Unit 1: Exploring and Understanding Data

Unit Overview: This unit introduces the foundations of statistics, the types of data collected, and how data is collected.

Major Instructional Goals: You will know you have achieved the learning goal when you can:

• Define appropriate quantities for the purpose of descriptive modeling. (N.Q.2)
• Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. (N.Q.3)
• Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. (S.IC.3)

Unit 2: Organizing Data

Unit Overview: In this unit, you will describe the different methods of displaying and organizing data and how to choose the appropriate display.

Major Instructional Goals: You will know you have achieved the learning goal when you can:

• Explore categorical data. Frequency tables and bar charts. (S.ID.SPS.3)
• Represent data with plots on the real number line (dot plots, histograms, stem plots, and box plots). (S.ID.1)
• Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). (S.ID.3)

Unit 3: Measures of Data

Unit Overview: In this unit, you will learn how to calculate the measures of center, variation, and position of a data set.

Major Instructional Goals: You will know you have achieved the learning goal when you can:

• Define appropriate quantities for the purpose of descriptive modeling. (N.Q.2)
• Compute measuring position: quartiles, percentiles,standardized scores (z-scores). (S.ID.SPS.1)

Unit 4: Probability

Unit Overview: In this unit, you will learn the rules of probabilities and how to apply them to real-world problems.

Major Instructional Goals: You will know you have achieved the learning goal when you can:

• Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). (S.CP.1)
• Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model. (S.CP.7)
• Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. (S.CP.8 (+))
• Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. (S.CP.4)
• Apply the ”Law of Large Numbers” concept. (S.MD.SPS.1)
• Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes. (S.MD.3 (+))
• Use diagrams to describe probabilities. (S.CP.10)
• (+) Use permutations and combinations to compute probabilities of compound events and solve problems. (S.CP.9)

Unit 5: Distributions

Unit Overview: In this unit, you will define random variables and use them to create binomial, geometric, and normal distributions and calculate their means and standard deviations.

Major Instructional Goals: You will know you have achieved the learning goal when you can:

• Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space. (S.MD.1)
• Interpret it as the mean of the probability distribution. (S.MD.2)
• Develop a binomial distribution from Bernoulli trials. Calculate the mean and standard deviation of the binomial distribution. (S.MS.6)
• Develop a geometric distribution from Bernoulli trials. Calculate the mean and standard deviation of the geometric distribution. (S.MD.8)
• Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. (S.MD.6)
• Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. (S.ID.4)
• Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. (S.MD.4)

Unit 6: Normal Distribution Applications

Unit Overview: Have you ever wondered how you can make a good decision, even when you don’t have all the information? In this section you’ll learn methods to evaluate incomplete information and make a sound decision based on those methods.

Major Instructional Goals: You will know you have achieved the learning goal when you can:

• Understand statistics as a process for making inferences about population parameters based on a random sample from that population. (S.IC.1)
• Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. (S.IC.2)
• Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. (S.ID.4)
• Apply the Central Limit Theorem. (S.MD.SPS.2)
• Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. (S.MD.3)
• Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. (S.IC.4)
• Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. (S.ID.4)

Unit 7: Confidence Intervals and Estimates

Unit Overview: How can you find an average or proportion of a population variable when it’s impossible to examine the whole population? How can you be sure that such value would even be close to the real value? You will learn how you can estimate those values and measure the confidence you can have in them.

Major Instructional Goals: You will know you have achieved the learning goal when you can:

• Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. (S.IC.4)
• Make decisions in hypothesis testing for one and/or two tailed tests including one- and two-sample proportions and one- and two-sample means (paired and unpaired) and Chi-square distributions (including Goodness-of-fit tests, tests for homogeneity, and tests for independence). (S.MD.SPS.4)

Unit 8: Hypothesis Testing

Unit Overview: Have you ever wondered how you can tell if a parameter of a population has changed over time? Is the average height of men still the same as it was 20 years ago? That would be impossible to tell without measuring everyone, right? In this unit you will learn methods to determine this from relatively small samples.

Major Instructional Goals: You will know you have achieved the learning goal when you can:

• Make decisions in hypothesis testing for one and/or two tailed tests including one- and two-sample proportions and one- and two-sample means (paired and unpaired) and Chi-square distributions (including Goodness-of-fit tests, tests for homogeneity, and tests for independence). (S.MD.SPS.4)
• Estimate by using point estimates and confidence intervals for one- and two-sample proportions and one- and two-sample means (including paired and unpaired data). (S.MD.SPS.3)

Unit 9: Correlation and Regressions

Unit Overview: Correlation provides a way to examine a relationship between two variables. Does one have an association with another? For example, we could see if smoking and education level have any type of relationship. And if they do, we may be able to use regression to predict data about the population.

Major Instructional Goals: You will know you have achieved the learning goal when you can:

• Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (A.CED.2)
• Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. (S.ID.6)
• Compute (using technology) and interpret the correlation coefficient of a linear fit. (S.ID.8)
• Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (A.CED.1)
• Construct linear and exponential functions given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). (F.LE.2)
• Distinguish between correlation and causation. (S.ID.9)
• Interpret the parameters in a linear or exponential function in terms of a context. (F.LE.5)
• Estimate by using point estimates and confidence intervals for one- and two-sample proportions and one- and two-sample means (including paired and unpaired data). (S.MD.SPS.3)
• Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. (S.ID.7)

Unit 10: Chi-Squared Analysis

Unit Overview: Forensic accountants examine records looking for fraud. One of the ways they can detect fraud is by comparing the frequency of digits in the numbers to a distribution known as Benford’s Law. The techniques in this unit are used to see if the patterns are unusual.

Major Instructional Goals: You will know you have achieved the learning goal when you can:

• Make decisions in hypothesis testing for one and/or two tailed tests including one- and two-sample proportions and one- and two-sample means (paired and unpaired) and Chi-square distributions (including Goodness-of-fit tests, tests for homogeneity, and tests for independence). (S.MD.SPS.4)