Statistics & Probability

Standard	Essential Question	Bloom’s Taxonomy Activities	Vocabulary	Pacing
S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).	What are the qualities of each of the following types of graphs and when should they be used? (dot plots, histograms, box plots)	-Conduct an informal survey about issues relevant to you and express your results in dot plots, histograms, and box plots.	-Data points -Dot plots -Histograms -Box plots	3 days
S.ID.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.	Why could the centers be different when considering data? What is the benefit of determining the inter-quartile range?	-Differentiate when to consider the median of a set of data and the mean value of a set of data. -Analyze a given set of data by gathering statistics on measures of central tendency, interquartile range, and standard deviation.	-Data distribution -Measures of central tendency -Mean -Median -Mode -Spread -Interquartile range -Standard deviation	3 days
S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).	How could outlier information skew the results of a data set?	-Consider data with outliers and support when to include extreme data points and when not to.	-Center -Outliers -Extreme data points	3 days
S.ID.4 Use the mean and standard deviation of a data set to fit in 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.	How would the U.S. Census use standard deviation when considering population?	-Choose a population set to research; Go to the U.S. Census information site; compare the data from the 2000 census with the 2010 census; display your results in a method of your choosing	-Mean -Standard deviation -Normal distribution -Population	3 days
S.ID.5 Summarize categorical data for two categories in two-way 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.	How are joint, marginal, and relative frequencies determined when looking at a two-way frequency table? What methods could be used to summarize large amounts of data?	- Compare the data presented in a two-way frequency table - Evaluate the information in two similar contingency tables using measures of central tendency.	-Categorical data -Two-way frequency table -Contingency table -Relative frequency -Joint frequency -Marginal frequency -Conditional frequency -Trend	3 days
S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.	How does a line of best fit assist in interpreting the data displayed on a scatter plot?	-Design and conduct a study which includes two variables. -Create a visual representation of your results including a scatter plot, line of best fit, and description of the data.	-Positive correlation -Negative correlation -No correlation	3 days
S.ID.6a 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.	How are graphing calculators and certain programs available on the internet useful in determining the function which best fits the data?	- Formulate a line of best fit given data presented in a table or in a graph. -Analyze the line of best fit to determine qualities of the data.	-Line of best fit	3 days
S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals.	How are residuals useful in determining the accuracy of a line of best fit?	-Analyze a line of best using residuals to determine the accuracy of the function.	-Residuals	3 days
S.ID.6c Fit a linear function for a scatter plot that suggest a linear association.	What is true about the scatter plots above and below a fitted linear function?	-Support the visual determination of the correlation of a set of data with its computed correlation coefficient.	-Correlation coefficient	3 days
S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.	What information can be determined when considering the equation of a function?	-Analyze the equation of a line of best fit to determine the rate of change and intercept.	-Slope -Rate of change -Intercept	3 days
S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.	How could technology be utilized to provide information pertaining to the qualities of a line of best fit?	-Experiment with different equations to determine the relationship between the correlation coefficient and the graph.	-Correlation coefficient	3 days
S.ID.9 Distinguish between correlation and causation.	How does correlation differ from causation? If it is determined that one variable causes another variable, what is also implied?	-Evaluate the usage of the term causation to determine if it is an accurate representation of the data	-Causation -Correlation	3 days
Standard	Essential Question	Bloom’s Taxonomy Activities	Vocabulary	Pacing
S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.	Why do most polls include a (+/-) number?	-View the U.S. Census page on Center of Population, (http://2010.census.gov/2010census/data/center-of-population.php) investigate why the center moved over the years	-Statistics -Inference -Random sample	2 days
S.IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls head up with a probability 0.5. Would a result of 5 tails in a row cause you to question the model?	What role does statistics play in market research?	-From Common Core: a model says a spinning coin falls head up with a probability 0.5. Would a result of 5 tails in a row cause you to question the model? -Create your own model.	-Model -Data-generating process	2 days
S.IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.	How does the television industry utilize sample surveys in developing programming?	-Create a Venn Diagram to compare and contrast: Sample surveys, experiments, and observational studies	-Sample surveys -Experiments -Observational studies -Randomization	3 days
S.IC.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.	How does margin of error affect the possible outcome of voting results?	-Using the internet research margin of error and political race; find an example when a poll could not predict an upcoming election; create a PowerPoint slide displaying your results	-Population mean -Population proportion -Margin of error	3 days
S.IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.	What is the quality of a randomized study in regard to validity and reliability?	-Conduct a study of a topic of your choosing using 1) randomized approach and 2) targeted approach. How are your results different than if you used a targeted sample of the population? Display your results in a method of your choosing	-Data -Randomized experiment -Parameters -Significance -Validity -Reliability	3 days
S.IC.6 Evaluate reports based on data.	How does the medical industry utilize pilot studies in the development of new pharmaceuticals and treatments?	-Choose a product you are interested in purchasing on the internet with no less than 45 comments from other consumers; Conduct an analysis of the comments on the product, write a conclusion, and display your results	-Pilot study	3 days
Standard	Essential Question	Bloom’s Taxonomy Activities	Vocabulary	Pacing
S.CP.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”).	Why are subsets relevant to areas beyond mathematics?	-Create and solve a word problem which uses unions and intersections of sets.	-Set -Subset -Union -Intersection -Sample space -Outcomes	1 day
S.CP.2 Understand that two events A and B are independent if the probability of A and B -occurring together is the product of the probabilities, and use this characterization to determine if they are independent	How can one check if two events are independent of each other?	-Compare and contrast the probabilities of two events to determine if the events are independent.	-Independent -Probabilities	1 day
S.CP.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 B given A is the same as the probability of B.	In what areas are conditional probabilities relative to everyday life?	-Create a Venn Diagram and determine the probabilities of each occurrence.	-Conditional probability -Venn diagram	1 day
S.CP.4 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.	How are frequency tables used to foresee possible election results?	From Common Core: 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.	-Frequency Table	1 day
S.CP.5 Recognize and explain in 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.	How do meteorologists utilize probability to forecast weather?	From Common Core: Compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.	-Conditional probability -Independence of events	1 day
S.CP.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.	How does ratio relate to conditional probability?	Complete the following problem from Dartmouth College and create a similar problem: one finds that in a population of 100,000 females, 89.835% can expect to live to age 60, while 57.062% can expect to live to age 80. Given that a woman is 60, what is the probability that she lives to age 80?	-Conditional probability -Outcomes	1 day
S.CP.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	What is the connection between intersection, union, and the Addition Rule?	Using a deck of cards, create a worksheet which requires the use of addition rule. Share your worksheet with your peers.	-Addition rule -Probability -Venn Diagram	1 day
S.CP.8 (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BǀA) = P(B)P(AǀB), and interpret the answer in terms of the model.	How does the multiplication rule relate to independent and dependent events?	Using a bag of candy, create a worksheet utilizing the Multiplication Rule with seven examples of picking candy in a particular order.	-Multiplication Rule	1 day
S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems.	What is the difference between a permutation and a combination?	Develop a worksheet in which your peers must determine if the question requires a permutation or a combination. http://www.regentsprep.org/Regents/math/algtrig/ATS5/PCPrac.htm	-Permutations -Combinations	1 day
Standard	Essential Question	Bloom’s Taxonomy Activities	Vocabulary	Pacing
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S.MD.6 (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).	When would it be appropriate to use a random number generator?	Explore the random calculators available on random.org and write a one paragraph reflection on any three tools. -Utilize an online Bingo caller to play Bingo as a class (http://www.bingoadvantage.com/online/bingo_caller.cfm) Evaluate how this method is different than if a Bingo tumbler was used or if numbers were chosen from cards off a table	-Random number generator	1 day
S.MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).	How does probability relate to drug-efficacy in patients?	Choose a form of testing which relates to probability. Read two articles related to your form of testing; write a one-page summary of your findings. -Go to http://www.sportsclubstats.com/ and choose a sports team to follow for the entire unit. Given the team’s current status, make a hypothesis as to the team’s success over a month. Track the team each week and create a graph of the changes; at the end of the study, review your hypothesis and adjust it for the remainder of the season	-Strategies	1 day