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# Oklahoma - Mathematics: Statistics and Probability

## Academic Standards | Adopted: 2022

### S.Q: : Statistical Questions

S.Q.1: : Understand the distinction between mathematical models and statistical models.

S.Q.1.1: : Distinguish among different sources of variability, including measurement, natural, induced, and sampling variability.

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

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

S.Q.2: : Distinguish between the distribution of a population, a distribution of sample data, and a sampling distribution.

S.Q.2.1: : Distinguish between sample statistics and population parameters.

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

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

S.Q.2.2: : Recognize a population distribution has fixed values of its parameters and that these parameter values are typically unknown.

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

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

S.Q.2.3: : Recognize that a sample data distribution is taken from a population distribution, and the data distribution is what is seen in practice.

Polling: City

Polling: Neighborhood

Populations and Samples

S.Q.2.4: : Recognize a sampling distribution is the distribution of a sample statistic (e.g., sample mean, sample proportion) obtained from repeated samples.

Polling: City

Polling: Neighborhood

Populations and Samples

S.Q.3: : Identify differences between categorical and quantitative data.

S.Q.3.2: : Compare and contrast different potential graphical or visual representations given the same data set.

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

Histograms

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. 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

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

### S.DC: : Data Collection

S.DC.1: : Distinguish among different types of study designs for collecting data, and know the scope of inference for each design type.

S.DC.1.2: : Compare and contrast the benefits of different sampling techniques.

Polling: City

Polling: Neighborhood

S.DC.1.3: : Determine the appropriate scope of inference for generalizing results.

Polling: City

Populations and Samples

S.DC.1.4: : Explain how sample size impacts the precision with which generalizations can be made.

Polling: City

Polling: Neighborhood

Populations and Samples

S.DC.2: : Identify common sources of bias and the role of randomization in study design.

S.DC.2.1: : Explain how randomization and sources of bias impact the results of a study.

Polling: City

Polling: Neighborhood

S.DC.2.2: : Understand the different roles of random selection and random assignment in study design.

Polling: City

Polling: Neighborhood

Populations and Samples

### S.DA: : Data Analysis

S.DA.1: : Use distributions of quantitative and categorical data to identify the key features of the data collected in context.

S.DA.1.1: : Summarize and represent the distribution for univariate quantitative data by describing and analyzing the shape of the distribution, the measures of center for the distribution, the patterns in variability for the distribution, and any outliers, gaps, or other unusual features in the distribution.

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

Populations and Samples

Reaction Time 1 (Graphs and Statistics)

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. 5 Minute Preview

Reaction Time 2 (Graphs and Statistics)

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. 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

S.DA.1.2: : Select and create an appropriate display (e.g., dot plots, histograms, box plots) for univariate data.

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

Histograms

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. 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

S.DA.1.3: : Use statistics appropriate to the shape of the data distribution to compare center and variability of two or more different data sets.

Box-and-Whisker Plots

Reaction Time 1 (Graphs and Statistics)

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. 5 Minute Preview

Reaction Time 2 (Graphs and Statistics)

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. 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

S.DA.3: : Compare two or more groups by analyzing distributions.

S.DA.3.2: : Use numerical attributes of distributions to make comparisons between distributions.

Box-and-Whisker Plots

S.DA.4: : Analyze associations between two variables.

S.DA.4.2: : Make predictions and draw conclusions from regression models (linear, exponential, quadratic) from two-variable quantitative 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. 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

Trends in Scatter Plots

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. 5 Minute Preview

S.DA.4.3: : Analyze scatter plots for patterns, linearity, 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

Trends in Scatter Plots

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. 5 Minute Preview

S.DA.4.4: : Using technology, compute and interpret the correlation coefficient.

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

S.DA.5: : Make statistical inferences and evaluate claims from studies.

S.DA.5.1: : Construct and interpret confidence intervals for the mean of a normally distributed population and for a population proportion.

Polling: City

Populations and Samples

S.DA.5.2: : Explain how a sample statistic and a confidence level are used in the construction of a confidence interval.

Polling: City

S.DA.5.3: : Explain how changes in the sample size, confidence level, and standard error affect the margin of error of a confidence interval.

Polling: City

### S.IR: : Interpretation of Results

S.IR.1: : Interpret and communicate the results of a statistical analysis in context.

S.IR.1.1: : Recognize when the difference between two sample proportions or two sample means is due to random variation or if the difference is statistically significant.

Populations and Samples

S.IR.1.2: : Understand the concept of a confidence interval, including the interpretation of confidence level, margin of error, and statistical significance.

Polling: City

S.IR.3: : Evaluate real-world claims and conclusions.

S.IR.3.1: : Evaluate strengths and weaknesses in the studies or methods used to generate data.

Polling: City

Polling: Neighborhood

S.IR.3.2: : Evaluate the statistical validity of claims made.

Polling: City

Polling: Neighborhood

### S.P: : Probability

S.P.1: : Connect basic probability concepts to statistical analysis.

S.P.1.2: : Describe the relationship between theoretical and empirical probabilities using the Law of Large Numbers.

Probability Simulations

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. 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

S.P.1.3: : Use counting techniques (e.g., permutations and combinations) to solve mathematical and real-world problems, including determining probabilities of compound events.

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. 5 Minute Preview

S.P.2: : Determine probabilities, including joint probabilities, conditional probabilities, probabilities of independent events, and probabilities of dependent events. Interpret the results.

S.P.2.1: : 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 two events 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. 5 Minute Preview

S.P.2.2: : Understand and calculate the conditional probability of A given B as P(A and B)/P(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. 5 Minute Preview

S.P.2.3: : Interpret independence of A and B as saying that the conditional probability of A, given B, is the same as the probability of A.

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

S.P.3: : Use probability to make decisions.

S.P.3.1: : Analyze decisions and strategies using probability concepts and 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. 5 Minute Preview

Correlation last revised: 9/30/2022

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