
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 scatterplots 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 x-values) 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 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





Optional Instructional
Resources
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”
8. Explain how least squares regression generates the equation of the line of best
fit by examining the formulas used in computation
Number
Of Blocks
3
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.
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”
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.
3
PS.11 The student will identify and describe two or more events as
complementary, dependent, independent, and/or mutually exclusive.
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.
2
Review, Assessments, and Intervention
Number
Of Blocks
2
Optional Instructional
Resources
Topics and Essential Questions
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.
OBJECTIVES: The student will be able to:

Have students design their
own games of chance where
they come up with their own
rules

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
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.
3
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 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


ActivStats
o Lesson 12: “Sample
Surveys”
Number
Of Blocks
3
Topics and Essential Questions
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 causeand-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.
Optional Instructional
Resources
 Students will work
together with a partner to
create an approved
experiment. A formal
report must be handed
 Workshop Statistics
 Topic 13: Designing
Studies

3
3
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
6. Calculate point estimates for parameters and discuss the limitations of point
estimates
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.
ActivStats
 Lesson 13: “Designed
Experiments”
Number
Of Blocks
Topics and Essential Questions
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.
3
2
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.
Optional Instructional
Resources
Number
Of Blocks
Topics and Essential Questions
PS.20 The student will identify properties of a t-distribution and apply tdistributions to single-sample and two-sample (independent and matched pairs) tprocedures, using tables or graphing calculators.
3
2
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
Review, Assessments, and Intervention
Optional Instructional
Resources
Additional information about the Standards of Learning can be found in the
VDOE Curriculum Framework
(click link above)
Additional information about math vocabulary can be found in the
VDOE Vocabulary Word Wall Cards
(click link above)