Download Bourbon County High School

Standards Curriculum Map
Bourbon County Schools
Level: High School
Grade and/or Course: AP Statistics
Updated: May 2012
Days
Unit/Topic
Standards
Days 125
Unit 1:
Exploring and
Understanding
Data
I. Exploring Data: Describing patterns and
departures from patterns
A. Constructing and interpreting graphical displays
of distributions of univariate data (dotplot, stemplot,
histogram, cumulative frequency plot)
1.Center and spread
2.Clusters and gaps
3.Outliers and other unusual features
4.Shape
B. Summarizing distributions of univariate data
1.Measuring center: median, mean
2.Measuring spread: range, interquartile range,
standard deviation
3.Measuring position: quartiles, percentiles,
standardized scores (z-scores)
4.Using boxplots
5.The effect of changing units on summary
measures
C._Comparing distributions of univariate data
(dotplots, back-to-back stemplots,
parallel boxplots)
1.Comparing center and spread: within group,
between group variation
2.Comparing clusters and gaps
3.Comparing outliers and other unusual features
4.Comparing shapes
E.Exploring categorical data
1.Frequency tables and bar charts
2.Marginal and joint frequencies for two-way
tables
3.Conditional relative frequencies and association
e.g. = Example only
Activities
AP Multiple Choice
Bellringers
FRQ Practice
Data Collection
Common assessment
Learning Targets (“I
Can” Statements)
• I can identify the
individuals and
variables in a
set of data.
• I can identify each
variable as categorical
or quantitative.
• I can make and
interpret bar graphs, pie
charts, dot plots, stem
plots, and histograms of
distributions of a
categorical variable.
• I can look for overall
patterns and skewness
in a distribution given in
any of the above forms.
• I can give appropriate
numerical measures of
center tendency and
dispersion.
• I can recognize
outliers.
• I can compare
distributions using
graphical methods.
• I can use a graphing
calculator to obtain
summary statistics, to
include the 5-number
summary.
Vocabulary
Categorical Variable
Quantitative Variable
Population
Sample
Bar Chart
Pie Chart
Marginal Distribution
Conditional
Distribution
Dotplot
Stemplot
Histogram
Shape
Center
Spread
Skewed
Outliers
Mode
Symmetric
Mean
Median
Range
IQR
Percentile
Variance
Standard Deviation
Boxplot
Normal model
Parameter
Statistic
z-score
1
4. Comparing distributions using bar charts
Days
Unit/Topic
Days
26-45
Unit 2:
Regression
Standards
I. Exploring Data: Describing patterns and
departures from patterns
Activities
AP Multiple Choice
• I can know that areas
under a density curve
represent proportions.
• I can approximate
median and mean on a
density curve.
• I can recognize the
shape and significant
characteristics of a
normal distribution,
including the 68-95-99.7
rule.
• I can find and interpret
the standardized value
(z-score) of an
observation.
• I can find proportions
above or below a stated
measurement given
relevant measures of
central tendency and
dispersion or between
two measures.
• I can determine
whether a distribution
Approaches normality.
• I can find marginal
distributions from a
two-way table.
• I can describe the
relationship between
two categorical
variables using
percents.
• I can recognize and
explain Simpson’s
paradox.
Learning Targets (“I
Can” Statements)
• I can identify variables
as quantitative or
Vocabulary
Scatterplot
Association
2
D.Exploring bivariate data
1.Analyzing patterns in scatterplots
2.Correlation and linearity
3.Least-squares regression line
4.Residual plots, outliers and influential points
Days
Unit/Topic
Days
46-65
Unit 3:
Collecting Data
Common Core Standards
II.Sampling and Experimentation: Planning and
conducting a study
A.Overview of methods of data collection
1.Census
2.Sample survey
3.Experiment
Bellringers
FRQ Practice
Data Collection
Common assessment
Activities
AP Multiple Choice
Bellringers
FRQ Practice
Data Collection
Common assessment
categorical.
• I can identify
explanatory and
response variables.
• I can make and
analyze scatter plots to
assess a relationship
between two variables.
• I can find and interpret
the correlation r
between two
quantitative variables.
• I can find and analyze
regression lines.
• I can use regression
lines to predict values
and assess the validity
of these predictions.
• I can calculate
residuals and use their
plots to recognize
unusual patterns.
• I can recognize
limitations in both r and
least-squares
regression lines due to
extreme values.
• I can recognize lurking
variables.
• I can explain the
difference between
correlation and
causality.
Learning Targets (“I
Can” Statements)
• I can identify
populations in sampling
situations.
• I can identify different
methods of sampling,
strengths and
Correlation
Correlation
Coefficient
Explanatory Variable
Response Variable
Lurking Variable
LSRL
Residual
Slope
Intercept
R-squared
Extrapolation
Leverage
Influential Point
Vocabulary
Random
Simulation
Sample survey
Bias
Sample Size
Census
3
4.Observational study
B.Planning and conducting surveys
1.Characteristics of a well-designed and wellconducted survey
2.Populations, samples and random selection
3.Sources of bias in sampling and surveys
4.Sampling methods, including simple random
sampling, stratified random sampling and cluster
sampling
C.Planning and conducting experiments
1.Characteristics of a well-designed and wellconducted experiment
2.Treatments, control groups, experimental units,
random assignmentsand replication
3.Sources of bias and confounding, including
placebo effect and blinding
4.Completely randomized design
5.Randomized block design, including matched
pairs design
D.Generalizability of results and types of
conclusions that can be drawn from
observational studies, experiments and surveys
Days
Unit/Topic
66-90
Unit 4:
Probability
Common Core Standards
III.Anticipating Patterns: Exploring random
phenomena using probability and simulation
A.Probability
1.Interpreting probability, including long-run
relative frequency interpretation
2.“Law of Large Numbers” concept
3.Addition rule, multiplication rule, conditional
probability and independence
4.Discrete random variables and their probability
distributions, including binomial and geometric
5.Simulation of random behavior and probability
distributions
Activities
AP Multiple Choice
Bellringers
FRQ Practice
Data Collection
Common assessment
weaknesses of each,
and possible bias that
might result from
sampling issues.
• I can recognize the
difference between an
observational study and
an experiment.
• I can design
randomized
experiments.
• I can recognize
confounding of
variables and the
placebo effect,
explaining when
double-blind and block
design would be
appropriate.
• I can explain how to
design an experiment to
support cause-andeffect relationships.
Simple Random
Sample (SRS)
Sampling Frame
Stratified Random
Sample
Cluster Sample
Systematic Sample
Voluntary Response
Bias
Response Bias
Nonresponse Bias
Convenience Sample
Undercoverage
Observational Study
Experiment
Factor
Level
Treatment
Control Group
Blocking
Replication
Control
Randomization
Blinding
Placebo
Confounding
Learning Targets (“I
Can” Statements)
• I can describe and
generate sample
spaces for random
events.
• I can apply the basic
rules of probability.
• I can use multiplication
and addition rules of
probability
appropriately.
• I can identify
disjointed,
Vocabulary
Trial
Outcome
Event
Sample Space
Law of Large
Numbers
Independence
Probability
Complement
Mutually Exclusive
(Disjoint)
Conditional
4
6.Mean (expected value) and standard deviation
of a random variable, and linear transformation of a
random variable
B.Combining independent random variables
1.Notion of independence versus dependence
2.Mean and standard deviation for sums and
differences of independent random variables
C.The normal distribution
1.Properties of the normal distribution
2.Using tables of the normal distribution
3.The normal distribution as a model for
measurements
complementary, and
independent events.
• I can use tree
diagrams, Venn
diagrams, and counting
techniques in solving
probability problems.
• I can recognize and
define discrete and
continuous variables.
• I can find probabilities
related to normal
random variables.
• I can calculate mean
and variance of discrete
random variable.
• I can use simulation
methods using the
graphing calculator and
the law of large
numbers to approximate
the mean of a
distribution.
• I can use rules for
means and rules for
variances to solve
problems involving
sums, differences, and
linear combinations of
random variables.
• I can verify four
conditions of a binomial
distribution: two
outcomes, fixed number
of trials, independent
trials, and the same
probability of success
for each trial.
• I can calculate
cumulative distribution
functions, cumulative
Probability
Random Variable
Probability Model
Expected Value
Bernoulii Trials
Geometric
Distribution
Binomial Distribution
5
Days
Unit/Topic
91-110
Unit 5:
Inference for
Proportions
Common Core Standards
III.Anticipating Patterns: Exploring random
phenomena using probability and simulation
D.Sampling distributions
1.Sampling distribution of a sample proportion
2.Sampling distribution of a sample mean
3.Central Limit Theorem
4.Sampling distribution of a difference between
two independent sample proportions
5.Sampling distribution of a difference between
two independent sample means
6.Simulation of sampling distributions
Activities
AP Multiple Choice
Bellringers
FRQ Practice
Data Collection
Common assessment
distribution tables and
histograms, means and
standard deviations of
binomial random
variables.
• I can use a normal
approximation to the
binomial distribution to
compute probabilities.
• I can verify four
conditions of a
geometric distribution:
two outcomes, the
same probability of
success for each trial,
independent trials, and
the count of interest
is the number of trials
required to get the
first success.
• I can calculate
cumulative distribution
functions, cumulative
distribution tables and
histograms, means and
standard deviations
of geometric random
variables.
Learning Targets (“I
Can” Statements)
• I can identify
parameters and
statistics in a sample.
• I can interpret a
sampling distribution,
including bias and
variability and how to
influence each.
• I can recognize when
a problem involves a
sample proportion.
Vocabulary
Sampling Distribution
Central Limit
Theorem
Standard Error
Confidence Interval
Margin of Error
Critical Value
Hypothesis Test
Null Hypothesis
Alternative
Hypothesis
6
IV.Statistical Inference: Estimating population
parameters and testing hypotheses
A.Estimation (point estimators and confidence
intervals)
1.Estimating population parameters and margins
of error
2.Properties of point estimators, including
unbiasedness and variability
3.Logic of confidence intervals, meaning of
confidence level and confidence intervals, and
properties of confidence intervals
4.Large sample confidence interval for a
proportion
5.Large sample confidence interval for a
difference between two proportions
B.Tests of significance
1.Logic of significance testing, null and alternative
hypotheses; p-values; one- and two-sided tests;
concepts of Type I and Type II errors; concept
of power
2.Large sample test for a proportion
3.Large sample test for a difference between two
proportions
Days
Unit/Topic
111-130
Unit 6:
Inference for
Means
Common Core Standards
IV.Statistical Inference: Estimating population
parameters and testing hypotheses
A.Estimation (point estimators and confidence
intervals)
1.Estimating population parameters and margins
of error
2.Properties of point estimators, including
Activities
AP Multiple Choice
Bellringers
FRQ Practice
Data Collection
Common assessment
• I can analyze
problems involving
sample proportions,
including using the
normal approximation to
calculate probabilities.
• I can describe
confidence intervals
and use them to
determine sample size.
• I can assess statistical
significance by
comparing values.
• I can analyze the
results of significance
tests.
• I can explain Type I
error, Type II error, and
power in significance
testing.
• I can use the z
procedure to test
significance of a
hypothesis about a
population proportion.
• I can use the twosample z procedure to
test the hypothesis
regarding equality of
proportions
in two distinct
populations.
Learning Targets (“I
Can” Statements)
• I can recognize when
a problem involves
sample means.
• I can analyze
problems involving
sample means and
understand how to use
P-value
Statistically
Significant
Alpha Level
Confidence Level
Type 1 Error
Type 2 Error
Power
Pooling
Vocabulary
Student’s t
Disribution
Matched Pairs
7
unbiasedness and variability
3.Logic of confidence intervals, meaning of
confidence level and confidence intervals, and
properties of confidence intervals
6.Confidence interval for a mean
7.Confidence interval for a difference between two
means (unpaired and paired)
B.Tests of significance
1.Logic of significance testing, null and alternative
hypotheses; p-values; one- and two-sided tests;
concepts of Type I and Type II errors; concept
of power
4.Test for a mean
5.Test for a difference between two means
(unpaired and paired)
Days
Unit/Topic
131-145
Unit 7:
Common Core Standards
III.Anticipating Patterns: Exploring random
Activities
AP Multiple Choice
the central limit theorem
to approximate a normal
distribution.
• I can state null and
alternative hypotheses
in a testing situation
involving a population
mean.
• I can calculate the
one-sample t statistics
and P-value for both
one-sided and twosided tests about the
mean μ using the
graphing calculator.
• I can recognize
whether one-sample,
matched pairs, or twosample procedures are
needed.
• I can recognize when
inference about a mean
or comparison of two
means is necessary.
• I can perform and
analyze a one-sample t
test to hypothesize a
population mean and
discuss the possible
problems inherent in the
test.
• I can perform and
analyze a two-sample t
test to compare the
difference between two
means and discuss the
possible problems
inherent in the test.
Learning Targets (“I
Can” Statements)
• I can choose the
Vocabulary
Chi-Squared
8
Inference for
Counts and
Slopes
Days
Unit/Topic
146-175
Unit 8: AP
Exam Review
phenomena using probability and simulation
D.Sampling distributions
8.Chi-square distribution
IV.Statistical Inference: Estimating population
parameters and testing hypotheses
A.Estimation (point estimators and confidence
intervals)
1.Estimating population parameters and margins
of error
2.Properties of point estimators, including
unbiasedness and variability
3.Logic of confidence intervals, meaning of
confidence level and confidence intervals, and
properties of confidence intervals
8.Confidence interval for the slope of a leastsquares regression line
B.Tests of significance
1.Logic of significance testing, null and alternative
hypotheses; p-values; one- and two-sided tests;
concepts of Type I and Type II errors; concept
of power
6.Chi-square test for goodness of fit, homogeneity
of proportions, and
independence (one- and two-way tables)
7.Test for the slope of a least-squares regression
line
I. Exploring Data: Describing patterns and
departures from patterns
D.Exploring bivariate data
5.Transformations to achieve linearity: logarithmic
andpower transformations
Common Core Standards
All of above
Bellringers
FRQ Practice
Data Collection
Common assessment
Activities
Mock Exam
AP Multiple Choice
Bellringers
FRQ Practice
Data Collection
appropriate chi-square
procedure for a given
situation.
• I can perform chisquare tests and
calculate the various
relevant components.
• I can interpret chisquare test results
obtained from computer
output.
• I can recognize when
linear regression
inference is appropriate
for a set of data.
• I can interpret the
meaning of a regression
for a given set of data.
• I can interpret the
results of computer
output for regression.
• I can recognize
exponential growth and
decay.
• I can use logarithmic
transformations to
model a linear pattern,
linear regression to find
a prediction equation for
the linear data, and
transform back to a
nonlinear model of the
original data.
Learning Targets (“I
Can” Statements)
All of above
Distribution
Goodness-of-Fit
Homogenity
Independence
Component
Residual Standard
Deviation
Re-expression
Vocabulary
All of above
9
10