Standard 5 : Data, Probability and Statistics (Mathematics)

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View this standard as a learning progression
Conceptual Strand
The Data Analysis and Probability Standard recommends that students formulate questions that can be answered using data and addresses what is involved in gathering and using the data wisely. The basic concepts and applications of probability are also addressed, with an emphasis on the way that probability and statistics are related.
Guiding Question
How do students’ experiences with the collection and analysis of data enable them to reason statistically and understand the various purposes of surveys, observational studies, and experiments?
 
Grade K
Grade Learning Expectations
GLE 0006.5.1  Sort objects and use one or more attributes to solve problems.
GLE 0006.5.2  Re-sort objects using new attributes.
Checks for Understanding
0006.5.1  Sort objects into sets and describe how the objects were sorted.
0006.5.2  Sort objects in different ways.
0006.5.3  Collect and count data.
State Performance Indicators
 
Grade 1
Grade Learning Expectations
GLE 0106.5.1  Use various representations to display and compare data.
Checks for Understanding
0106.5.1  Represent measurements and discrete data using concrete objects, picture graphs, and bar graphs.
0106.5.2  Represent data in both horizontal and vertical form.
0106.5.3  Display data using appropriate titles and labels.
0106.5.4  Count and compare collected data.
State Performance Indicators
 
Grade 2
Grade Learning Expectations
GLE 0206.5.1  Use and understand various representations to depict and analyze data measurements.
GLE 0206.5.2  Determine whether an event is likely or unlikely.
Checks for Understanding
0206.5.1  Read, interpret, and analyze data shown in tables, bar graphs and picture graphs.
0206.5.2  Read, interpret, and create tables using tally marks.
0206.5.3  Explain whether a real world event is likely or unlikely.
0206.5.4  Predict outcomes of events based on data gathered and displayed.
State Performance Indicators
 
Grade 3
Grade Learning Expectations
GLE 0306.5.1  Organize, display, and analyze data using various representations to solve problems.
Checks for Understanding
0306.5.1  Collect and organize data using observations, surveys, and experiments.
0306.5.2  Construct a frequency table, bar graph, pictograph, or line plot of collected data.
0306.5.3  Compare and interpret different representations of the same data.
0306.5.4  Solve problems using data from frequency tables, bar graphs, pictographs, or line plots.
State Performance Indicators
SPI 0306.5.1  Interpret a frequency table, bar graph, pictograph, or line plot.
SPI 0306.5.2  Solve problems in which data is represented in tables or graph.
SPI 0305.5.3  Make predictions based on various representations of data.
 
Grade 4
Grade Learning Expectations
GLE 0406.5.1  Collect, record, arrange, present, and interpret data using tables and various representations.
GLE 0406.5.2  Use probability to describe chance events.
Checks for Understanding
0406.5.1  Create and label appropriate scales for graphs.
0406.5.2  Evaluate how well various representations show the collected data.
0406.5.3  Interpret and prepare pie charts using appropriate measurements of angles.
0406.5.4  Develop and use stem-and-leaf plots.
0406.5.5  Use measures of central tendency to compare two sets of related data.
0406.5.6  Determine a simple probability.
0406.5.7  Express a probability pictorially.
State Performance Indicators
SPI 0406.5.1  Depict data using various representations (e.g., tables, pictographs, line graphs, bar graphs).
SPI 0406.5.2  Solve problems using estimation and comparison within a single set of data.
SPI 0406.5.3  Given a set of data or a graph, describe the distribution of the data using median, range, or mode.
SPI 0406.5.4  List all possible outcomes of a given situation or event.
 
Grade 5
Grade Learning Expectations
GLE 0506.5.1  Make, record, display and interpret data and graphs that include whole numbers, decimals, and fractions.
GLE 0506.5.2  Describe the shape and important features of a set of data using the measures of central tendency.
Checks for Understanding
0506.5.1  Construct and analyze double bar and line graphs.
0506.5.2  Represent data using ordered pairs in the first quadrant of the coordinate system.
0506.5.3  Design investigations to address a question and consider how data collection methods affect the nature of the data set.
0506.5.4  Recognize the differences in representing categorical and numerical data.
0506.5.5  Evaluate how different measures of central tendency describe data.
0506.5.6  Identify outliers and determine their effect on mean, median, mode and range.
State Performance Indicators
SPI 0506.5.1  Depict data using various representations, including decimal and/or fractional data.
SPI 0506.5.2  Make predictions based on various data representations, including double bar and line graphs.
SPI 0506.5.3  Calculate measures of central tendency to analyze data.
 
Grade 6
Grade Learning Expectations
GLE 0606.5.1  Understand the meaning of probability and how it is expressed.
GLE 0606.5.2  Interpret representations of data from surveys and polls, and describe sample bias and how data representations can be misleading.
Checks for Understanding
0606.5.1  Understand that the probability of an event is a number between zero and one that expresses the likelihood of its occurrence.
0606.5.2  Identify the probability of an event as the ratio of the number of its actual occurrences to the total number of its possible occurrences.
0606.5.3  Express probabilities in different ways.
0606.5.4  Understand the difference between probability and odds.
0606.5.5  Analyze a situation that involves probability of an independent event.
0606.5.6  Estimate the probability of simple and compound events through experimentation or simulation.
0606.5.7  Apply procedures to calculate the probability of complimentary events.
0606.5.8  Connect data sets and their graphical representations (such as bar graphs, circle, graphs, and stem-and-leaf plots).
0606.5.9  Determine the sample space for a given situation.
0606.5.10  Distinguish between a random and nonrandom sample.
0606.5.11  Select the appropriate measure of center to describe a data set.
0606.5.12  Predict the characteristics of a population based on the analysis of sample data.
State Performance Indicators
SPI 0606.5.1  Determine the theoretical probability of simple and compound events in familiar contexts.
SPI 0606.5.2  Identify features of graphs that may be misleading.
SPI 0606.5.3  Determine whether or not a sample is biased.
 
Grade 7
Grade Learning Expectations
GLE 0706.5.1  Collect, organize, and analyze both single- and two-variable data.
GLE 0706.5.2  Select, create, and use appropriate graphical representations of data.
GLE 0706.5.3  Formulate questions and design studies to collect data about a characteristic shared by two populations, or different characteristics within one population.
GLE 0706.5.4  Use descriptive statistics to summarize and compare data.
GLE 0706.5.5  Understand and apply basic concepts of probability.
Checks for Understanding
0706.5.1  Create and interpret box-and-whisker plots and stem-and-leaf plots.
0706.5.2  Interpret and solve problems using information presented in various visual forms.
0706.5.3  Predict and compare the characteristics of two populations based on the analysis of sample data.
0706.5.4  Use proportional reasoning to make predictions about results of experiments and simulations.
0706.5.5  Evaluate the design of an experiment.
0706.5.6  Apply percentages to make and interpret histograms and circle graphs.
0706.5.7  Use a tree diagram or organized list to determine all possible outcomes of a simple probability experiment.
State Performance Indicators
SPI 0706.5.1  Interpret and employ various graphs and charts to represent data.
SPI 0706.5.2  Select suitable graph types (such as bar graphs, histograms, line graphs, circle graphs, box-and-whisker plots, and stem-and-leaf plots) and use them to create accurate representations of given data.
SPI 0706.5.3  Calculate and interpret the mean, median, upper-quartile, lower-quartile, and interquartile range of a set of data.
SPI 0706.5.4  Use theoretical probability to make predictions.
 
Grade 8
Grade Learning Expectations
GLE 0806.5.1  Explore probabilities for compound, independent and/or dependent events.
GLE 0806.5.2  Select, create, and use appropriate graphical representations of data (including scatterplots with lines of best fit) to make and test conjectures.
GLE 0806.5.3  Evaluate the use of statistics in media reports.
Checks for Understanding
0806.5.1  Solve simple problems involving probability and relative frequency.
0806.5.2  Compare probabilities of two or more events and recognize when certain events are equally likely.
0806.5.3  Recognize common misconceptions associated with dependent and independent events.
0806.5.4  Explain the benefits and the limitations of various representations (i.e., bar graphs, line graphs, circle graphs, histograms, stem-and-leaf plots, box plots, scatterplots) of data.
0806.5.5  Create and interpret box-and-whisker plots and scatterplots.
0806.5.6  Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken.
0806.5.7  Estimate lines of best fit to make and test conjectures.
0806.5.8  Consider the source, design, analysis, and display of data to evaluate statistics reported in the media.
State Performance Indicators
SPI 0806.5.1  Calculate probabilities of events for simple experiments with equally probable outcomes.
SPI 0806.5.2  Use a variety of methods to compute probabilities for compound events (e.g., multiplication, organized lists, tree diagrams, area models).
SPI 0806.5.3  Generalize the relationship between two sets of data using scatterplots and lines of best fit.
SPI 0806.5.4  Recognize misrepresentations of published data in the media.
 
Algebra I
Course Learning Expectations
CLE 3102.5.1  Describe and interpret quantitative information.
CLE 3102.5.2  Use statistical thinking to draw conclusions and make predictions.
CLE 3102.5.3  Understand basic counting procedures and concepts of probability.
Checks for Understanding
3102.5.1  Identify patterns or trends in data.
3102.5.2  Develop a meaning for and identify outliers in a data set and verify.
3102.5.3  When a set of data is changed, identify effects on measures of central tendency, range, and inter-quartile range.
3102.5.4  Explore quartiles, deciles, and percentiles of a distribution.
3102.5.5  Construct and interpret various forms of data representations, (including line graphs, bar graphs, circle graphs, histograms, scatter-plots, box-and-whiskers, stem-and-leaf, and frequency tables).
3102.5.6  Draw qualitative graphs of functions and describe a general trend or shape.
3102.5.7  Compare two data sets using graphs and descriptive statistics.
3102.5.8  Examine real-world graphical relationship (including scatter-plots) to determine type of relationship (linear or nonlinear) and any association (positive, negative or none) between the variables of the data set.
3102.5.9  Determine an equation for a line that fits real-world linear data; interpret the meaning of the slope and y-intercept in context of the data.
3102.5.10  Using technology with a set of contextual linear data to examine the line of best fit; determine and interpret the correlation coefficient.
3102.5.11  Use an equation that fits data to make a prediction.
3102.5.12  Use techniques (Venn Diagrams, tree diagrams, or counting procedures) to identify the possible outcomes of an experiment or sample space and compute the probability of an event.
3102.5.13  Determine the complement of an event and the probability of that complement.
3102.5.14  Determine if two events are independent or dependent.
3102.5.15  Explore joint and conditional probability.
3102.5.16  Identify situations for which the Law of Large Numbers applies.
3102.5.17  Perform simulations to estimate probabilities.
3102.5.18  Make informed decisions about practical situations using probability concepts.
State Performance Indicators
SPI 3102.5.1  Interpret displays of data to answer questions about the data set(s) (e.g., identify pattern, trends, and/or outliers in a data set).
SPI 3102.5.2  Identify the effect on mean, median, mode, and range when values in the data set are changed.
SPI 3102.5.3  Using a scatter-plot, determine if a linear relationship exists and describe the association between variables.
SPI 3102.5.4  Generate the equation of a line that fits linear data and use it to make a prediction.
SPI 3102.5.5  Determine theoretical and/or experimental probability of an event and/or its complement including using relative frequency.
 
Geometry
Course Learning Expectations
CLE 3108.5.1  Analyze, interpret, employ and construct accurate statistical graphs.
CLE 3108.5.2  Develop the basic principles of geometric probability.
Checks for Understanding
3108.5.1  Determine the area of each sector and the degree measure of each intercepted arc in a pie chart.
3108.5.2  Translate from one representation of data to another (e.g., bar graph to pie graph, pie graph to bar graph, table to pie graph, pie graph to chart) accurately using the area of a sector.
3108.5.3  Estimate or calculate simple geometric probabilities (e.g., number line, area model, using length, circles).
State Performance Indicators
SPI 3108.5.1  Use area to solve problems involving geometric probability (e.g. dartboard problem, shaded sector of a circle, shaded region of a geometric figure).
 
Algebra II
Course Learning Expectations
CLE 3103.5.1  Describe, interpret, and apply quantitative data.
CLE 3103.5.2  Evaluate and critique various ways of collecting data and using information based on data published in the media.
CLE 3103.5.3  Use data and statistical thinking to draw inferences, make predictions, justify conclusions and identify and explain misleading uses of data.
CLE 3103.5.4  Develop an understanding of probability concepts in order to make informed decisions.
Checks for Understanding
3103.5.1  Collect, represent and describe both linear and non-linear data developed from contextual situations.
3103.5.2  Organize and display data using appropriate methods (including spreadsheets and technology tools) to detect patterns and departures from patterns.
3103.5.3  Read and interpret data from a two-way table.
3103.5.4  Understand the impact of various sampling methods and use them to draw valid conclusions.
3103.5.5  Calculate measures of central tendency and spread (variance and standard deviation).
3103.5.6  Use technology to find the appropriate regression equation for both linear and non-linear data.
3103.5.7  Recognize when the correlation coefficient measures goodness of fit and does not imply causation.
3103.5.8  Know the Empirical Rule for one, two and three standard deviations for a normal distribution.
3103.5.9  Use data to detect patterns.
3103.5.10  Design simple experiments to collect data to answer questions of interest.
3103.5.11  Evaluate published data by considering the source, the design of the study and the analysis and representation (or misrepresentation) of the data.
3103.5.12  Investigate bias and the phrasing of questions during data acquisition to formulate reasonable conclusions,
3103.5.13  Apply both theoretical and experimental probability to analyze the likelihood of an event.
State Performance Indicators
SPI 3103.5.1  Compute, compare and explain summary statistics for distributions of data including measures of center and spread.
SPI 3103.5.2  Compare data sets using graphs and summary statistics.
SPI 3103.5.3  Analyze patterns in a scatter-plot and describe relationships in both linear and non-linear data.
SPI 3103.5.4  Apply the characteristics of the normal distribution.
SPI 3103.5.5  Determine differences between randomized experiments and observational studies.
SPI 3103.5.6  Find the regression curve that best fits both linear and non-linear data (using technology such as a graphing calculator) and use it to make predictions.
SPI 3103.5.7  Determine/recognize when the correlation coefficient measures goodness of fit.
SPI 3103.5.8  Apply probability concepts such as conditional probability and independent events to calculate simple probability.