Interpreting Categorical and Quantitative Data  eTAP Lesson 

Summarize, represent, and interpret data on a single count or measurement variable  
Represent data with plots on the real number line (dot plots, histograms, and box plots).
CCSS.Math.Content.HSS.ID.A.1 
Probability Data Plots What is Statistics? Boxplot, Interquartile Range, and Midhinge 
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
CCSS.Math.Content.HSS.ID.A.2 
Data Calculations What is Probability? Methods of Collecting, Representing, and Displaying Data 
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
CCSS.Math.Content.HSS.ID.A.3 
Paired Data Sets and Scatterplots Visually Representing Numerical Data 
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.
CCSS.Math.Content.HSS.ID.A.4 
Standard Deviation of Random Variable Basic Methods of Describing Data 
Summarize, represent, and interpret data on two categorical and quantitative variables  
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
CCSS.Math.Content.HSS.ID.B.6.a 

Informally assess the fit of a function by plotting and analyzing residuals.
CCSS.Math.Content.HSS.ID.B.6.b 
Frequency Distribution Table, Summation Notation, and Mean Formula 
Fit a linear function for a scatter plot that suggests a linear association.
CCSS.Math.Content.HSS.ID.B.6.c 
Paired Data Sets and Scatterplots 
Interpret linear models  
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
CCSS.Math.Content.HSS.ID.C.7 
Geometric Mean, Harmonic Mean, and Weighted Arithmetic Mean 
Compute (using technology) and interpret the correlation coefficient of a linear fit.
CCSS.Math.Content.HSS.ID.C.8 
Position Formula and Finding Median in Frequency Distribution Table 
Distinguish between correlation and causation.
CCSS.Math.Content.HSS.ID.C.9 
Data Classification, Range, and Midrange 
Making Inferences and Justifying Conclusions  eTAP Lesson 
Understand and evaluate random processes underlying statistical experiments  
Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
CCSS.Math.Content.HSS.IC.A.1 
Quartiles, Deciles, and Percentiles 
Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
CSS.Math.Content.HSS.IC.A.2 

Make inferences and justify conclusions from sample surveys, experiments, and observational studies  
Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
CCSS.Math.Content.HSS.IC.B.3 
Correlations Regression Models and Least Square Methods 
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.
CCSS.Math.Content.HSS.IC.B.4 
Fundamental Counting Principle, Factorial 
Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
CCSS.Math.Content.HSS.IC.B.5 
Permutation and Combination 
Evaluate reports based on data.
CCSS.Math.Content.HSS.IC.B.6 
Sample Space, Basics of Probability 
Conditional Probability and the Rules of Probability  eTAP Lesson 
Understand independence and conditional probability and use them to interpret data  
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").
CCSS.Math.Content.HSS.CP.A.1 
Multiple Events 
None  
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
CCSS.Math.Content.HSS.CP.A.2 
Binomial Distributions 
Understand independence and conditional probability and use them to interpret data  
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
CCSS.Math.Content.HSS.CP.A.3 
Conditional Probability 
Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway 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.
CCSS.Math.Content.HSS.CP.A.4 
Normal Distributions 
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.
CCSS.Math.Content.HSS.CP.A.5 
Probability Data Plots 
Use the rules of probability to compute probabilities of compound events.  
Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
CCSS.Math.Content.HSS.CP.B.6 
Probability of Events 
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.
CCSS.Math.Content.HSS.CP.B.7 
Geometric Probability 
Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model.
CCSS.Math.Content.HSS.CP.B.8 

Use permutations and combinations to compute probabilities of compound events and solve problems.
CCSS.Math.Content.HSS.CP.B.9 
Relationships Between Events 
Using Probability to Make Decisions  eTAP Lesson 
Calculate expected values and use them to solve problems  
Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
CCSS.Math.Content.HSS.MD.A.1 
Multiple Events 
Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
CCSS.Math.Content.HSS.MD.A.2 
Expected Value 
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 multiplechoice test where each question has four choices, and find the expected grade under various grading schemes.
CCSS.Math.Content.HSS.MD.A.3 
Dependent & Independent Variables 
Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?
CCSS.Math.Content.HSS.MD.A.4 
Discrete Probability Distribution 
Use probability to evaluate outcomes of decisions  
Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fastfood restaurant.
CCSS.Math.Content.HSS.MD.B.5.a 
Conditional Probability 
Evaluate and compare strategies on the basis of expected values. For example, compare a highdeductible versus a lowdeductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.
CCSS.Math.Content.HSS.MD.B.5.b 
Independent and Dependent Events 
Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
CSS.Math.Content.HSS.MD.B.6 

Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
CCSS.Math.Content.HSS.MD.B.7 
Mean and Variance of Random Variable 