# Probability and Statistics Curriculum Pacing Guide

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1 Unit 1 Terms PS.SPMJ.3 PS.SPMJ.5 Plan and conduct a survey to answer a statistical question. Recognize how the plan addresses sampling technique, randomization, measurement of experimental error and methods to reduce bias. Distinguish between experiments and observational studies. Determine which of two or more possible experimental designs will best answer a given research question and justify the choice based on statistical significance. Unit 1 - Terms Differentiate between descriptive and inferential statistics. Identify and classify variables as discrete or continuous and qualitative or quantitative. Distinguish between a statistic and a parameter. (PS.SPMJ.3, PS.SPMJ.5) Identify and classify methods of data collection as a survey, an observational study, or a controlled experiment. (PS.SPMJ.3, PS.SPMJ.5) Compare various random sampling techniques including simple, stratified, cluster, and systematic. (PS.SPMJ.3) Define bias and explain how you can minimize it. (PS.SPMJ.5) Evaluate experimental designs. Random Rectangles Lab Farm Activity Newspaper Activity Chapter 1 5 Anderson School District Five Page

2 Unit 2 Tables and Graphs PS.SPID.1* PS.SPID.2* Select and create an appropriate display, including dot plots, histograms, and box plots, for data that includes only real numbers. Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets that include all real numbers. Unit 2 Tables and Graphs (PS.SPID.1) Construct dot plots, pictograph, time-series, circle graphs, bar graphs, dot plots, Pareto charts, categorical frequency distribution, and stem and leaf plots. Construct frequency distribution, histogram, frequency polygon, and ogive. Lab: Qualitative vs. Quantitative Stock Tracker Activity Chapter 2 5 (PS.SPID.2) Describe the skewness and symmetry of a graph. Anderson School District Five Page

3 Unit 3 Measures of Central Tendency, Variation, and Position PS.SPID.1* PS.SPID.2* PS.SPID.3* Select and create an appropriate display, including dot plots, histograms, and box plots, for data that includes only real numbers. Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets that include all real numbers. Summarize and represent data from a single data set. Interpret differences in shape, center, and spread in the context of the data set, accounting for possible effects of extreme data points (outliers). Unit 3 Measures of Central Tendency, Variation, and Position (PS.SPID.2) Determine the mean, median, mode, and midrange of a data array by hand and using a graphing calculator. Determine the range, variance, and standard deviation of a data array by hand and using a graphing calculator. Determine the mean, median, and mode for ungrouped and grouped data by hand. (Show on graphing calculator after test.) (PS.SPID.2, PS.SPID.3) Determine the variance and standard deviation for ungrouped and grouped data by hand. (Show on graphing calculator after test.) Determine z-scores and discuss and apply the empirical rule. (PS.SPID.2, PS.SPID.3) Determine quartiles, percentiles, and Interquartile range. (PS.SPID.1, PS.SPID.2, PS.SPID.3) Draw box-and-whisker plots and determine outliers. Predict the effect of transformations of data on measures of central tendency, variability, and the shape of the distribution. Hand Span Lab Unit 2 and 3 Project Chapter 2 10 Anderson School District Five Page

4 Unit 4 Descriptive Analysis and Presentation of Bivariate Data PS.SPID.5* PS.SPID.6* PS.SPID.7* PS.SPID.8* PS.SPID.9 PS.SPID.10 Analyze bivariate categorical data using two-way tables and identify possible associations between the two categories using marginal, joint, and conditional frequencies. Using technology, create scatterplots and analyze those plots to compare the fit of linear, quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the data set, and use the function to solve problems in the context of the data. Find linear models using median fit and regression methods to make predictions. Interpret the slope and intercept of a linear model in the context of the data. Compute using technology and interpret the correlation coefficient of a linear fit. Differentiate between correlation and causation when describing the relationship between two variables. Identify potential lurking variables which may explain an association between two variables. Create residual plots and analyze those plots to compare the fit of linear, quadratic, and exponential models to a given data set. Select the appropriate model and use it for interpolation. Unit 4 - Descriptive Analysis and Presentation of Bivariate Data (PS.SPID.5, PS.SPID.6) Constructing contingency tables and scatter plots for bivariate data. Classify a scatterplot by shape including linear, quadratic, and exponential. (PS.SPID.7, PS.SPID.8, PS.SPID.9), Describe the linear correlation between two variables as positive, negative, or no correlation. Determine and explain the correlation coefficient. Guess My Age M & M Lab Cooling Coffee Chapter 3 7 (SP.SPID.6, SP.SPID.7) Determine the line of best fit with visual approximation and technology and understand the meaning of the y-intercept and the slope. Anderson School District Five Page

5 Unit 4 - Descriptive Analysis and Presentation of Bivariate Data (SP.SPID.10) Make predictions using the line of best fit by using interpolation or extrapolation. Anderson School District Five Page

6 Unit 5 Counting Rules PS.SPCR.1c PS.SPCR.8 Represent sample spaces for compound events using Venn diagrams. Use permutations and combinations to solve mathematical and real-world problems, including determining probabilities of compound events. Justify the results. Unit 5 Counting Rules (PS.SPCR.1c) Display sample spaces. (PS.SPCR.8) Determine the probability of an event using counting rules (permutations) with and without replacement. Determine the probability of an event using combinations. Determine whether a probability problem is a permutation or a combination and solve it. Turkey npr/ncr Activity Chapter 4 5 Anderson School District Five Page

7 Unit 6 Probability PS.SPCR.1 PS.SPCR.1a PS.SPCR.1b PS.SPCR.1c PS.SPCR.2 PS.SPCR.3 PS.SPCR.4 PS.SPCR.5 PS.SPCR.6 PS.SPCR.7 PS.SPMJ.2* Describe events as subsets of a sample space. Use Venn diagrams to represent intersections, unions, and complements. Relate intersections, unions, and complements to the words and, or, and not. Represent sample spaces for compound events using Venn diagrams. Use the multiplication rule to calculate probabilities for independent and dependent events. 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. Understand the conditional probability of A and 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. 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. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. Calculate the conditional probability of an event A given event B as the fraction of B s outcomes that also belong to A, and interpret the answer in terms of the model. Apply the Addition Rule and the Multiplication Rule to determine probabilities, including conditional probabilities, and interpret the results in terms of the probability model. Distinguish between experimental and theoretical probabilities. Collect data on a chance event and use the relative frequency to estimate the theoretical probability of that event. Determine whether a given probability model is consistent with experimental results. Unit 6 Probability (PS.SPMJ.2) Use the Law of Large Numbers in probability experiments. (PS.SPCR.3, PS.SPCR.4, PS.SPCR.5, PS.SPCR.6, PS.SPCR.7, PS.SPMJ.2) Determine the theoretical probability of an event. Compare theoretical and experimental probabilities. Is This Game Fair? M & M Let s Race Chapter 4 7 (PS.SPCR.1, PS.SPCR.1a, PS.SPCR.1b, PS.SPCR.1c) Use the concept of complementary sets to compute probabilities. Anderson School District Five Page

8 Unit 6 Probability (PS.SPCR.1, PS.SPCR.1a, PS.SPCR.1b, PS.SPCR.7) Categorize two events either as mutually exclusive or as not mutually exclusive of one another. Use the addition rule to find the probability of mutually exclusive events. (PS.SPCR.2, PS.SPCR.7) Classify events as either dependent or independent. Use the multiplication rule to find the probability of independent and dependent events. (PS.SPCR.3, PS.SPCR.4, PS.SPCR.5, PS.SPCR.6, PS.SPCR.7) Find Conditional probability. MIDTERM EXAM Anderson School District Five Page

9 Unit 7 Probability Distribution Probability and Statistics Curriculum Pacing Guide PS.SPMD.1 Develop the probability distribution for a random variable defined for a sample space in which a theoretical probability can be calculated and graph the distribution. PS.SPMD.2 Calculate the expected value of a random variable as the mean of its probability distribution. Find expected values by assigning probabilities to payoff values. Use expected values to evaluate and compare strategies in real-world scenarios. PS.SPMD.3 Construct and compare theoretical and experimental probability distributions and use those distributions to find expected values. PS.SPMD.4* Use probability to evaluate outcomes of decisions by finding expected values and determine if decisions are fair. PS.SPMD.5* Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions. PS.SPMD.6* Analyze decisions and strategies using probability concepts. Unit 7 Probability Distribution (PS.SPMD.3) Identify random variables. Determine the probability distribution of a discrete random variable and graphs. (PS.SPMD.1, PS.SPMD.2, PS.SPMD.3, PS.SPMD.4, PS.SPMD.5, PS.SPMD.6*) Determine the mean, variance, and standard deviation of a discrete probability distribution. Chapter 5 3 Use procedures to find the expected value of discrete random variables and construct meaning within contexts. Anderson School District Five Page

10 Unit 8 Binomial Distribution Probability and Statistics Curriculum Pacing Guide PS.SPMD.1 Develop the probability distribution for a random variable defined for a sample space in which a theoretical probability can be calculated and graph the distribution. Unit 8 Binomial Distribution (PS.SPMD.1) Determine the probability of a specific number of trials from a binomial experiment using graphing calculators for a real world problem. Chapter 5 4 Determine the mean and standard deviation of a binomial distribution. Anderson School District Five Page

11 Unit 9 Normal Probability PS.SPID.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. Unit 9 Normal Probability (PS.SPID.4) Identify properties of a normal distribution and find the area under the standard normal curve using tables and graphing calculators. Determine the z-score for a given probability. Chapter 6 8 Solve real life applications involving the normal distributions (finding area, probability, and cut-off scores). Anderson School District Five Page

12 Unit 10 Sample Variability PS.SPID.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. Unit 10 Sample Variability (PS.SPID.4) Forming a sampling distribution of means and ranges. (PS.SPID.4) Constructing a sampling distribution of sample means and proportions using the central limits theorem. Chapter 7 5 (PS.SPID.4) Applications involving the central limits theorem. Anderson School District Five Page

13 Unit 11 Confidence Intervals and Minimum Sample Size PS.SPMJ.1* PS.SPMJ.4 Understand statistics and sampling distributions as a process for making inferences about population parameters based on a random sample from that population. 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. Unit 11 Confidence Intervals and Minimum Sample Size (PS.SPMJ.1, PS.SPMJ.4) Determine the confidence interval for the mean for a large sample. Baseball Project Chapter 8 (PS.SPMJ.1, PS.SPMJ.4) Determine the minimum sample size for a large sample (z). (PS.SPMJ.1, PS.SPMJ.4) Determine the confidence interval for the mean of a small sample. (PS.SPMJ.1, PS.SPMJ.4) Determine the confidence interval for a proportion. (PS.SPMJ.1, PS.SPMJ.4) Determine the minimum sample size for a proportion. (PS.SPMJ.1, PS.SPMJ.4) Determine the confidence interval for a variance and standard deviation (chi-squared). M & M Lab Chapter 9 6 Anderson School District Five Page

14 Unit 12 One Sample Hypothesis Testing Probability and Statistics Curriculum Pacing Guide PS.SPMJ.1* PS.SPMJ.6 Understand statistics and sampling distributions as a process for making inferences about population parameters based on a random sample from that population. Evaluate claims and conclusions in published reports or articles based on data by analyzing study design and the collection, analysis, and display of the data. Unit 12 One Sample Hypothesis Testing Understanding the techniques of hypothesis testing. Investigate type I and type II errors. Chapter 8 Perform hypothesis testing for a large sample size. Perform hypothesis testing for a large sample size using the p- value. 6 Perform hypothesis testing for a small sample size. Chapter 9 Perform hypothesis testing for a proportion. Perform hypothesis testing for chi-squared. Anderson School District Five Page

15 Unit 13 Two-Sample Hypothesis Testing Probability and Statistics Curriculum Pacing Guide PS.SPMJ.1* PS.SPMJ.6 Understand statistics and sampling distributions as a process for making inferences about population parameters based on a random sample from that population. Evaluate claims and conclusions in published reports or articles based on data by analyzing study design and the collection, analysis, and display of the data. Unit 13 Two-Sample Hypothesis Testing Perform hypothesis testing for the mean using the p-value. With time permitting you can do more two-sample tests. Chapter 10 5 END OF COURSE EXAM Anderson School District Five Page

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