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Course Details:
Course Details:
Grades: 9-12
Length: one semester
Credit: 0.5 credit
Prerequisite: Algebra 1 or teacher recommendation
Course Description:
Course Description:
Introduction to Statistics is a semester-long course that provides an introduction to the topics of statistics and data analysis. Topics include data analysis, probability, simulations, inferential statistics, and techniques of sampling. Students use exploratory methods to identify patterns and make decisions. Emphasis is placed on applications and the use of statistics to solve real-life problems.
Mathematical Topics
Mathematical Topics
(Recommended Order)
Analyzing One-Variable Data
Analyzing Two-Variable Data
Collecting Data
Probability and Distributions
Course/ Grade Competencies
Course/ Grade Competencies
M1.9-12.1: The learner will write, apply, and provide a rationale for a mathematical model representing a given situation.
M1.9-12.2: The learner will interpret and use symbols to express relationships and justify reasoning when solving problems.
M3.9-12.1: The learner will use computational strategies and algorithms and provide rationale for their use.
M3.9-12.2: The learner will reason quantitatively when analyzing, representing, and solving problems.
M3.9-12.3: The learner will compare the effectiveness or logic of two plausible arguments or models.
M5.9-12.3: The learner will interpret, analyze, and use relations and functions applied in a variety of contexts, including real-world phenomena.
M7.9-12.1: The learner will formulate questions to clarify the problem at hand and formulate one (or more) questions that can be answered with data.
M7.9-12.2: The learner will design and implement a plan to collect the appropriate data to answer the statistical question.
M7.9-12.3: The learner will summarize data using appropriate statistics.
M7.9-12.4: The learner will select appropriate graphical and numerical methods, and use these methods to represent the data in a way that supports interpretation.
M7.9-12.5: The learner will interpret descriptive statistics and linear models within the context of the data and the original question.
M7.9-12.6: The learner will apply probability concepts to analyze and evaluate potential decisions and strategies.
Analyzing One-Variable Data
Analyzing One-Variable Data
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M7 – Data, Analysis, Probability, and Statistics: The learner will apply statistical methods to summarize, represent, analyze, and interpret data.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M3.9-12.1
M3.9-12.2
M3.9-12.3
M7.9-12.3
M7.9-12.4
M7.9-12.5
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
In a data set, identify the individuals and variables (categorical vs. quantitative) and summarize the distribution with a frequency or relative frequency table.
Create bar charts from categorical data, and interpret and compare bar charts and pie charts.
Make, interpret, and compare dot plots of quantitative data.
Make, interpret, and compare stem plots of quantitative data.
Make, interpret, and compare histograms of quantitative data.
Find the mean and median of a distribution of quantitative data, and identify the more appropriate measure of center in a given situation.
Calculate (using technology) and interpret the following measures of spread: range, interquartile range, and standard deviation.
Use the 1.5 x interquartile range rule to identify outliers in a data set.
Make, interpret, and compare boxplots of quantitative data.
Can be Covered:
The learner will:
Find and interpret a percentile from a distribution of quantitative data.
Find and interpret standardized scores (z-scores).
Standards:
Standards:
AKSS
S-ID.1, S-ID.2,
S-ID.3, S-ID.4
Mathematical Practices
All mathematical practices are present in each unit.
Analyzing Two-Variable Data
Analyzing Two-Variable Data
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M5 – Algebraic Functions, Patterns and Relations: The learner will utilize patterns, relations, and functions to compare, interpret, and analyze situations.
M7 – Data, Analysis, Probability, and Statistics: The learner will apply statistical methods to summarize, represent, analyze, and interpret data.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M1.9-12.2
M3.9-12.1
M3.9-12.2
M3.9-12.3
M5.9-12.3
M7.9-12.3
M7.9-12.4
M7.9-12.5
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Display relationships between two categorical variables.
Make a scatter plot of and describe the relationship between two quantitative variables.
Estimate and interpret the correlation between two quantitative variables displayed in a scatterplot.
Distinguish between correlation and causation.
Calculate the correlation between two quantitative variables, apply properties of the correlation, and describe how outliers influence the correlation.
Determine and assess the viability of a linear regression model.
Use regression lines to make predictions.
Interpret the slope and y-intercept of a regression line.
Can be Covered:
The learner will:
Calculate and interpret residuals.
Use residuals to determine if the relationship between two quantitative variables is best modeled by quadratic or exponential functions.
Standards:
Standards:
AKSS
S-ID.5, S-ID.6,
S-ID.7, S-ID.8,
S-ID.9
Mathematical Practices
All mathematical practices are present in each unit.
Collecting Data
Collecting Data
Graduate-Level Competency:
Graduate-Level Competency:
M1 – Symbolic Expression: The learner will be able to reason abstractly and utilize symbolic expressions and mathematical models.
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M7 – Data, Analysis, Probability, and Statistics: The learner will apply statistical methods to summarize, represent, analyze, and interpret data.
Course/ Grade Competencies:
Course/ Grade Competencies:
M1.9-12.1
M3.9-12.1
M3.9-12.2
M3.9-12.3
M7.9-12.1
M7.9-12.2
M7.9-12.3
M7.9-12.4
M7.9-12.5
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Identify good statistical questions, and identify the population and sample in a statistical study.
Distinguish between an observational study and an experiment.
Define and describe convenience, voluntary response, and random sampling.
Describe how sampling method affects bias.
Describe how to obtain a simple random sample.
Explain the concepts of sampling variability and how to reduce it.
Use simulations to test a claim about a population proportion.
Find the margin of error for a sample proportion and sample mean using simulation.
Explain how under-coverage, nonresponse, and other aspects of a sample survey can lead to bias.
Explain confounding and the placebo effect.
Explain the purpose of comparison and blinding in an experiment.
Describe how to randomly assign treatments and explain the purpose.
Identify other sources of variability in an experiment.
Outline an experiment that uses a completely randomized design.
Determine if it is appropriate to make an inference about cause and effect.
Evaluate if a study has been carried out ethically.
Standards:
Standards:
AKSS
S-IC.1, S-IC.2,
S-IC.3, S-IC.4,
S-IC.5, S-IC.6
Mathematical Practices
All mathematical practices are present in each unit.
Probability and Distributions
Probability and Distributions
Graduate-Level Competency:
Graduate-Level Competency:
M3 – Reasoning and Strategic Thinking: The learner will use evidence to support authentic application of concepts and support mathematical arguments.
M7 – Data, Analysis, Probability, and Statistics: The learner will apply statistical methods to summarize, represent, analyze, and interpret data.
Course/ Grade Competencies:
Course/ Grade Competencies:
M3.9-12.1
M3.9-12.2
M3.9-12.3
M7.9-12.5
M7.9-12.6
Content Objectives:
Content Objectives:
Must be Covered:
The learner will:
Interpret probability as a long-run relative frequency and use simulation to model chance behavior.
Use probability models, the complement rule, and the addition rule for mutually exclusive events to find probabilities.
Use two-way tables and Venn diagrams to find probabilities.
Use two-way tables to find and interpret conditional probabilities.
Use the general multiplication rule to calculate probabilities of independent events.
Compute the number of permutations of n individuals taken r at a time.
Compute the number of combinations of n individuals taken r at a time.
Can be Covered:
The learner will:
Use the conditional probability formula to calculate probabilities and determine independence.
Standards:
Standards:
AKSS
S-CP.1, S-CP.2,
S-CP.3, S-CP.4,
S-CP.5, S-CP.6,
S-CP.7, S-CP.8,
S-CP.9
Mathematical Practices
All mathematical practices are present in each unit.
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