Statistics Honors

Course Essential Questions

• How can we collect, organize, and analyze data to reveal trends and patterns?
• How can we avoid the ethical dilemmas of data collection and analysis?
• How can we quantify and explain the uncertain?
• How can we use statistics to make informed decisions?

Course Learning Objectives

• Analyze data graphically and numerically.
• Apply proper sampling methods to best analyze a population.
• Evaluate the advantages and disadvantages of different sampling methods.
• Interpret probabilities of real-life phenomena to compare predicted and actual outcomes.
• Interpret the concept of randomness.
• Interpret data to make predictions, conclusions, and decisions.

Unit 1: One-Variable Data (Weeks 1-4)

Unit Level Essential Questions

• How can we organize data?
• How can we analyze data graphically and numerically?
• What do measures of center, spread, and location tell us about data as a whole?
• How can we determine if the data is normal?

Week 1: Types of Data

Weekly Learning Objectives

• Classify different types of data.
• Identify the difference between a population and a sample.

Week 2: Displaying, Measuring, and Summarizing Data

Weekly Learning Objectives

• Construct graphs of categorical and quantitative data.
• Identify and interpret any outliers.
• Describe the shape of a data distribution.
• Calculate and interpret measures of center.
• Calculate and interpret measures of spread.
• Compare graphs and numerical summaries to draw conclusions.

Week 3: Describing Location and Transforming Data

Weekly Learning Objectives

• Find and interpret percentiles.
• Find and interpret standardized scores.
• Compare percentiles and standardized scores in terms of location.
• Describe the effect of adding or subtracting a constant on a distribution.
• Describe the effect of multiplying or dividing by a constant on a distribution.
• Analyze the effect of adding or subtracting and multiplying or dividing by a constant on measures of center, spread, and location.

Week 4: Density Curves and the Normal Distribution

Weekly Learning Objectives

• Apply a density curve to a model distribution.
• Compare the mean and the median of a density curve.
• Draw a normal curve to model a distribution.
• Apply the empirical rule to estimate the proportion of values in an interval in a normal distribution.
• Find the proportion of values of a specified boundary in a normal distribution.
• Find the value that corresponds to a given percentile in a normal distribution.

Unit 2: Two-Variable Data (Weeks 5-6)

Unit Level Essential Questions

• How can we determine if there is a relationship between two variables?
• How can we measure the relationship between two variables?
• How can we create a model to represent the relationship between two variables?

Week 5: Relationship Between Two Variables

Weekly Learning Objectives

• Identify explanatory and response variables.
• Construct a scatter plot.
• Describe the direction and strength of the association of two quantitative variables.

Week 6: Correlation & Linear Regression

Weekly Learning Objectives

• Describe what correlation measures.
• Calculate and interpret the correlation coefficient.
• Calculate the equation of the regression line for a scatter plot.
• Interpret the slope and y-intercept of a regression line within the context of the data.
• Make predictions using regression lines.
• Investigate limitations of regression lines.

Unit 3: Collecting Data (Weeks 7-8)

Unit Level Essential Questions

• How can we determine the best way to collect data?
• How can we prevent bias?
• How much data is enough to make reasonable conclusions?

Week 7: Sampling and Surveys

• Weekly Learning Objectives
• Identify the population and sample in a statistical study.
• Justify the use of different sampling methods.
• Explain how some sampling methods and question wording can lead to bias.

Week 8: Observational Studies and Experiments

Weekly Learning Objectives

• Identify the difference between observational studies and experiments.
• Identify variables of observational studies and experiments.
• Describe the placebo effect.

Unit 4: Probability (Weeks 9-11)

Unit Level Essential Questions

• Can we use simulations to make predictions of events?
• How can we make decisions based on chance?

Week 9: Randomness and Simulation

Weekly Learning Objectives

• Interpret randomness.
• Apply simulation to model a random process.
• Compare experimental and theoretical probabilities.

Week 10: Basic Probability Rules

Weekly Learning Objectives

• Calculate probabilities of different events.
• Interpret the complement of an event and calculate its probability.
• Identify mutually exclusive events and calculate their probabilities.
• Compare probabilities using a Venn diagram.

Week 11: Conditional Probability and Independence

Weekly Learning Objectives

• Calculate and interpret conditional probabilities.
• Determine if two events are independent or dependent.
• Calculate and interpret the probabilities of independent and dependent events.

Unit 5: Random Variables (Weeks 12-13)

Unit Level Essential Questions

• How can we model randomness?
• How can we illustrate successes and failures through repeated trials?

Week 12: Introduction to Random Variables

Weekly Learning Objectives

• Classify a random variable as discrete or continuous.
• Verify the probability distribution of a discrete random variable.
• Verify the probability distribution of a continuous random variable.
• Describe how a normal distribution determines the probabilities of a continuous random variable.

Week 13: Binomial and Geometric Distributions

Weekly Learning Objectives

• Determine if a given scenario describes a binomial distribution.
• Calculate and interpret probabilities involving a binomial random variable.
• Calculate and interpret the mean and standard deviation of a binomial distribution.
• Determine if a given scenario describes a geometric distribution.
• Calculate and interpret probabilities involving a geometric random variable.
• Calculate and interpret the mean and standard deviation of a geometric distribution.

Unit 6: Statistics in the Real World (Weeks 14-15)

Unit Level Essential Questions

• How are statistics applied in our world?

Week 14: Statistics in Today’s World

Weekly Learning Objectives

• Analyze how statistics is used in the world around us.
• Analyze probabilities and how they are used to make decisions.
• Describe how statistics and probabilities influence our world.

Week 15: Applications of Statistics

Weekly Learning Objectives

• Describe how statistics and probabilities influence our world.
• Explain how data can be collected in appropriate and unbiased ways.
• Provide feedback to VHS Learning about the course and your experience.