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- Mathematics: Probability and Statistics

# Virginia - Mathematics: Probability and Statistics

## Standards of Learning | Adopted: 2009

### PS.1: : The student will analyze graphical displays of univariate data, including dotplots, stemplots, and histograms, to identify and describe patterns and departures from patterns, using central tendency, spread, clusters, gaps, and outliers. Appropriate technology will be used to create graphical displays.

PS.1: : The student will analyze graphical displays of univariate data, including dotplots, stemplots, and histograms, to identify and describe patterns and departures from patterns, using central tendency, spread, clusters, gaps, and outliers. Appropriate technology will be used to create graphical displays.

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. 5 Minute Preview

Mean, Median, and Mode

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. 5 Minute Preview

Stem-and-Leaf Plots

Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview

PS.10: : The student will plan and conduct an experiment. The plan will address control, randomization, and measurement of experimental error.

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. 5 Minute Preview

Polling: Neighborhood

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. 5 Minute Preview

PS.11: : The student will identify and describe two or more events as complementary, dependent, independent, and/or mutually exclusive.

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. 5 Minute Preview

PS.12: : The student will find probabilities (relative frequency and theoretical), including conditional probabilities for events that are either dependent or independent, by applying the Law of Large Numbers concept, the addition rule, and the multiplication rule.

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. 5 Minute Preview

Theoretical and Experimental Probability

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. 5 Minute Preview

PS.14: : The student will simulate probability distributions, including binomial and geometric.

Binomial Probabilities

Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation. 5 Minute Preview

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 5 Minute Preview

PS.16: : The student will identify properties of a normal distribution and apply the normal distribution to determine probabilities, using a table or graphing calculator.

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. 5 Minute Preview

PS.19: : The student will identify the meaning of sampling distribution with reference to random variable, sampling statistic, and parameter and explain the Central Limit Theorem. This will include sampling distribution of a sample proportion, a sample mean, a difference between two sample proportions, and a difference between two sample means.

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. 5 Minute Preview

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. 5 Minute Preview

### PS.2: : The student will analyze numerical characteristics of univariate data sets to describe patterns and departures from patterns, using mean, median, mode, variance, standard deviation, interquartile range, range, and outliers.

PS.2: : The student will analyze numerical characteristics of univariate data sets to describe patterns and departures from patterns, using mean, median, mode, variance, standard deviation, interquartile range, range, and outliers.

Mean, Median, and Mode

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. 5 Minute Preview

Stem-and-Leaf Plots

Build a data set and compare the line plot of the data set to the stem-and-leaf plot. 5 Minute Preview

### PS.3: : The student will compare distributions of two or more univariate data sets, analyzing center and spread (within group and between group variations), clusters and gaps, shapes, outliers, or other unusual features.

PS.3: : The student will compare distributions of two or more univariate data sets, analyzing center and spread (within group and between group variations), clusters and gaps, shapes, outliers, or other unusual features.

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. 5 Minute Preview

Describing Data Using Statistics

Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview

Mean, Median, and Mode

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. 5 Minute Preview

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. 5 Minute Preview

Real-Time Histogram

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. 5 Minute Preview

### PS.4: : The student will analyze scatterplots to identify and describe the relationship between two variables, using shape; strength of relationship; clusters; positive, negative, or no association; outliers; and influential points.

PS.4: : The student will analyze scatterplots to identify and describe the relationship between two variables, using shape; strength of relationship; clusters; positive, negative, or no association; outliers; and influential points.

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. 5 Minute Preview

Least-Squares Best Fit Lines

Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines

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. 5 Minute Preview

### PS.5: : The student will find and interpret linear correlation, use the method of least squares regression to model the linear relationship between two variables, and use the residual plots to assess linearity.

PS.5: : The student will find and interpret linear correlation, use the method of least squares regression to model the linear relationship between two variables, and use the residual plots to assess linearity.

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. 5 Minute Preview

Least-Squares Best Fit Lines

Fit a line to the data in a scatter plot using your own judgment. Then compare the least squares line of best fit. 5 Minute Preview

Solving Using Trend Lines

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. 5 Minute Preview

### PS.8: : The student will describe the methods of data collection in a census, sample survey, experiment, and observational study and identify an appropriate method of solution for a given problem setting.

PS.8: : The student will describe the methods of data collection in a census, sample survey, experiment, and observational study and identify an appropriate method of solution for a given problem setting.

Describing Data Using Statistics

Investigate the mean, median, mode, and range of a data set through its graph. Manipulate the data and watch how the mean, median, mode, and range change (or, in some cases, how they don't change). 5 Minute Preview

Polling: City

Polling: Neighborhood

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. 5 Minute Preview

### PS.9: : The student will plan and conduct a survey. The plan will address sampling techniques (e.g., simple random, stratified) and methods to reduce bias.

PS.9: : The student will plan and conduct a survey. The plan will address sampling techniques (e.g., simple random, stratified) and methods to reduce bias.

Polling: City

Polling: Neighborhood

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. 5 Minute Preview

### PS.10: : The student will plan and conduct an experiment. The plan will address control, randomization, and measurement of experimental error.

PS.10: : The student will plan and conduct an experiment. The plan will address control, randomization, and measurement of experimental error.

Polling: City

Polling: Neighborhood

### PS.11: : The student will identify and describe two or more events as complementary, dependent, independent, and/or mutually exclusive.

PS.11: : The student will identify and describe two or more events as complementary, dependent, independent, and/or mutually exclusive.

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. 5 Minute Preview

### PS.12: : The student will find probabilities (relative frequency and theoretical), including conditional probabilities for events that are either dependent or independent, by applying the Law of Large Numbers concept, the addition rule, and the multiplication rule.

PS.12: : The student will find probabilities (relative frequency and theoretical), including conditional probabilities for events that are either dependent or independent, by applying the Law of Large Numbers concept, the addition rule, and the multiplication rule.

Independent and Dependent Events

Theoretical and Experimental Probability

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. 5 Minute Preview

### PS.14: : The student will simulate probability distributions, including binomial and geometric.

PS.14: : The student will simulate probability distributions, including binomial and geometric.

Binomial Probabilities

Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation. 5 Minute Preview

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 5 Minute Preview

### PS.16: : The student will identify properties of a normal distribution and apply the normal distribution to determine probabilities, using a table or graphing calculator.

PS.16: : The student will identify properties of a normal distribution and apply the normal distribution to determine probabilities, using a table or graphing calculator.

Polling: City

### PS.19: : The student will identify the meaning of sampling distribution with reference to random variable, sampling statistic, and parameter and explain the Central Limit Theorem. This will include sampling distribution of a sample proportion, a sample mean, a difference between two sample proportions, and a difference between two sample means.

PS.19: : The student will identify the meaning of sampling distribution with reference to random variable, sampling statistic, and parameter and explain the Central Limit Theorem. This will include sampling distribution of a sample proportion, a sample mean, a difference between two sample proportions, and a difference between two sample means.

Polling: City

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. 5 Minute Preview

Correlation last revised: 9/16/2020

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