Interpreting Categorical and Quantitative Data
Standard 
Lessons 
Worksheets 
HSSID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). 

HSSID.A.2 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. 
Explore
Mean and Median 

HSSID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). 

HSSID.A.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. 

HSSID.B.5 Summarize categorical data for two categories in twoway frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. 
Trends in categorical data 

HSSID.B.6, HSSID.B.6a, HSSID.B.6b, HSSID.B.6c Represent data on two quantitative variables on a scatter
plot, and describe how the variables are related. 
Interpret Scatter
Plots 

HSSID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. 

HSSID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit. 

HSSID.C.9 Distinguish between correlation and causation. 
Types of Statistical Studies 
Making Inferences and Justifying Conclusions
Standard 
Lessons 
Worksheets/Games 
HSSIC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. 
Valid Claims Statistic Games 

HSSIC.A.2 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? 
Simple Hypothesis Testing  Simple Hypothesis Testing 
HSSIC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. 
Types of Statistical Studies 

HSSIC.B.4 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. 

HSSIC.B.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. 
Hypothesis Testing in Experiments 

HSSIC.B.6 Evaluate reports based on data. 
Types of Statistical Studies 
Conditional Probability & the Rules of Probability
Standard 
Lessons 
Worksheets/Games 
HSSCP.A.1 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?). 

HSSCP.A.2 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. 

HSSCP.A.3 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. 
Identify dependent and independent events 

HSSCP.A.4 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. 
Trends in categorical data 

HSSCP.A.5 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. 
Trends in categorical data 

HSSCP.B.6 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. 

HSSCP.B.7 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. 
Adding Probabilities 

HSSCP.B.8 (+) 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. 
Multiplying dependent probabilities 

HSSCP.B.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems. 
Combinations Permutations Permutations and Combinations Probability with Permutations and Combinations 
Using Probability to Make Decisions
Standard 
Lessons 
Worksheets/Games 
HSSMD.A.1 (+) 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. 
Construct Probability Distributions 

HSSMD.A.2 (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. 

HSSMD.A.3 (+) 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. 
Expected value with calculated probabilities 

HSSMD.A.4 (+) 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? 
Expected values with empirical probabilities 

HSSMD.B.5, HSSMD.B.5a, HSSMD.B.5b (+) Weigh the possible outcomes of a decision by
assigning probabilities to payoff values and finding
expected values. 
Expected value Make decisions with expected values 

HSSMD.B.6 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). 
Use probability to make fair decisions 

HSSMD.B.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). 
Make decisions with expected values 
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