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Lakewood City Schools
Course of Study for Statistics
Scope and Sequence – Statistics is an elective course wherein students are introduced to major theories and techniques for
collecting, analyzing, and drawing conclusions from data. Students in this course will be exposed to three broad conceptual
themes: exploring data, planning a study, and anticipating a pattern in advance. The direct application of statistical
techniques on standard problems and the analysis of graphical representations will be emphasized. Technology will be used
to develop understanding.
More class time will be used to practice the basic concepts of the course. It is open to students in Grades 10-12.
The prerequisite is one year of Algebra 2 with a C average or better.
Course Overview: The General Organizational for this Course
Unit numbers correspond to sub-chapter numbers in our textbook.
Exploring Data: Describing patterns and departures from patterns (~40%) Exploratory analysis of data makes use of graphical and
numerical techniques to study patterns and departures from patterns. Emphasis will be placed on interpreting information from
graphical and numerical displays and summaries. This theme is covered in Chapters 1-4 of this course.
Sampling and Experimentation: Planning and conducting a study (~20%) Data must be collected according to a well-developed plan
if valid information on a conjecture is to be obtained. This plan includes clarifying the question and deciding upon a method of data
collection and analysis. This theme is covered in Chapter 5 of this course; ideas regarding planning and conducting a study are
presented in Chapter 4 as well.
Anticipating Patterns: Exploring random phenomena using probability and simulation (~40%) Probability is the tool used for
anticipating what the distribution of data should look like under a given model. This theme is covered primarily in Chapters 7-9 of
this course; the t distribution is covered in Chapter 10.
Course of Study for Statistics
Revised: 6/10/2009
Page 1 of 38
Lakewood City Schools
Course of Study for Statistics
Scope and Sequence – Statistics is an elective course wherein students are introduced to major theories and techniques for
collecting, analyzing, and drawing conclusions from data. Students in this course will be exposed to three broad conceptual
themes: exploring data, planning a study, and anticipating a pattern in advance. The direct application of statistical
techniques on standard problems and the analysis of graphical representations will be emphasized. Technology will be used
to develop understanding.
More class time will be used to practice the basic concepts of the course. It is open to students in Grades 10-12.
The prerequisite is one year of Algebra 2 with a C average or better.
Course Overview: The General Organizational for this Course
Unit numbers correspond to sub-chapter numbers in our textbook.
Throughout this document, Ohio Academic Content Standards are abbreviated as follows. “NNO” indicates the Number, Number
Sense, and Operations Standard. “M” indicates the Measurement Standard. “GSS” indicates the Geometry and Spatial Sense
Standard. “PFA” indicates the Patterns, Functions, and Algebra Standard. “DAP” indicates the Data Analysis and Probability
Standard. “MP” indicates the Mathematical Processes Standard. In each case the abbreviation is followed by a grade range or
individual grade and then a letter or number; to indicate each relevant benchmark (grade range/letter) or indicator (grade/number).
Please note that the Mathematical Processes Standard does not include indicators.
In addition, references are made to the American Statistical Association’s Guidelines for Assessment and Instruction in Statistics
Education (GAISE) Report. The abbreviation “G” followed by a letter indicating a level defined in this report indicates
correspondence to this curricular framework.
Course of Study for Statistics
Revised: 6/10/2009
Page 2 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 1.1: Displaying Distributions with Graphs
Use a variety of graphical techniques to display a distribution. These will include bar graphs, pie charts, stemplots, histograms, ogives, time plots, and boxplots. Interpret graphical
displays in terms of the shape, center, and spread of the distribution, as well as gaps and outliers.
Standard and Benchmark
Grade Level Indicators
DAP_11-12/A
DAP_11-12/A
DAP_11-12/A
DAP_11-12/A
DAP_11-12/A
DAP_11-12/A
DAP_11-12/A
DAP_11-12/A
DAP_11/8
DAP_11-12/A
DAP_11/8
DAP_11-12/A
DAP_11-12/A
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
Strategies/Resources
Describe what is meant by exploratory
data analysis.
Explain what is meant by the
distribution of a variable.
Differentiate between categorical
variables and quantitative variables.
Construct bar graphs and pie charts for
a set of categorical data.
Construct a stemplot for a set of
quantitative data.
Construct a back-to-back stemplot to
compare two related distributions.
Construct a stemplot using split stems.
YMS text § 1.1
Construct a histogram for a set of
quantitative data, and discuss how
changing the class width can change the
impression of the data given by the
histogram.
Describe the overall pattern of a
distribution by its shape, center, and
spread.
Explain what is meant by the mode of a
distribution.
Recognize and identify symmetric and
skewed distributions.
YMS text § 1.1
YMS text § 1.1
YMS text § 1.1
YMS text § 1.1
YMS text § 1.1
YMS text § 1.1
YMS text § 1.1
YMS text § 1.1
YMS text § 1.1
YMS text § 1.1
Page 3 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 1.1: Displaying Distributions with Graphs
Use a variety of graphical techniques to display a distribution. These will include bar graphs, pie charts, stemplots, histograms, ogives, time plots, and boxplots. Interpret graphical
displays in terms of the shape, center, and spread of the distribution, as well as gaps and outliers.
DAP_11-12/A
DAP_11-12/A
DAP_11-12/A
Course of Study for Statistics
Revised: 6/10/2009
DAP_11/8
Explain what is meant by an outlier in a
stemplot or histogram.
Construct and interpret an ogive
(relative cumulative frequency graph)
from a relative frequency table.
Construct a time plot for a set of data
collected over time.
YMS text § 1.1
YMS text § 1.1
YMS text § 1.1
Page 4 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 1.2: Describing Distributions with Numbers
Use a variety of numerical techniques to describe a distribution. These will include mean, median, quartiles, five-number summary, interquartile range, standard deviation, range, and
variance. Interpret numerical measures in the context of the situation in which they occur. Learn to identify outliers in a data set. Explore the effects of a linear transformation of a data
set.
Standard and Benchmark
Grade Level Indicators
DAP_11-12/B
DAP_12/3
DAP_11-12/B
DAP_11/8
DAP_11-12/B
DAP_11/8
DAP_11-12/B, DAP_11-12/D
DAP_12/3
DAP_11-12/B, DAP_11-12/D
DAP_12/3
DAP_11-12/B
DAP_12/3
DAP_11-12/B
DAP_12/3
DAP_11-12/B, DAP_11-12/D
DAP_12/3
DAP_11-12/B, DAP_11-12/D
DAP_11/6
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
Strategies/Resources
Given a data set, compute the mean and
median as measures of center.
Explain what is meant by a resistant
measure.
Identify situations in which the mean is
the most appropriate measure of center
and situations in which the median is
the most appropriate measure.
Given a data set, find the quartiles.
YMS text § 1.2
Given a data set, find the five-number
summary.
Use the five-number summary of a data
set to construct a boxplot for the data.
Compute the interquartile range (IQR)
of a data set.
Given a data set, use the 1.5 × IQR rule
to identify outliers.
Given a data set, compute the standard
deviation and variance as measures of
spread.
YMS text § 1.2
YMS text § 1.2
YMS text § 1.2
YMS text § 1.2
YMS text § 1.2
YMS text § 1.2
YMS text § 1.2
YMS text § 1.2
Page 5 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 1.2: Describing Distributions with Numbers
Use a variety of numerical techniques to describe a distribution. These will include mean, median, quartiles, five-number summary, interquartile range, standard deviation, range, and
variance. Interpret numerical measures in the context of the situation in which they occur. Learn to identify outliers in a data set. Explore the effects of a linear transformation of a data
set.
DAP_11-12/B
DAP_11/6
DAP_11-12/B
DAP_11-12/B
DAP_11/8
DAP_11-12/B
DAP_11/3, DAP_12/3
DAP_11-12/B
DAP_11/8
Course of Study for Statistics
Revised: 6/10/2009
Give two reasons why we use squared
deviations rather than just average
deviations from the mean.
Explain what is meant by degrees of
freedom.
Identify situations in which the
standard deviation is the most
appropriate measure of spread and
situations in which the interquartile
range is the most appropriate measure.
Explain the effect of a linear
transformation of a data set on the
mean, median, and standard deviation
of the set.
Use numerical and graphical techniques
to compare two or more data sets.
YMS text § 1.2
YMS text § 1.2
YMS text § 1.2
YMS text § 1.2
YMS text § 1.2
Page 6 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 2.1: Measures of Relative Standing and Density Curves
Be able to compute measures of relative standing for individual values in a distribution. This includes standardized values (z-scores) and percentile ranks.
Use Chebyshev’s inequality to describe the percentage of values in a distribution within an interval centered at the mean. Demonstrate an understanding of
a density curve, including its mean and median.
Standard and Benchmark
DAP_11-12/B+
DAP_11-12/B+
DAP_11-12/B+
DAP_11-12/B+
DAP_11-12/B+
DAP_11-12/B+
DAP_11-12/B+
DAP_11-12/B+
Course of Study for Statistics
Revised: 6/10/2009
Grade Level Indicators
Clear Learning Targets
Strategies/Resources
Explain what is meant by a
standardized value.
Compute the z-score of an observation
given the mean and standard deviation
of a distribution.
Compute the pth percentile of an
observation.
Define Chebyshev’s inequality, and give
an example of its use.
Explain what is meant by a
mathematical model.
Define a density curve.
YMS text § 2.1
Explain where the mean and median of
a density curve are to be found.
Describe the relative position of the
mean and median in a symmetric
density curve and in a skewed density
curve.
YMS text § 2.1
YMS text § 2.1
YMS text § 2.1
YMS text § 2.1
YMS text § 2.1
YMS text § 2.1
YMS text § 2.1
Page 7 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 2.2: Normal Distributions
Demonstrate and understanding of the Normal distribution and the 68-95-99.7 Rule. Use tables and technology to find (a) the proportion of values on an
interval of the Normal distribution and (b) a value with a given proportion of observations above or below it. Use a variety of techniques, including
construction of a normal probability plot, to assess the Normality of a distribution.
Standard and Benchmark
Grade Level Indicators
DAP_11/7
DAP_11/7
DAP_11/7
DAP_11/7
DAP_11/7
DAP_11/7
DAP_11/7
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
Identify the main properties of the
Normal curve as a particular density
curve.
List three reasons why Normal
distributions are important in statistics.
Explain the 68-95-99.7 rule (the
empirical rule).
Explain the notation N(  ,  ).
Strategies/Resources
YMS text § 2.2
YMS text § 2.2
YMS text § 2.2
YMS text § 2.2
Use a table of values for the standard
YMS text § 2.2
Normal curve to compute the proportion
of observations that are (a) less than a
given z-score, (b) greater than a given zscore, or (c) between two given zscores.
Use a table of values for the standard
YMS text § 2.2
Normal curve to find the proportion of
observations in any region given any
Normal distribution (i.e., given raw data
rather than z-scores).
Use a table of values for the standard
YMS text § 2.2
Normal curve to find a value with a
given proportion of observations above
or below it (inverse Normal).
Page 8 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 2.2: Normal Distributions
Demonstrate and understanding of the Normal distribution and the 68-95-99.7 Rule. Use tables and technology to find (a) the proportion of values on an
interval of the Normal distribution and (b) a value with a given proportion of observations above or below it. Use a variety of techniques, including
construction of a normal probability plot, to assess the Normality of a distribution.
DAP_11/7
Course of Study for Statistics
Revised: 6/10/2009
Identify at least two graphical
techniques for assessing Normality.
Explain what is meant by a Normal
probability plot; use it to help assess the
Normality of a given data set.
Use technology to perform Normal
distribution calculations and to make
Normal probability plots.
YMS text § 2.2
YMS text § 2.2
YMS text § 2.2
Page 9 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 3.1: Scatterplots and Correlation
Construct and interpret a scatterplot for a set of bivariate data. Compute and interpret the correlation r between two variables. Demonstrate an
understanding of the basic properties of the correlation r.
Standard and Benchmark
DAP_11-12/D
Grade Level Indicators
DAP_11/4
DAP_11/4
DAP_11/4
DAP_11/4
DAP_11/4
DAP_11-12/D
DAP_11/5
DAP_11-12/D
DAP_11/5
DAP_11/8
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
Explain the difference between an
explanatory variable and a response
variable.
Given a set of bivariate data, construct a
scatterplot.
Explain what is meant by the direction,
form, and strength of the overall pattern
of a scatterplot.
Explain how to recognize an outlier in a
scatterplot.
Explain what it means for two variables
to be positively or negatively
associated.
Explain how to add categorical
variables to a scatterplot.
Use a graphing calculator to construct a
scatterplot. {Construct a scatterplot by
hand.} {Construct a scatterplot using
computer software.}
Define the correlation r and describe
what it measures.
Given a set of bivariate data, use
technology to compute the correlation r.
{Manually compute r for a small data
set.}
List the four basic properties of the
correlation r that you need to know to
interpret any correlation.
Strategies/Resources
YMS text § 3.1
YMS text § 3.1
YMS text § 3.1
YMS text § 3.1
YMS text § 3.1
YMS text § 3.1
YMS text § 3.1
YMS text § 3.1
YMS text § 3.1
YMS text § 3.1
Page 10 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 3.1: Scatterplots and Correlation
Construct and interpret a scatterplot for a set of bivariate data. Compute and interpret the correlation r between two variables. Demonstrate an
understanding of the basic properties of the correlation r.
DAP_11/8
Course of Study for Statistics
Revised: 6/10/2009
List four other facts about correlation
that must be kept in mind when using r.
YMS text § 3.1
Page 11 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 3.2: Least-Squares Regression
Explain the meaning of a least squares regression line. Given a bivariate data set, construct and interpret a regression line. Demonstrate an understanding of
how one measures the quality of a regression line as a model for bivariate data.
Standard and Benchmark
Grade Level Indicators
DAP_11/5
DAP_11/5
DAP_11/5
DAP_11/5
DAP_11-12/D
DAP_11/5
DAP_11-12/D
DAP_11/8
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
Strategies/Resources
Explain what is meant by a regression
line.
Given a regression equation, interpret
the slope and y-intercept in context.
Explain what is meant by extrapolation.
YMS text § 3.2
Explain why the regression line is
called the “least-squares regression
line” (LSRL).
Explain how the coefficients of the
regression equation, ŷ  a  bx , can be
found given r, sx, sy, and (x, y) .
Given a bivariate data set, use
technology to construct a least-squares
regression line. {Manually construct a
least-squares regression line for a small
data set.}
Define a residual.
YMS text § 3.2
Given a bivariate data set, use
technology to construct a residual plot
for a linear regression.
List two things to consider about a
residual plot when checking to see if a
straight line is a good model for a
bivariate data set.
Explain what is meant by the standard
deviation of the residuals.
YMS text § 3.2
YMS text § 3.2
YMS text § 3.2
YMS text § 3.2
YMS text § 3.2
YMS text § 3.2
YMS text § 3.2
YMS text § 3.2
Page 12 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 3.2: Least-Squares Regression
Explain the meaning of a least squares regression line. Given a bivariate data set, construct and interpret a regression line. Demonstrate an understanding of
how one measures the quality of a regression line as a model for bivariate data.
DAP_11/8
DAP_11/8
Course of Study for Statistics
Revised: 6/10/2009
Define the coefficient of determination,
r2, and explain how it is used in
determining how well a linear model
fits a bivariate set of data.
List and explain four important facts
about least-squares regression.
YMS text § 3.2
YMS text § 3.2
Page 13 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 3.3: Correlation and Regression Wisdom
A short description of the unit in narrative form goes here.
Standard and Benchmark
DAP_11-12/D
Grade Level Indicators
Strategies/Resources
DAP_11/8
Recall the three limitations on the use of
correlation and regression.
YMS text § 3.3
DAP_11/8
Explain what is meant by an outlier in
bivariate data.
YMS text § 3.3
DAP_11/8
Explain what is meant by an influential
observation and how it relates to regression.
YMS text § 3.3
DAP_11/8
Given a scatterplot in a regression setting,
identify outliers and influential
observations.
Define a lurking variable.
YMS text § 3.3
Give an example of what it means to say
“association does not imply causation.”
YMS text § 3.3
Explain how correlations based on averages
differ from correlations based on
individuals.
YMS text § 3.3
DAP_11/8
DAP_11/8
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
YMS text § 3.3
Page 14 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 4.1: Transforming to Achieve Linearity
Identify settings in which a transformation might be necessary to achieve linearity. Use transformations involving powers and logarithms to linearize
curved relationships.
Standard and Benchmark
Grade Level Indicators
DAP_12/2
DAP_12/2
DAP_12/2
DAP_12/2
DAP_12/2
DAP_12/2
DAP_12/2
DAP_12/2
DAP_12/2
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
Explain what is meant by transforming
(re-expressing) data.
Discuss the advantages of transforming
nonlinear data.
Tell where y  log(x) fits into the
hierarchy of power transformations.
Explain the ladder of power
transformations.
Explain how linear growth differs from
exponential growth.
Identify real-life situations in which a
transformation can be used to linearize
data from an exponential growth model.
Use a logarithmic transformation to
linearize a data set that can be modeled
by an exponential model.
Identify situations in which a
transformation is required to linearize a
power model.
Use a transformation to linearize a data
set that can be modeled by a power
model.
Strategies/Resources
YMS text § 4.1
YMS text § 4.1
YMS text § 4.1
YMS text § 4.1
YMS text § 4.1
YMS text § 4.1
YMS text § 4.1
YMS text § 4.1
YMS text § 4.1
Page 15 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 4.2: Relationships between Categorical Variables
Explain what is meant by a two-way table, and describe its parts. Give an example of Simpson’s paradox.
Standard and Benchmark
Grade Level Indicators
Clear Learning Targets
Explain what is meant by a two-way
table.
Explain what is meant by marginal
distributions in a two-way table.
Describe how changing counts to
percents is helpful in describing
relationships between categorical
variables.
Explain what is meant by a conditional
distribution.
Define Simpson’s paradox, and give an
example of it.
Course of Study for Statistics
Revised: 6/10/2009
Strategies/Resources
YMS text § 4.2
YMS text § 4.2
YMS text § 4.2
YMS text § 4.2
YMS text § 4.2
Page 16 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 4.3: Establishing Causation
Explain what gives the best evidence for causation. Explain the criteria for establishing causation when experimentation is not feasible.
Standard and Benchmark
Grade Level Indicators
DAP_11/8
DAP_11/8
DAP_11/8
DAP_11/9
DAP_11/9
DAP_11/9
DAP_11/9
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
Identify the three ways in which the
association between two variables can
be explained.
Explain what process provides the best
evidence for causation.
Define what is meant by a common
response.
Define what it means to say that two
variables are confounded.
Discuss why establishing a cause-andeffect relationship through
experimentation is not always possible.
Explain what it means to say that a lack
of evidence for cause-and-effect
relationship does not necessarily mean
that there is no cause-and-effect
relationship.
List five criteria for establishing
causation when you cannot conduct a
controlled experiment.
Strategies/Resources
YMS text § 4.3
YMS text § 4.3
YMS text § 4.3
YMS text § 4.3
YMS text § 4.3
YMS text § 4.3
YMS text § 4.3
Page 17 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 5.1: Designing Samples
Distinguish between, and discuss the advantages of, observational studies and experiments. Identify and give examples of different types of sampling
methods, including a clear definition of a simple random sample. Identify and give examples of sources of bias in sample surveys.
Standard and Benchmark
Grade Level Indicators
Define population and sample.
YMS text § 5.1
DAP_11/2, DAP_12/1
Explain how sampling differs from
census.
Explain what is meant by a voluntary
response sample. Give an example of a
voluntary response sample.
Explain what is meant by convenience
sampling.
Define what it means for a sampling
method to be biased.
Define, carefully, a simple random
sample (SRS).
List the four steps involved in choosing
an SRS.
Explain what is meant by systematic
random sampling.
Use a table of random digits to select a
simple random sample.
Define a probability sample.
YMS text § 5.1
Given a population, determine the
strata of interest, and select a stratified
random sample.
Define a cluster sample.
YMS text § 5.1
Define undercoverage and nonresponse
as sources of bias in sample surveys.
YMS text § 5.1
DAP_11/2, DAP_12/1
DAP_11/2, DAP_12/1
DAP_11/2, DAP_12/1
DAP_11/2, DAP_12/1
DAP_11/2, DAP_12/1
DAP_11/2, DAP_12/1
DAP_11/2, DAP_12/1
DAP_11/2, DAP_12/1
DAP_11/2, DAP_12/1
DAP_11/2, DAP_12/1
Course of Study for Statistics
Revised: 6/10/2009
Strategies/Resources
DAP_11/2
DAP_11/2, DAP_12/1
DAP_11-12/D
Clear Learning Targets
YMS text § 5.1
YMS text § 5.1
YMS text § 5.1
YMS text § 5.1
YMS text § 5.1
YMS text § 5.1
YMS text § 5.1
YMS text § 5.1
YMS text § 5.1
Page 18 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 5.1: Designing Samples
Distinguish between, and discuss the advantages of, observational studies and experiments. Identify and give examples of different types of sampling
methods, including a clear definition of a simple random sample. Identify and give examples of sources of bias in sample surveys.
DAP_11/2
DAP_11/2
DAP_11/2, DAP_12/1
Course of Study for Statistics
Revised: 6/10/2009
Give an example of response bias in a
survey question.
Write a survey question in which the
wording of the question is likely to
influence the response.
Identify the major advantage of large
random samples.
YMS text § 5.1
YMS text § 5.1
YMS text § 5.1
Page 19 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 5.2: Designing Experiments
Identify and explain the three basic principles of experimental design. Explain what is meant by a completely randomized design. Distinguish between the
purposes of randomization and blocking in an experimental design. Use random numbers from a table or technology to select a random sample.
Standard and Benchmark
Grade Level Indicators
DAP_11-12/C
DAP_11/1
DAP_11-12/C
DAP_11/1
DAP_11-12/C
DAP_11/1
DAP_11-12/C
DAP_11/1
DAP_11-12/C
Clear Learning Targets
Strategies/Resources
Define experimental units, subjects, and
treatment.
Define factor and level.
YMS text § 5.2
YMS text § 5.2
DAP_11/1
Given a number of factors and the
number of levels for each factor,
determine the number of treatments.
Explain the major advantage of an
experiment over an observational study.
Give an example of the placebo effect.
DAP_11-12/C
DAP_11/1
Explain the purpose of a control group.
YMS text § 5.2
DAP_11-12/C
DAP_11/1
YMS text § 5.2
DAP_11-12/C
DAP_11/1
DAP_11-12/C
DAP_11/1
DAP_11-12/C, DAP_11-12/D
DAP_11/1
DAP_11-12/C
DAP_11/1
DAP_11-12/C
DAP_11/1, DAP_11/9
Explain the difference between control
and a control group.
Discuss the purpose of replication, and
give an example of replication in the
design of an experiment.
Discuss the purpose of randomization in
the design of an experiment.
Given a list of subjects, use a table of
random numbers to assign individuals
to treatment and control groups.
List the three main principles of
experimental design.
Explain what it means to say that an
observed effect is statistically
significant.
Course of Study for Statistics
Revised: 6/10/2009
YMS text § 5.2
YMS text § 5.2
YMS text § 5.2
YMS text § 5.2
YMS text § 5.2
YMS text § 5.2
YMS text § 5.2
YMS text § 5.2
Page 20 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 5.2: Designing Experiments
Identify and explain the three basic principles of experimental design. Explain what is meant by a completely randomized design. Distinguish between the
purposes of randomization and blocking in an experimental design. Use random numbers from a table or technology to select a random sample.
DAP_11-12/C
DAP_11/1
Define a completely randomized design.
YMS text § 5.2
DAP_11-12/C
DAP_11/1
YMS text § 5.2
DAP_11-12/C
DAP_11/1
For an experiment, generate an outline
of a completely randomized design.
Define a block.
DAP_11-12/C
DAP_11/1
YMS text § 5.2
DAP_11-12/C
DAP_11/1
DAP_11-12/C
DAP_11/1
DAP_11-12/C
DAP_11/1
DAP_11-12/C
DAP_11/1, DAP_11/9
Give an example of block design in an
experiment.
Explain how block design may be better
than a completely randomized design.
Give an example of matched pairs
design, and explain why matched pairs
are an example of block designs.
Explain what is meant by a study being
double blind.
Give an example in which a lack of
realism negatively affects our ability to
generalize the results of a study.
Course of Study for Statistics
Revised: 6/10/2009
YMS text § 5.2
YMS text § 5.2
YMS text § 5.2
YMS text § 5.2
YMS text § 5.2
Page 21 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 6.1: Simulation
Perform a simulation of probability problem using a table of random numbers or technology.
Standard and Benchmark
Grade Level Indicators
Clear Learning Targets
Strategies/Resources
DAP_11-12/C
DAP_12/6
Define simulation.
YMS text § 6.1
DAP_11-12/C
DAP_12/6
YMS text § 6.1
DAP_11-12/C
DAP_12/6
DAP_11-12/C
DAP_12/6
DAP_11-12/C, DAP_11-12/D
DAP_12/6
DAP_11-12/C
DAP_12/6
List the five steps involved in a
simulation.
Explain what is meant by independent
trials.
Use a table of random digits to carry
out a simulation.
Given a probability problem, conduct a
simulation in order to estimate the
probability desired.
Use both calculator and computer to
conduct a simulation of a probability
problem.
Course of Study for Statistics
Revised: 6/10/2009
YMS text § 6.1
YMS text § 6.1
YMS text § 6.1
YMS text § 6.1
Page 22 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 6.2: Probability Models
Use the basic rules of probability to solve probability problems. Write out the sample space for a probability random phenomenon, and use it to answer
probability questions. Describe what is meant by the intersection and union of two events. Discuss the concept of independence.
Standard and Benchmark
Grade Level Indicators
DAP_12/6
Strategies/Resources
YMS text § 6.2
DAP_12/6
Explain how the behavior of a chance
event differs in the short-run and longrun.
Explain what is meant by a random
phenomenon.
Explain what it means to say that the
idea of probability is empirical.
Define probability in terms of relative
frequency.
Define sample space.
DAP_12/6
Define event.
YMS text § 6.2
DAP_12/6
Explain what is meant by a probability
model.
Construct a tree diagram.
YMS text § 6.2
Use the multiplication principle to
determine the number of outcomes in a
sample space.
Explain what is meant by sampling with
replacement and sampling without
replacement.
List the four rules that must be true for
any assignment of probability.
Explain what is meant by {A  B} and
{A  B} .
YMS text § 6.2
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
Page 23 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 6.2: Probability Models
Use the basic rules of probability to solve probability problems. Write out the sample space for a probability random phenomenon, and use it to answer
probability questions. Describe what is meant by the intersection and union of two events. Discuss the concept of independence.
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_11-12/D
Course of Study for Statistics
Revised: 6/10/2009
DAP_12/6
Explain what is meant by each of the
regions in a Venn diagram.
Give an example of two events A and B
where A  B   .
Use a Venn diagram to illustrate the
intersection of two events A and B.
Compute the probability of an event
given the probabilities of the outcomes
that make up the event.
Explain what is meant by equally likely
outcomes.
Compute the probability of an event in
the special case of equally likely
outcomes.
Define what it means for two events to
be independent.
Give the multiplication rule for
independent events.
Given two events, determine if they are
independent.
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
YMS text § 6.2
Page 24 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 6.3: General Probability Rules
Use general addition and multiplication rules to solve probability problems. Solve problems involving conditional probability, using Bayes’s rule when
appropriate.
Standard and Benchmark
Grade Level Indicators
DAP_12/6
DAP_12/6
DAP_11-12/D
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
DAP_12/6
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
Strategies/Resources
State the addition rule for disjoint
events.
State the general addition rule for union
of two events.
Given any two events A and B, compute
P(A  B) .
Define what is meant by a joint event
and joint probability.
Explain what is meant by the
conditional probability P(B | A) .
State the general multiplication rule for
any two events.
Use the general multiplication rule to
define P(B | A) .
Explain what is meant by Bayes’s rule.
YMS text § 6.3
Define independent events in terms of a
conditional probability.
YMS text § 6.3
YMS text § 6.3
YMS text § 6.3
YMS text § 6.3
YMS text § 6.3
YMS text § 6.3
YMS text § 6.3
YMS text § 6.3
Page 25 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 7.1: Discrete and Continuous Random Variables
Define what is meant by a random variable. Define a discrete random variable. Define a continuous random variable. Explain what is meant by the
probability distribution for a random variable.
Standard and Benchmark
Grade Level Indicators
Strategies/Resources
DAP_11/10, DAP_12/4
Define a discrete random variable.
YMS text § 7.1
DAP_11/10, DAP_12/4
Explain what is meant by a probability
distribution.
Construct the probability distribution
for a discrete random variable.
Given a probability distribution for a
discrete random variable, construct a
probability histogram.
Review: define a density curve.
YMS text § 7.1
Explain what is meant by a uniform
distribution.
Define a continuous random variable
and probability distribution for a
continuous random variable.
YMS text § 7.1
DAP_11/10
DAP_11/10
DAP_11/10
DAP_11/10
DAP_11/10
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
YMS text § 7.1
YMS text § 7.1
YMS text § 7.1
YMS text § 7.1
Page 26 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 7.2: Means and Variances of Random Variables
Explain what is meant by the probability distribution for a random variable. Explain what is meant by the law of large numbers. Calculate the mean and
variance of a discrete random variable. Calculate the mean and variance of distributions formed by combining two random variables.
Standard and Benchmark
Grade Level Indicators
DAP_12/4
DAP_12/4
DAP_12/4
Clear Learning Targets
Define what is meant by the mean of a
random variable.
Calculate the mean of a discrete
random variable.
Calculate the variance and standard
deviation of a discrete random variable.
Explain, and illustrate with an example,
what is meant by the law of large
numbers.
Explain what is meant by the law of
small numbers.
Given  X and Y , calculate a bX ,
and  X Y .
YMS text § 7.2
Given  X and  Y , calculate  2a bX
YMS text § 7.2
and  2X Y (where X and Y are
independent).
Explain how standard deviations are
calculated when combining random
variables.
Discuss the shape of linear combination
of independent Normal random
variables.
Course of Study for Statistics
Revised: 6/10/2009
Strategies/Resources
YMS text § 7.2
YMS text § 7.2
YMS text § 7.2
YMS text § 7.2
YMS text § 7.2
YMS text § 7.2
YMS text § 7.2
Page 27 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 8.1: The Binomial Distributions
Explain what is meant by a binomial setting and binomial distribution. Use technology to solve probability questions in a binomial setting. Calculate the
mean and variance of a binomial random variable. Solve a binomial probability problem using a Normal approximation.
Standard and Benchmark
Course of Study for Statistics
Revised: 6/10/2009
Grade Level Indicators
Clear Learning Targets
Strategies/Resources
Describe the conditions that need to be
present to have a binomial setting.
Define a binomial distribution.
YMS text § 8.1
Explain when it might be all right to
assume a binomial setting even though
the independence condition is not
satisfied.
Explain what is meant by the sampling
distribution of a count.
State the mathematical expression that
gives the value of a binomial
coefficient. Explain how to find the
value of that expression.
State the mathematical expression used
to calculate the value of binomial
probability.
Evaluate a binomial probability by
using the mathematical formula for
P(X  k) .
Explain the difference between
binompdf(n,p,X) and
binomcdf(n,p,X).
Use both calculator and computer to
help evaluate a binomial probability.
If X is B(n, p) , find  X and  X (that
is, calculate the mean and variance of a
binomial distribution).
YMS text § 8.1
YMS text § 8.1
YMS text § 8.1
YMS text § 8.1
YMS text § 8.1
YMS text § 8.1
YMS text § 8.1
YMS text § 8.1
YMS text § 8.1
Page 28 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 8.1: The Binomial Distributions
Explain what is meant by a binomial setting and binomial distribution. Use technology to solve probability questions in a binomial setting. Calculate the
mean and variance of a binomial random variable. Solve a binomial probability problem using a Normal approximation.
Use a Normal approximation for a
binomial distribution to solve questions
involving binomial probability.
Course of Study for Statistics
Revised: 6/10/2009
YMS text § 8.1
Page 29 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 8.2: The Geometric Distributions
Explain what is meant by a geometric setting. Solve probability questions in a geometric setting. Calculate the mean and variance of a geometric random
variable.
Standard and Benchmark
Grade Level Indicators
Clear Learning Targets
Describe what is meant by a geometric
setting.
Given the probability of success, p,
calculate the probability of getting the
first success on the nth trial.
Calculate the mean (expected value) and
the variance of a geometric random
variable.
Calculate the probability that it takes
more than n trials to see the first success
for a geometric random variable.
Use simulation to solve geometric
probability problems.
Course of Study for Statistics
Revised: 6/10/2009
Strategies/Resources
YMS text § 8.2
YMS text § 8.2
YMS text § 8.2
YMS text § 8.2
YMS text § 8.2
Page 30 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 9.1: Sampling Distributions
Define a sampling distribution. Contrast bias and variability.
Standard and Benchmark
Grade Level Indicators
DAP_12/5
DAP_12/5
DAP_12/5
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
Compare and contrast parameter and
statistic.
Explain what is meant by sampling
variability.
Define the sampling distribution of a
statistic.
Explain how to describe a sampling
distribution.
Define an unbiased statistic and an
unbiased estimator.
Describe what is meant by the
variability of a statistic.
Explain how bias and variability are
related to estimating with a sample.
Strategies/Resources
YMS text § 9.1
YMS text § 9.1
YMS text § 9.1
YMS text § 9.1
YMS text § 9.1
YMS text § 9.1
YMS text § 9.1
Page 31 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 9.2: Sampling Proportions
Describe the sampling distribution of a sample proportion (shape, center, and spread). Use a Normal approximation to solve probability problems involving
the sampling distribution of a sample proportion.
Standard and Benchmark
Grade Level Indicators
Clear Learning Targets
Describe the sampling distribution of a
sample proportion. (Remember:
“describe” means tell about shape,
center, and spread.)
Compute the mean and standard
deviation for the sampling distribution
of p̂ .
Identify the “rule of thumb” that
justifies the use of the recipe for the
standard deviation of p̂ .
Identify the conditions necessary to use
a Normal approximation to the
sampling distribution of p̂ .
Use a Normal approximation to the
sampling distribution of p̂ to solve
probability problems involving p̂ .
Course of Study for Statistics
Revised: 6/10/2009
Strategies/Resources
YMS text § 9.2
YMS text § 9.2
YMS text § 9.2
YMS text § 9.2
YMS text § 9.2
Page 32 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 9.3: Sample Means
Describe the sampling distribution of a sample mean. State the central limit theorem. Solve probability problems involving the sampling distribution of a
sample mean.
Standard and Benchmark
Grade Level Indicators
DAP_12/5
DAP_12/5
Course of Study for Statistics
Revised: 6/10/2009
Clear Learning Targets
Strategies/Resources
Given the mean and standard deviation
of a population, calculate the mean and
standard deviation for the sampling
distribution of a sample mean.
Identify the shape of the sampling
distribution of a sample mean drawn
from a population that has a Normal
distribution.
State the central limit theorem.
YMS text § 9.3
Use the central limit theorem to solve
probability problems for the sampling
distribution of a sample mean.
YMS text § 9.3
YMS text § 9.3
YMS text § 9.3
Page 33 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 10.1: Confidence Intervals – The Basics
Describe statistical inference. Describe the basic form of all confidence intervals. Construct and interpret a confidence interval for a population mean
(including paired data) and for a population proportion. Describe a margin of error, and explain ways in which you can control the size of the margin of
error. Determine the sample size necessary to construct a confidence interval for a fixed margin of error.
Standard and Benchmark
Grade Level Indicators
Clear Learning Targets
List the (six) basic steps in the
reasoning of statistical estimation.
Distinguish between a point estimate
and an interval estimate.
Identify the basic form of all confidence
intervals.
Explain what is meant by margin of
error.
State in nontechnical language what is
meant by a “level C confidence
interval.”
State the three conditions that need to
be present in order to construct a valid
confidence interval.
Explain what it means by the “upper p
critical value” of the standard Normal
distribution.
For a known population standard
deviation  , construct a level C
confidence interval for a population
mean.
List the four necessary steps in the
creation of a confidence interval (see
Inference Toolbox).
Identify three ways to make the margin
of error smaller when constructing a
confidence interval.
Course of Study for Statistics
Revised: 6/10/2009
Strategies/Resources
YMS text § 10.1
YMS text § 10.1
YMS text § 10.1
YMS text § 10.1
YMS text § 10.1
YMS text § 10.1
YMS text § 10.1
YMS text § 10.1
YMS text § 10.1
YMS text § 10.1
Page 34 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 10.1: Confidence Intervals – The Basics
Describe statistical inference. Describe the basic form of all confidence intervals. Construct and interpret a confidence interval for a population mean
(including paired data) and for a population proportion. Describe a margin of error, and explain ways in which you can control the size of the margin of
error. Determine the sample size necessary to construct a confidence interval for a fixed margin of error.
Once a confidence interval has been
constructed for a population value,
interpret the interval in the context of
the problem.
Determine the sample size necessary to
construct a level C confidence interval
for a population mean with a specified
margin of error.
Identify as many of the six “warnings”
about constructing confidence intervals
as you can. (For example, a nice
formula cannot correct for bad data.)
Course of Study for Statistics
Revised: 6/10/2009
YMS text § 10.1
YMS text § 10.1
YMS text § 10.1
Page 35 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 10.2: Estimating a Population Mean
Compare and contrast the t distribution and the Normal distribution.
Standard and Benchmark
Grade Level Indicators
Clear Learning Targets
Identify the three conditions that must
be present before estimating a
population mean.
Explain what is meant by the standard
error of a statistic in general and by the
standard error of the sample mean in
particular.
List three important facts about the t
distributions. Include comparisons to
the standard Normal curve.
Use Table C to determine critical t
value for a given level C confidence
interval for a mean and a specified
number of degrees of freedom.
Construct a one-sample t confidence
interval for a population mean
(remembering to use the four-step
procedure).
Describe what is meant by paired t
procedures.
Calculate a level C t confidence interval
for a set of paired data.
Explain what is meant by a robust
inference procedure and comment on
the robustness of t procedures.
Discuss how sample size affects the
usefulness of t procedures.
Course of Study for Statistics
Revised: 6/10/2009
Strategies/Resources
YMS text § 10.2
YMS text § 10.2
YMS text § 10.2
YMS text § 10.2
YMS text § 10.2
YMS text § 10.2
YMS text § 10.2
YMS text § 10.2
YMS text § 10.2
Page 36 of 38
Lakewood City Schools
Course of Study for Statistics
Unit 10.3: Estimating a Population Proportion
List the conditions that must be present to construct a confidence interval for a population mean or a population proportion. Explain what is meant by the
standard error, and determine the standard error of x and the standard error of p̂ .
Standard and Benchmark
Grade Level Indicators
Clear Learning Targets
Given a sample proportion, p̂ ,
determine the standard error of p̂ .
List the three conditions that must be
present before constructing a
confidence interval for an unknown
population proportion.
Construct a confidence interval for a
population proportion, remembering to
use the four-step procedure (see the
Inference Toolbox).
Determine the sample size necessary to
construct a level C confidence interval
for a population proportion with a
specified margin of error.
Course of Study for Statistics
Revised: 6/10/2009
Strategies/Resources
YMS text § 10.3
YMS text § 10.3
YMS text § 10.3
YMS text § 10.3
Page 37 of 38
Lakewood City Schools
Course of Study for Statistics
Unit Z: tbd
A short description of the unit in narrative form goes here.
Standard and Benchmark
Cut and paste the ODE Academic
Content Standards and Benchmarks that
are covered in this unit.
These can be accessed on the ODE
website.
Course of Study for Statistics
Revised: 6/10/2009
Grade Level Indicators
Cut and paste the ODE Indicators that
are covered in this unit.
These can be accessed on the ODE
website.
Clear Learning Targets
I can…
Strategies/Resources
Add your resources and strategies here
(Add newly created “I Can” statements
that are the Clear Learning Targets in
this column, based on the grade level
indicator listed to the left.)
Page 38 of 38