Okla. Admin. Code § 210:15-3-65

Current through Vol. 42, No. 8, January 2, 2025

Section 210:15-3-65 - Standard Four: Data and Probability

(a)Statement of the standard. Students will have an increased emphasis on understanding data and probability to enable all students to formulate questions that can be addressed by appropriate statistical methods. Students will analyze data, develop and evaluate inferences and predictions that are based on data, and understand and apply basic concepts of probability. Students will have an opportunity to apply the basic skills of computing with number and being an educated consumer of information providing application and use of fractions in daily life.

(b)Standard Four objectives for Pre-Kindergarten. The following objectives apply for students in Pre-Kindergarten:

(1) Collect and organize categorical data.

(A)Objective 1. Collect and organize information about objects and events in the environment.

(B)Objective 2. Use categorical data to create real-object graphs, with guidance and support.

(c)Standard Four objectives for Kindergarten. The following objectives apply for students in Kindergarten:

(1) Collect, organize, and interpret categorical data.

(A)Objective 1. Collect and organize information about objects and events in the environment.

(B)Objective 2. Use categorical data to create real-object graphs and pictographs.

(C)Objective 3. Draw conclusions from real-object graphs and pictographs.

(d)Standard Four objectives for Grade 1. The following objectives apply for students in Grade 1:

(1) Collect, organize, and interpret categorical and numerical data.

(A)Objective 1. Collect, sort, and organize data in up to three categories using representations (e.g. tally marks, tables, Venn diagrams).

(B)Objective 2. Use data to create pictographs and bar graphs that demonstrate one-to-one correspondence.

(C)Objective 3. Draw conclusions from pictographs and bar graphs.

(e)Standard Four objectives for Grade 2. The following objectives apply for students in Grade 2:

(1) Collect, organize, and interpret data.

(A)Objective 1. Explain that the length of a bar in a bar graph and the number of objects in a pictograph represents the number of data points for a given category.

(B)Objective 2. Organize a collection of data with up to four categories using pictographs and bar graphs with intervals of 1s, 2s, 5s, or 10s.

(C)Objective 3. Write and solve one-step word problems involving addition or subtraction using data represented within pictographs and bar graphs with intervals of one.

(D)Objective 4. Draw conclusions and make predictions from information in a pictograph and bar graph.

(f)Standard Four objectives for Grade 3. The following objectives apply for students in Grade 3:

(1) Collect, organize, and analyze data.

(A)Objective 1. Collect and organize a data set with multiple categories using a frequency table, line plot, pictograph, or bar graph with scaled intervals.

(B)Objective 2. Solve one- and two-step word problems using categorical data represented with a frequency table, pictograph, or bar graph with scaled intervals.

(g)Standard Four objectives for Grade 4. The following objectives apply for students in Grade 4:

(1) Summarize, construct, and analyze data.

(A)Objective 1. Create and organize data on a frequency table or line plot marked with whole numbers and fractions using appropriate titles, labels, and units.

(B)Objective 2. Organize data sets to create tables, bar graphs, timelines, and Venn diagrams. The data may include benchmark fractions or decimals (1/4, 1/3, 1/2, 2/3, 3/4, 0.25, 0.50, 0.75).

(C)Objective 3. Solve one- and two-step problems by analyzing data in whole number, decimal, or fraction form in a frequency table and line plot.

(h)Standard Four objectives for Grade 5. The following objectives apply for students in Grade 5:

(1) Create and analyze data to find the range and measures of central tendency (mean, median, and mode).

(A)Objective 1. Find the measures of central tendency (ie., mean, median, mode) and range of a set of data. Understand that the mean is a "leveling out" or central balance point of the data.

(B)Objective 2. Create and analyze line and double-bar graphs with increments of whole numbers, fractions, and decimals.

(i)Standard Four objectives for Grade 6. The following objectives apply for students in Grade 6:

(1) Interpret and analyze data.

(A)Objective 1. Interpret the mean, median, and mode for a set of data.

(B)Objective 2. Explain and justify which measure of center (mean, median, or mode) would provide the most descriptive information for a given set of data.

(2) Use probability to model and solve mathematical problems; represent probabilities using fractions and decimals.

(A)Objective 1. Represent possible outcomes using a probability continuum from impossible to certain.

(B)Objective 2. Determine the sample space for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables, or pictorial representations.

(C)Objective 3. Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there may be differences between the two results.

(j)Standard Four objectives for Grade 7. The following objectives apply for students in Grade 7:

(1) Interpret and analyze data, creating the most appropriate display, using a variety of tools.

(A)Objective 1. Design simple experiments, collect data, and calculate measures of center (mean, median, and mode) and spread (range and interquartile range). Use these quantities to draw conclusions about the data collected and make predictions.

(B)Objective 2. Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms.

(C)Objective 3. Use technology to create and analyze box plots.

(2) Calculate and use proportional reasoning with probabilities to model and solve mathematical problems.

(A)Objective 1. Determine the theoretical probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions, and decimals between 0 and 1.

(B)Objective 2. Calculate probability as fraction of same space or as a fraction of area. Express probabilities as percents, decimals, and fractions.

(C)Objective 3. Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on theoretical probabilities.

(k)Standard Four objectives for Pre-Algebra. The following objectives apply for students in Pre-Algebra:

(1) Display and interpret data in a variety of ways, including using scatterplots and approximate lines of best fit. Use lines of best fit and average rate of change to make predictions and draw conclusions about data.

(A)Objective 1. Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Create data displays using technology to examine this impact.

(B)Objective 2. Explain how outliers affect measures of center and spread.

(C)Objective 3. Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to find the informal line of best fit, make statements about average rate of change, and make predictions about values not in the original data set. Use appropriate titles, labels and units.

(2) Calculate experimental probabilities and reason about probabilities to model and solve problems.

(A)Objective 1. Calculate experimental probabilities and represent them as percents, fractions, and decimals between 0 and 1. Use experimental probabilities to predict relative frequencies when actual probabilities are unknown.

(B)Objective 2. Determine how samples are chosen (randomness) to draw and support conclusions about generalizing a sample to a population, including identifying limitations and biases.

(C)Objective 3. Define, compare and contrast the probabilities of dependent and independent events.

(l)Standard Four objectives for Algebra 1. The following objectives apply for students in Algebra 1:

(1) Display, describe, and compare data. For linear relationships make predictions and assess the reliability of those predictions.

(A)Objective 1. Display, describe, and compare data sets using summary statistics (central tendency and spread (range)). Utilize technology (e.g., spreadsheets, calculators) to display data and calculate summary statistics.

(B)Objective 2. Collect data and analyze scatterplots for patterns, linearity, and outliers.

(C)Objective 3. Make predictions based upon the linear regression, and use the correlation coefficient to assess the reliability of those predictions using graphing technology.

(2) Calculate probabilities and apply probability concepts.

(A)Objective 1. Apply simple counting procedures (factorials, permutations, combinations, and tree diagrams) to determine sample size, sample space, and calculate probabilities.

(B)Objective 2. Given a Venn diagram, determine the probability of the union of events, the intersection of events, and the complement of an event. Understand the relationships between these concepts and the words "AND," "OR," and "NOT."

(C)Objective 3. Use simulations and experiments to calculate experimental probabilities.

(D)Objective 4. Apply probability concepts to real-world situations to make informed decisions.

(m)Standard Four objectives for Algebra 2. The following objectives apply for students in Algebra 2:

(1) Display, describe, and compare data. For linear and nonlinear relationships, make predictions and assess the reliability of those predictions.

(A)Objective 1. Use the mean and standard deviation of a data set to create a normal distribution (bell-shaped curve).

(B)Objective 2. Collect data and use scatterplots to analyze patterns and describe linear, exponential, or quadratic relationships between two variables.

(C)Objective 3. Make predictions based upon the regression equation (linear, exponential, or quadratic), and use the correlation coefficient to assess the reliability of those predictions using graphing technology.

(2) Analyze statistical thinking to draw inferences, make predictions, and justify conclusions.

(A)Objective 1. Evaluate reports by making inferences, justifying conclusions, and determining appropriateness of data collection methods. Show how graphs and data can be distorted to support different points of view.

(B)Objective 2. Identify and explain misleading conclusions and graphical representations of data sets.

(C)Objective 3. Differentiate between correlation and causation when describing the relationship between two variables.

(n)Standard Four objectives for Statistics and Probability. The following objectives apply for students in Statistics and Probability:

(1)Statistical Questions. Understand the distinction between mathematical models and statistical models.

(A)Objective 1. Distinguish among different sources of variability, including measurement, natural, induced, and sampling variability.

(B)Objective 2. Formulate meaningful statistical questions to clarify the problem at hand.

(2)Statistical Questions. Distinguish between the distribution of a population, a distribution of sample data, and a sampling distribution.

(A)Objective 1. Distinguish between sample statistics and population parameters.

(B)Objective 2. Recognize a population distribution has fixed values of its parameters and that these parameter values are typically unknown.

(C)Objective 3. Recognize that a sample data distribution is taken from a population distribution and the data distribution is what is seen in practice.

(D)Objective 4. Recognize a sampling distribution is the distribution of a sample statistic (e.g., sample mean, sample proportion) obtained from repeated samples.

(3)Statistical Questions. Identify differences between categorical and quantitative data.

(A)Objective 1. Determine whether categorical or quantitative data is appropriate to answer a statistical question.

(B)Objective 2. Compare and contrast different potential graphical or visual representations given the same data set.

(4)Data Collection. Distinguish among different types of study designs for collecting data and know the scope of inference for each design type.

(A)Objective 1. Distinguish among sample surveys, experiments, and observational studies.

(B)Objective 2. Compare and contrast the benefits of different sampling techniques.

(C)Objective 3. Determine the appropriate scope of inference for generalizing results.

(D)Objective 4. Explain how sample size impacts the precision with which generalizations can be made.

(E)Objective 5. Determine when a cause-and-effect inference can be drawn from an association, based on how the data were collected.

(5)Data Collection. Identify common sources of bias and the role of randomization in study design.

(A)Objective 1. Explain how randomization and sources of bias impact the results of a study.

(B)Objective 2. Understand the different roles of random selection and random assignment in study design.

(6)Data Analysis. Use distributions of quantitative and categorical data to identify the key features of the data collected in context.

(A)Objective 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.

(B)Objective 2. Select and create an appropriate display (e.g., dot plots, histograms, and box plots) for univariate data.

(C)Objective 3. Use statistics appropriate to the shape of the data distribution to compare center and variability of two or more different data sets.

(D)Objective 4. Describe and analyze the distribution of univariate categorical data.

(7)Data Analysis. Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages.

(A)Objective 1. Use calculators, computers, or tables to estimate areas under the normal curve. Recognize that there are data sets for which such a procedure is not appropriate.

(8)Data Analysis. Compare two or more groups by analyzing distributions.

(A)Objective 1. Construct appropriate parallel graphical displays of distributions.

(B)Objective 2. Use numerical attributes of distributions to make comparisons between distributions.

(9)Data Analysis. Analyze associations between two variables.

(A)Objective 1. Create two-way tables for bivariate categorical data and analyze for possible associations between the two categories using marginal, joint, and conditional frequencies.

(B)Objective 2. Make predictions and draw conclusions from regression models (linear, exponential, quadratic) from two-variable quantitative data.

(C)Objective 3. Analyze scatter plots for patterns, linearity, outliers, and influential points.

(D)Objective 4. Using technology, compute and interpret the correlation coefficient.

(E)Objective 5. Understand the implications of extrapolating data to make predictions.

(10)Data Analysis. Make statistical inferences and evaluate claims from studies.

(A)Objective 1. Construct and interpret confidence intervals for the mean of a normally distributed population and for a population proportion.

(B)Objective 2. Explain how a sample statistic and a confidence level are used in the construction of a confidence interval.

(C)Objective 3. Explain how changes in the sample size, confidence level, and standard error affect the margin of error of a confidence interval.

(D)Objective 4. Construct a confidence interval for the mean of a normally distributed population (with a known standard deviation) and for a population proportion. Use confidence intervals to evaluate claims.

(E)Objective 5. Use confidence intervals to evaluate claims for a single population parameter.

(11)Interpretation of Results. Interpret and communicate the results of a statistical analysis in context.

(A)Objective 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.

(B)Objective 2. Understand the concept of a confidence interval, including the interpretation of confidence level, margin of error, and statistical significance.

(C)Objective 3. Develop inferences or predictions to construct resulting decisions or recommendations.

(D)Objective 4. Create and evaluate recommendations for areas of future research.

(12)Interpretation of Results. Evaluate practical implications of statistical significance, or lack thereof.

(A)Objective 1. Develop and critique arguments for practical implications based on statistical significance.

(B)Objective 2. Identify potential lurking variables which may explain an association between two variables.

(13)Interpretation of Results. Evaluate real-world claims and conclusions.

(A)Objective 1. Evaluate strengths and weaknesses in the studies or methods used to generate the data.

(B)Objective 2. Evaluate the statistical validity of claims made.

(14)Probability. Connect basic probability concepts to statistical analysis.

(A)Objective 1. Describe events as subsets of a sample space.

(B)Objective 2. Describe the relationship between theoretical and empirical probabilities using the Law of Large Numbers.

(C)Objective 3. Use counting techniques (e.g., permutations and combinations) to solve mathematical and real-world problems, including determining probabilities of compound events.

(15)Probability. Determine probabilities, including joint probabilities, conditional probabilities, probabilities of independent events, probabilities of dependent events. Interpret the results.

(A)Objective 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.

(B)Objective 2. Understand and calculate the conditional probability of A given B as P(A and B)/P(B).

(C)Objective 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.

(16)Probability. Use probability to make decisions.

(A)Objective 1. Analyze decisions and strategies using probability concepts and expected values.

(B)Objective 2. Analyze decisions about statistical significance based on reported p-values.

Okla. Admin. Code § 210:15-3-65

Adopted by Oklahoma Register, Volume 40, Issue 5, November 15, 2022, eff. 12/11/2022