Mathematics: High School: Statistics and Probability
Illinois - Mathematics: High School: Statistics and Probability
Learning Standards | Adopted: 2010
This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.
Math.Content.HSS-ID: : Interpreting Categorical and Quantitative Data
Math.Content.HSS-ID.A: : Summarize, represent, and interpret data on a single count or measurement variable
Math.Content.HSS-ID.A.1: : Represent data with plots on the real number line (dot plots, histograms, and box plots).
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes.
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Change the values in a data set and examine how the dynamic histogram changes in response. Adjust the interval size of the histogram and see how the shape of the histogram is affected.
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Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height.
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Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median.
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Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean.
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Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
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Math.Content.HSS-ID.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.
Box-and-Whisker Plots
Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes.
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Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 1 Student Exploration focuses on range, mode, and median.
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Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean.
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Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
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Math.Content.HSS-ID.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).
Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population.
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Test your reaction time by catching a falling ruler or clicking a target. Create a data set of experiment results, and calculate the range, mode, median, and mean of your data. Data can be displayed on a list, table, bar graph or dot plot. The Reaction Time 2 Student Exploration focuses on mean.
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Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
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Math.Content.HSS-ID.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.
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
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Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population.
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Try to click your mouse once every 2 seconds. The time interval between each click is recorded, as well as the error and percent error. Data can be displayed in a table, histogram, or scatter plot. Observe and measure the characteristics of the resulting distribution when large amounts of data are collected.
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Measure your reaction time by clicking your mouse as quickly as possible when visual or auditory stimuli are presented. The individual response times are recorded, as well as the mean and standard deviation for each test. A histogram of data shows overall trends in sight and sound response times. The type of test as well as the symbols and sounds used are chosen by the user.
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Math.Content.HSS-ID.B: : Summarize, represent, and interpret data on two categorical and quantitative variables
Math.Content.HSS-ID.B.6: : Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
Math.Content.HSS-ID.B.6.a: : Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line.
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Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line.
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Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line.
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Math.Content.HSS-ID.B.6.c: : Fit a linear function for a scatter plot that suggests a linear association.
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line.
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Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line.
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Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line.
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Math.Content.HSS-ID.C.7: : Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line.
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Examine the scatter plots for data related to weather at different latitudes. The Gizmo includes three different data sets, one with negative correlation, one positive, and one with no correlation. Compare the least squares best-fit line.
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Examine the scatter plot for a random data set with negative or positive correlation. Vary the correlation and explore how correlation is reflected in the scatter plot and the trend line.
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Math.Content.HSS-ID.C.8: : Compute (using technology) and interpret the correlation coefficient of a linear fit.
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line.
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Math.Content.HSS-ID.C.9: : Distinguish between correlation and causation.
Correlation
Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line.
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Math.Content.HSS-IC: : Making Inferences and Justifying Conclusions
Math.Content.HSS-IC.A: : Understand and evaluate random processes underlying statistical experiments
Math.Content.HSS-IC.A.1: : Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
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Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling.
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Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population.
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Math.Content.HSS-IC.A.2: : Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it
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Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes.
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Experiment with spinners and compare the experimental probability of a particular outcome to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes.
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Math.Content.HSS-IC.B: : Make inferences and justify conclusions from sample surveys, experiments, and observational studies
Math.Content.HSS-IC.B.3: : Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
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Conduct a phone poll of citizens in a small neighborhood to determine their response to a yes-or-no question. Use the results to estimate the sentiment of the entire population. Investigate how the error of this estimate becomes smaller as more people are polled. Compare random versus non-random sampling.
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Math.Content.HSS-IC.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.
Polling: City
Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
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Math.Content.HSS-IC.B.5: : Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.
Populations and Samples
Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population.
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Math.Content.HSS-CP: : Conditional Probability and the Rules of Probability
Math.Content.HSS-CP.A: : Understand independence and conditional probability and use them to interpret data
Math.Content.HSS-CP.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.
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
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Math.Content.HSS-CP.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.
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
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Math.Content.HSS-CP.A.5: : Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
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Math.Content.HSS-CP.B: : Use the rules of probability to compute probabilities of compound events in a uniform probability model
Math.Content.HSS-CP.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.
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
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Math.Content.HSS-CP.B.8: : Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
Independent and Dependent Events
Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
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Math.Content.HSS-CP.B.9: : Use permutations and combinations to compute probabilities of compound events and solve problems.
Permutations and Combinations
Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle.
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Math.Content.HSS-MD: : Using Probability to Make Decisions
Math.Content.HSS-MD.A: : Calculate expected values and use them to solve problems
Math.Content.HSS-MD.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.
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
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Math.Content.HSS-MD.A.2: : Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
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Math.Content.HSS-MD.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.
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
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Math.Content.HSS-MD.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.
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
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Math.Content.HSS-MD.B: : Use probability to evaluate outcomes of decisions
Math.Content.HSS-MD.B.5: : Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
Math.Content.HSS-MD.B.5.a: : Find the expected payoff for a game of chance.
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
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Math.Content.HSS-MD.B.5.b: : Evaluate and compare strategies on the basis of expected values.
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
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Math.Content.HSS-MD.B.6: : Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
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Math.Content.HSS-MD.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).
Lucky Duck (Expected Value)
Pick a duck, win a prize! Help Arnie the carnie design his game so that he makes money (or at least breaks even). How many ducks of each type should there be? What are the prizes worth? How much should he charge to play? Lucky Duck is a fun way to learn about probabilities and expected value.
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Students assume the role of a scientist trying to solve a real world problem. They use scientific practices to collect and analyze data, and form and test a hypothesis as they solve the problems.
