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Data, Statistics, Probability
Collecting, organizing, and displaying data, as well as interpreting and analyzing the information to make decisions and predictions, have become very important in our society. Statistical instruction should be carried out in a spirit of investigation and exploration so students can answer and formulate questions about data. Probability should be studied in familiar contexts. Students need to investigate fairness, chances of winning, and uncertainty. Technology should be used as a tool throughout the investigation process.
Grade K |
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Grade 1 |
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Grade 2 |
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Grade 3 |
M:DSP:K:1 Interprets a given representation created by the class (models and tally charts) to answer questions related to the data, or to analyze the data to formulate conclusions using words, diagrams, or verbal/scribed responses to express answers.
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M:DSP:1:1 Interprets a given representation created by the class (models, tally charts, pictographs with one-to-one correspondence , and tables ) to answer questions related to the data, or to analyze the data to formulate conclusions using words, diagrams, or verbal/scribed responses to express answers.
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M:DSP:2:1 Interprets a given representation (pictographs with one-to-one correspondence, line plots , tally charts, or tables) to answer questions related to the data, or to analyze the data to formulate conclusions. |
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M:DSP:3:1
Interprets a given representation (line plots, tally charts, tables, or bar graphs) to answer questions related to the data, to analyze the data to formulate conclusions, or to make predictions.
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M:DSP:K:2
Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using more, less, or equal (e.g., Have there been more, less, or the same number of cloudy days compared to sunny days this week?). |
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M:DSP:1:2
Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using more, less, or equal.
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M:DSP:2:2
Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using more, less, or equal.
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M:DSP:3:2
Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using most frequent (mode), least frequent, largest, or smallest. |
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M:DSP:K:3
No standard at this grade
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M:DSP:1:3
No standard at this grade
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M:DSP:2:3
No standard at this grade |
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M:DSP:3:3
Identifies or describes representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M:DSP:3:1.
M:DSP:3:3
Organizes and displays data using tables, tally charts, and bar graphs, to answer questions related to the data, to analyze the data to formulate conclusions, to make predictions, or to solve problems.
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M:DSP:K:4
No standard at this grade
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M:DSP:1:4
No standard at this grade
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M:DSP:2:4
Uses counting techniques to solve problems involving combinations using a variety of strategies (e.g., student diagrams, organized lists, tables, tree diagrams, or sc others); (e.g., How many ways can you make 50 cents using nickels, dimes, and quarters?)
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M:DSP:3:4
Uses counting techniques to solve problems involving combinations and simple permutations using a variety of strategies (e.g., student diagrams, organized lists, tables, tree diagrams, orsc others).
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M:DSP:K:5
No standard at this grade
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M:DSP:1:5
For a probability event in which the sample space may or may not contain equally likely outcomes, groups use experiments to describes the likelihood or chance of an event (using “more likely,” “less likely”, or “equally likely”). |
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M:DSP:2:5
For a probability event in which the sample space may or may not contain equally likely outcomes, uses experiments to describe the likelihood or chance of an event using “more likely,” |
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M:DSP:3:5
For a probability event in which the sample space may or may not contain equally likely outcomes, predicts the likelihood of an event using “more likely,” “less likely,” “equally likely,” certain, or impossible and tests the prediction through experiments; and determines if a game is fair.
M:DSP:3:5
For a probability event in which the sample space may or may not contain equally likely outcomes, determines the likelihood of the occurrence of an event (using “more likely”, “less likely”, or “equally likely”). |
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M:DSP:K:6
No standard at this grade |
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M:DSP:1:6
No standard at this grade |
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M:DSP:2:6
In response to a teacher or student generated question or hypothesis, groups decide the most effective method (e.g., survey, observation, experimentation) to collect the data (numerical or categorical) necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the question or hypothesis being tested, and when appropriate makes predictions. |
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M:DSP:3:6
In response to a teacher or student generated question or hypothesis, groups decide the most effective method (e.g., survey, observation, experimentation) to collect the data (numerical or categorical) necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the question or hypothesis being tested, and when appropriate makes predictions. |
Return to Standards
Grade 4 |
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Grade 5 |
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Grade 6 |
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Grade 7 |
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M:DSP:4:1
Interprets a given representation (line plots, tables, bar graphs, pictographs, or circle graphs) to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. |
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M:DSP:5:1
Interprets a given representation (tables, bar graphs, circle graphs, or line graphs) to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. |
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M:DSP:6:1
Interprets a given representation (circle graphs, line graphs, or stem-and-leaf plots) to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. |
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M:DSP:7:1
Interprets a given representation (circle graphs, scatter plots that represent discrete linear relationships, or histograms) to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. |
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M:DSP:4:2
Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of central tendency (median or mode), or range. |
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M:DSP:5:2
Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of central tendency (mean, median, or mode) or range to analyze situations, or to solve problems. |
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M:DSP:6:2
Analyzes patterns, trends or distributions in data in a variety of contexts by determining or using measures of central tendency (mean, median, or mode) or dispersion (range) to analyze situations, or to solve problems.
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M:DSP:7:2
Analyzes patterns, trends, or distributions in data in a variety of contexts by solving problems using measures of central tendency (mean, median, or mode), dispersion (range or variation), or outliers to analyze situations to determine their effect on mean, median, or mode; and evaluates the sample from which the statistics were developed (bias). |
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M:DSP:4:3
Organizes and displays data using tables, line plots, bar graphs, and pictographs to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. |
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M:DSP:5:3
Organizes and displays data using tables, bar graphs, or line graphs to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems.
M:DSP:5:3
Identifies or describes representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M:DSP:5:1. |
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M:DSP:6:3
Organizes and displays data using tables, line graphs, or stem-and-leaf plots to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. |
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M:DSP:7:3
Organizes and displays data using tables, line graphs, scatter plots, and circle graphs to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems.
M:DSP:7:3
Identifies or describes representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M:DSP:7:1.
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M:DSP:4:4
Uses counting techniques to solve problems in context involving combinations or simple permutations (e.g., Given a map – Determine the number of paths from point A to point B.) using a variety of strategies (e.g., organized lists, tables, tree diagrams, orsc others).
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M:DSP:5:4
No standard at this grade |
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M:DSP:6:4
Uses counting techniques to solve problems in context involving combinations or simple permutations using a variety of strategies (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting Principle, orsc others). |
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M:DSP:7:4
Uses counting techniques to solve problems in context involving combinations or permutations (e.g., How many different ways can eight students place first, second, and third in a race?) using a variety of strategies (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting Principle, orsc others). |
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M:DSP:4:5
For a probability event in which the sample space may or may not contain equally likely outcomes, predicts the likelihood of an event as a part to whole relationship (e.g., two out of five, zero out of five, five out of five) and tests the prediction through experiments; and determines if a game is fair.
M:DSP:4:5
For a probability event in which the sample space may or may not contain equally likely outcomes, determines the theoretical probability of an event and expresses the result as part to whole (e.g., two out of five).
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M:DSP:5:5
For a probability event in which the sample space may or may not contain equally likely outcomes, predicts the likelihood of an event as a fraction and tests the prediction through experiments; and determines if a game is fair.
M:DSP:5.5
For a probability event in which the sample space may or may not contain equally likely outcomes, determines the experimental or theoretical probability of an event and expresses the result as a fraction. |
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M:DSP:6:5
For a probability event in which the sample space may or may not contain equally likely outcomes, predicts the theoretical probability of an event and tests the prediction through experiments and simulations; and designs fair games.
M:DSP:6:5
For a probability event in which the sample space may or may not contain equally likely outcomes, determines the experimental or theoretical probability of an event in a problem-solving situation.
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M:DSP:7:5
For a probability event in which the sample space may or may not contain equally likely outcomes, predicts the theoretical probability of an event and tests the prediction through experiments and simulations; and compares and contrasts theoretical and experimental probabilities.
M:DSP:7:5
For a probability event in which the sample space may or may not contain equally likely outcomes, determines the experimental or theoretical probability of an event in a problem-solving situation.
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M:DSP:4:6
In response to a teacher or student generated question or hypothesis, groups decide the most effective method (e.g., survey, observation, experimentation) to collect the data (numerical or categorical) necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the question or hypothesis being tested, and when appropriate makes predictions; and asks new questions and makes connections to real world situations. |
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M:DSP:5:6
In response to a teacher or student generated question or hypothesis decides the most effective method (e.g., survey, observation, experimentation) to collect the data (numerical or categorical) necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the question or hypothesis being tested, and when appropriate makes predictions; and asks new questions and makes connections to real world situations. |
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M:DSP:6:6
In response to a teacher or student generated question or hypothesis decides the most effective method (e.g., survey, observation, experimentation) to collect the data (numerical or categorical) necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the question or hypothesis being tested, and when appropriate makes predictions; and asks new questions and makes connections to real world situations. |
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M:DSP:7:6
In response to a teacher or student generated question or hypothesis decides the most effective method (e.g., survey, observation, experimentation) to collect the data (numerical or categorical) necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the question or hypothesis being tested while considering the limitations that could affect interpretations; and when appropriate makes predictions; and asks new questions and makes connections to real world situations. |
Grade 8 |
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High School |
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Advanced |
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M:DSP:8:1
Interprets a given representation (line graphs, scatter plots , histograms, or box-and-whisker plots ) to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems. |
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M:DSP:HS:1
Interprets a given representation(s) (e.g., regression function including linear, quadratic, and exponential) to analyze the data to make inferences and to formulate, justify, and critique conclusions.
M:DSP:10:1
Interprets a given representation(s) (e.g., box-and-whisker plots, scatter plots, bar graphs, line graphs, circle graphs, histograms, frequency charts) to make observations, to answer questions, to analyze the data to formulate or justify conclusions, critique conclusions, make predictions, or to solve problems within mathematics or across disciplines or contexts (e.g., media, workplace, social and environmental situations). |
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M:DSP:AM:1
No standard at this level |
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M:DSP:8:2
Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of central tendency (mean, median, or mode), dispersion (range or variation), outliers, quartile values, or estimated line of best fit to analyze situations, or to solve problems; and evaluates the sample from which the statistics were developed (bias, random, or non-random). |
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M:DSP:HS:2
Analyzes patterns, trends, or distributions in data in a variety of contexts by determining or using measures of dispersion (standard deviation, variance, and percentiles).
M:DSP:10:2
Analyzes patterns, trends, or distributions in data in a variety of contexts by determining, using, or analyzing measures of central tendency (mean, median, or mode), dispersion (range or variation), outliers, quartile values, estimated line of best fit, regression line, or correlation (strong positive, strong negative, or no correlation) to solve problems; and solve problems involving conceptual understanding of the sample from which the statistics were developed. |
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M:DSP:AM:2
Analyzes and interprets measures of dispersion (standard deviation, variance, and percentiles) and central tendency for the normal distribution; and interprets the correlation coefficient and the coefficient of determination in the context of data. |
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M:DSP:8:3
Organizes and displays data using scatter plots to answer questions related to the data, to analyze the data to formulate or justify conclusions, to make predictions, or to solve problems; or identifies representations or elements of representations that best display a given set of data or situation, consistent with the representations required in M:DSP:8:1. |
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M:DSP:HS: 3
Organizes and displays one- and two-variable data using a variety of representations (e.g., box-and-whisker plots, scatter plots, bar graphs, line graphs, circle graphs, histograms, frequency charts, linear, quadratic, and exponential regression functions ) to analyze the data to formulate or justify conclusions, make predictions, or to solve problems with or without using technology.
M:DSP:10:3
Identifies or describes representations or elements of representations that best display a given set of data or situation , consistent with the representations required in M:DSP:10:1. |
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M:DSP:AM: 3
Uses technology to explore the method of least squares and median-median for linear regression. |
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M:DSP:8:4
Uses counting techniques to solve problems in context involving combinations or permutations using a variety of strategies (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting Principle, orsc others).
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M:DSP:HS:4
Uses counting techniques to solve problems in context involving combination or permutations using a variety of strategies (e.g., nCr, nPr, or n!); and finds unions, intersections, and complements of sets.
M:DSP:10:4
Uses counting techniques to solve problems in context involving combinations or permutations using a variety of strategies (e.g., organized lists, tables, tree diagrams, models, Fundamental Counting Principle, orsc others). |
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M:DSP:AM:4
No standard at this level |
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M:DSP:8:5
For a probability event in which the sample space may or may not contain equally likely outcomes, determines the experimental or theoretical probability of an event in a problem-solving situation; and predicts the theoretical probability of an event and tests the prediction through experiments and simulations; compares and contrasts theoretical and experimental probabilities; finds the odds of an event and understands the relationship between probability and odds. |
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M:DSP:HS:5
For a probability event in which the sample space may or may not contain equally likely outcomes, predicts the theoretical probability of an event and tests the prediction through experiments and simulations; compares and contrasts theoretical and experimental probabilities; finds the odds of an event and understands the relationship between probability and odds.
M:DSP:10:5
Solves problems involving experimental or theoretical probability. |
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M:DSP:AM:5
Solves probability problems (e.g., by applying concepts of counting, random variables, independence/dependence of events, and conditional probability). |
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M:DSP:8:6
In response to a teacher or student generated question or hypothesis decides the most effective method (e.g., survey, observation, experimentation) to collect the data (numerical or categorical) necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the question or hypothesis being tested while considering the limitations that could affect interpretations; and when appropriate makes predictions; and asks new questions and makes connections to real-world situations. |
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M:DSP:HS:6
In response to a teacher or student generated question or hypothesis decides the most effective method (e.g., survey, observation, research, experimentation) and sampling techniques (e.g., random sample, stratified random sample) to collect the data necessary to answer the question; collects, organizes, and appropriately displays the data; analyzes the data to draw conclusions about the questions or hypotheses being tested while considering the limitations of the data that could effect interpretations; and when appropriate makes predications, asks new questions, or makes connections to real-world situations. |
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M:DSP:AM:6
No standard at this level |
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