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2016.17, Statistics, Quarter 2 The following practice standards will be used throughout the quarter: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Ongoing Standards WCE.ST.1 Apply mathematical concepts to describe, model and solve applied problems related to the relevant content. WCE.ST.2 Construct mathematical arguments regarding the relevant mathematics and critique the reasoning of others. WCE.ST.3 Solve non-routine mathematical equations using technology, graphs, formulas, and tables of values interpreting the solutions in the appropriate contexts. Standards Student Friendly “I Can” Statements Unit 4 Designing Studies S.IC.1 Understand the differences among various kinds of studies and I can demonstrate the difference between descriptive statistics and which types of inferences can be legitimately drawn from each. inferential statistics. I can identify whether data is qualitative or quantitative. I can classify data at the four levels of measurement: nominal, ordinal, interval and ratio. S.IC.2 Compare census sample survey, experiments, and observational study. I can compare and use census, sample survey, experiment, and observational study to determine which method should be used in a given situation. Page 1 of 6 I can collect data by doing an observational study, performing an experiment, using a simulation, or using a survey. S.IC.8 Compare and use sampling methods, including simple random sampling, stratified random sampling, and cluster sampling. I can design and conduct a statistical experiment to study a problem, then interpret and communicate the outcomes. I can select an appropriate sampling method. I can create a sample using random sampling, simple random sampling, stratified sampling, cluster sampling and systematic sampling. I can identify a biased sample and demonstrate understanding of how it affects a statistical study. I can explain what blind and double-blind studies do and how they are used in an experiment. S.IC.3 Describe the role of randomization in surveys and experiments. I can identify confounding variables. I can read a random number table. I can use the random number generator on my calculator. I can analyze the effect of changing units on summary measures. S.IC.7 Select a method to collect data and plan and conduct surveys and experiments. I can determine a method to collect data. S.IC.4 Demonstrate and understanding of bias in sampling. I can use a survey and experiment to collect and analyze data. I can recognize and explain instances of bias in sampling. S.IC.9 Test hypotheses using appropriate statistics. I can test my hypotheses using appropriate statistics. Page 2 of 6 S.IC.10 Analyze results and make conclusions from observational studies, experiments, and surveys. I can analyze results and make conclusions from observational studies, experiments, and surveys. S.IC.11 Evaluate reports based on data. I can evaluate reports based on data. Unit 5 Probability: What are the chances? S.CP.1 Describe events as subsets of a sample space (the set of I can identify the sample space of a probability experiment. outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” I can identify simple events. “not”). S.CP.2 Use permutations and combinations to compute probabilities of compound events and solve problems. I can create and use formulas and tree diagrams to solve probability problems. I can find the number of ways a group of objects can be arranged in order. I can find the number of ways to choose several objects from a group without regard to order. I can use counting principles to find probabilities. I can use the Fundamental Counting Principle to find the number of ways two or more events can occur. I can use permutations and combinations to compute probabilities using the formula and using technology. S.CP.3 Demonstrate an understanding of the Law of Large Numbers (strong and weak). I can demonstrate an understanding of the Law of Large Numbers. S.CP.4 Demonstrate an understanding of the addition rule, the multiplication rule, conditional probability, and independence. I can find the probability of an event. I can find the probability of the complement of an event Page 3 of 6 I can use a tree diagram to find the probability of an event. I can find the probability of an event given another event has occurred. I can distinguish between independent and dependent events. I can determine if two events are mutually exclusive. I can use the Addition Rule to find the probability of two events. I can 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.5 Apply the general Multiplication Rule in a uniform probability I can use the Multiplication Rule to find the probability of two events model, P(A and B) = P(A)P(B|A)=P(B)P(A|B), and interpret the answer occurring in sequence. in terms of the model. Unit 6 Random Variables S.MD.1. Define a random variable for a quantity of interest by I can define a random variable to investigate, create a sample space assigning a numerical value to each event in a sample space; graph the and graph the probability distribution. corresponding probability distribution using the same graphical displays as for data distributions. S.MD.2.Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. I can find a theoretical probability distribution and find the expected value under various situations. I can find a current data distribution and calculate the expected value. S.MD.3. Design a simulation of random variables and their probability distributions. I can distinguish between discrete random variables and continuous random variables. I can construct a discrete probability distribution and its graph. I can determine if a distribution is a probability distribution. Page 4 of 6 S.MD.10 Calculate the mean (expected value) and standard deviation of both a random variable and a linear transformation of a random variable. I can calculate the mean and standard deviation of both a random variable and a linear transformation of a random variable. S.IC.18 Apply the properties of the normal distribution in appropriate situations in order to make inferences about a data set. I can find the correction for continuity. I can use a normal distribution to approximate binomial probabilities. S.MD.4.Analyze discrete random variables and their probability distributions, including binomial and geometric. I can find the mean, variance, and standard deviation of a discrete probability distribution. I can find the expected value of a discrete probability distribution. I can find the expected payoff for a game of chance. I can determine if a probability experiment is a binomial experiment. I can find binomial probabilities using the binomial probability formula. I can find binomial probabilities using technology I can find binomial probabilities using the binomial probability table. I can graph a binomial distribution. I can find the mean, variance, and standard deviation of a binomial probability distribution. I can find probabilities using the geometric distribution. Page 5 of 6 S.MD.6 Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. I can use a random digit table or random integer function in my calculator to make predictions. I can interpret graphs of normal probability distributions. I can find areas under the standard normal curve I can find probabilities for normally distributed variables using a table and using technology. I can find a z-score given the area under the normal curve. S.MD.5 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.9 Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). I can transform a z-score to an x-value. I can find a specific data value of a normal distribution given the probability. I can find sampling distributions and verify their properties. I can use probability to analyze decisions and strategies. S.MD.7 Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. I can weigh possible outcomes by assigning probabilities to payoff values and finding expected values. S.MD.8 Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). I can use probabilities to make fair decisions. Page 6 of 6