# data[].attributes.body
4.C.6 Use multivariate thinking to understand how variables impact one another

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4.C.7 Communicate statistical reasoning and results to others in a variety of formats (verbal, written, visual)

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4.C.1 Use statistical evidence from analyses to answer the statistical investigative questions and communicate results through more formal reports and presentations
4.C.3 Understand what it means for an outcome or an estimate of a population characteristic to be plausible or not plausible compared to chance variation

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[HSS.ID.C.7]

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High School: Statistics & Probability " Interpreting Categorical & Quantitative Data " Interpret linear models " 7

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Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

# data[].attributes.body
[HSS.ID.C.8]

# data[].attributes.attachment_link.title
High School: Statistics & Probability " Interpreting Categorical & Quantitative Data " Interpret linear models " 8

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Compute (using technology) and interpret the correlation coefficient of a linear fit.

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4.B.5 State the limitations of sample information (e.g., a sample may or may not be representative of the larger population, measurement variability)
4.B.6 Compare results for different conditions in an experiment

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4.B.3 Generalize beyond the sample providing statistical evidence for the generalization and including a statement of uncertainty and plausibility when needed
4.B.4 Recognize the uncertainty caused by sample to sample variability

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4.B.2 Acknowledge that looking beyond the data is feasible

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4.B.1 Use statistical evidence from analyses to answer the statistical investigative questions and communicate results with comprehensive answers and some teacher guidance

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4.A.3 Describe the difference between two groups with different conditions

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4.A.2 Make statements about the group or population from which the data were collected, recognizing that conclusions are limited to these groups and cannot be generalized to other groups

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4.A.1 Use statistical evidence from analyses to answer the statistical investigative questions and communicate results through structured answers with teacher guidance.

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3.C.4 Understand how sampling distributions (developed through simulation) are used to describe the sample-to-sample variability of sample statistics.
3.C.1 Use technology to subset and filter data sets and transform variables, including smoothing for time series data.

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3.C.6 Describe associations between two categorical variables using measures such as difference in proportions and relative risk.
3.C.7 Describe the relationship between two quantitative variables by interpreting Pearson’s correlation coefficient and a least-squares regression line.

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3.C.2 Identify appropriate ways to summarize quantitative or categorical data using tables, graphical displays, and numerical summary statistics, which includes using standard deviation as a measure of variability and a modified boxplot for identifying outliers

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3.B.4 Explore patterns of association between two quantitative variables or two categorical variables:

measures of correlation: quadrant count ratio (QCR)

comparison of conditional proportions across categorical variables

# data[].attributes.body
3.B.2 Learn to use the key features of distributions for quantitative variables, such as:

center: mean as a balance point, and median as the middle-ordered value

variability: interquartile range and mean absolute deviation (MAD)

shape: symmetric or asymmetric and number of modes

3.B.3 Use reasoning about distributions to compare two groups based on quantitative variables

# data[].attributes.body
3.B.1 Represent the variability of quantitative variables using appropriate displays (e.g., dotplots, boxplots)

# data[].attributes.body
3.A.3 Describe key features of distributions for quantitative variables, such as:

center: mean as the equal share, and median as the middle-ordered value of the data

variability: range as the difference between the greatest and least value, and dispersion as how many units from the equal share value

shape: number of clusters, symmetric or not, and gaps

3.A.4 Recognize distributions can be used to compare two groups.
3.A.5 Observe whether there appears to be an association between two variables

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3.A.2 Represent the variability of categorical variables or quantitative variables using appropriate displays (e.g., tables, picture graphs, dotplots, bar graphs)

# data[].attributes.body
3.A.1 Understand that the distribution of a categorical variable or quantitative variable describes the number of times a particular outcome occurs

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2.C.3 Understand what constitutes good practice in designing a sample survey, an experiment, and an observational study.
2.C.8 Understand how concerns about privacy and human subjects may affect the collection and distribution of data.
2.C.7 Understand practices for handling data that enhance reproducibility and ensure ethical use, including descriptions of alterations, and an understanding of when data may contain sensitive information.
2.C.9 Understand that in some circumstances, the data collected or considered may not generalize to the desired population, or this data may be the entire population.

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2.C.2 Distinguish between surveys, observational studies, and experiments.
2.C.5 Understand the role of random assignment in experiments and its implications for cause-and-effect interpretations

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2.C.1 Apply an appropriate data collection plan when collecting primary data or selecting secondary data for the statistical investigative question of interest.
2.C.6 Understand the issues of bias and confounding variables in observational studies and their implications for interpretation.

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2.B.5 Understand that quantitative variables may be either discrete or continuous.
2.B.6 Understand how to interrogate the data to determine how the data were collected, from whom they were collected, what types of variables are in the data, how the variables were measured (including units used), and the possible outcomes for the variables.
2.B.8 Understand how random assignment in comparative experiments is used to control for characteristics that might affect responses.

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2.B.3 Understand that data can be used to make comparisons between different groups at one point in time and the same group over time.
2.B.4 Recognize that data can be collected using surveys and measurements, and develop a critical attitude in analyzing data collection methods.
2.B.7 Understand that data can be collected (primary data) or existing data can be obtained from other sources (secondary data).

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2.B.1 Understand that data are information collected and recorded with a purpose and can be organized and stored in a variety of structures (e.g., spreadsheets)
2.B.2 Understand that a sample can be used to answer statistical investigative questions about a population. Recognize the limitations and scope of the data collected by describing the group or population from which the data are collected

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2.A.6 Understand that data are not always pristine but may contain errors, have missing values, etc., and that decisions have to be made about how to account for these issues

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2.A.5 Interrogate the data set to understand the context of the variables as they may relate to statistical investigative questions

# data[].attributes.body
2.A.4 Understand that within a data set there can be different types of variables (e.g., categorical or quantitative)

# data[].attributes.body
2.A.3 Understand that a variable measures the same characteristic on several individuals or objects and results in data values that may fluctuate

# data[].attributes.body
2.A.2 Understand how to collect and record information from the group of interest using surveys and measurements collected from observations and simple experiments

# data[].attributes.body
2.A.1 Understand that data are information; recognize that to answer a statistical investigative question, a person may collect data themselves specifically for that purpose, or a person may use data that have been collected by other people for another purpose

# data[].attributes.body
[Example 5] Evaluate a question to determine if it is testable and relevant.
[Example 6] Ask questions that can be investigated within the scope of the school laboratory, research facilities, or field (e.g., outdoor environment) with available resources and, when appropriate, frame a hypothesis based on a model or theory.
[Example 7] Ask and/or evaluate questions that challenge the premise(s) of an argument, the interpretation of a data set, or the suitability of a design.

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[Example 1] Ask questions that arise from careful observation of phenomena, or unexpected results, to clarify and/or seek additional information.
[Example 2] Ask questions that arise from examining models or a theory, to clarify and/or seek additional information and relationships.
[Example 3] Ask questions to determine relationships, including quantitative relationships, between independent and dependent variables.
[Example 4] Ask questions to clarify and refine a model, an explanation, or an engineering problem.

# data[].attributes.body
Asking questions and defining problems in 9–12 builds on K–8 experiences and progresses to formulating, refining, and evaluating empirically testable questions and design problems using models and simulations.

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1.C.1 Formulate multivariable statistical investigative questions and determine how data can be collected and analyzed to provide an answer
1.C.2 Pose summary, comparative, and association statistical investigative questions for surveys, observational studies, and experiments using primary or secondary data
1.C.3 Pose inferential statistical investigative questions regarding causality and prediction

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[Example 7] Challenge the premise(s) of an argument or the interpretation of a data set.
[Example 8] Define a design problem that can be solved through the development of an object, tool, process or system and includes multiple criteria and constraints, including scientific knowledge that may limit possible solutions.

# data[].attributes.body
[Example 4] Clarify and/or refine a model, an explanation, or an engineering problem.
[Example 5] Require sufficient and appropriate empirical evidence to answer.
[Example 6] Investigate questions within the scope of the classroom, outdoor environment, and museums and other public facilities with available resources and, when appropriate, frame a hypothesis based on observations and scientific principles.

# data[].attributes.body
[Example 1]That arise from careful observation of phenomena, models, or unexpected results, to clarify and/or seek additional information.
[Example 2] Identify and/or clarify evidence and/or the premise(s) of an argument.
[Example 3] Determine relationships between independent and dependent variables and relationships in models.

# data[].attributes.body
Asking questions and defining problems in 6–8 builds on K–5 experiences and progresses to specifying relationships between variables, and clarifying arguments and models.

# data[].attributes.body
1.B.4 Pose statistical investigative questions that require looking at a variable over time.
1.B.5 Understand that there are different types of questions in statistics: those used to frame an investigation, those used to collect data, and those used to guide analysis and interpretation.
1.B.6 Pose statistical investigative questions for data collected from online sources and websites, smartphones, fitness devices, sensors, and other modern devices.

# data[].attributes.body
1.B.1 Recognize that statistical investigative questions can be used to articulate research topics and that multiple statistical investigative questions can be asked about any research topic.
1.B.2 Understand that statistical investigative questions take into account context as well as variability present in data.
1.B.3 Pose summary, comparative, and association statistical investigative questions about a broader population using samples taken from the population

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1.A.4  Experience different types of questions in statistics: those used to frame an investigation, those used to collect data, and those used to guide analysis and interpretation

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1.A.3 Pose summary (or descriptive) statistical investigative questions about one variable regarding small, well-defined groups (e.g., subset of a classroom, classroom, school, town) and extend these to include  comparison and association statistical investigative questions between variables

# data[].attributes.body
Ask questions that can be investigated and predict reasonable outcomes based on patterns such as cause and effect relationships.

# data[].attributes.body
Asking questions and defining problems in 3–5 builds on K–2 experiences and progresses to specifying qualitative relationships.

# data[].attributes.body
Define a simple design problem that can be solved through the development of an object, tool, process, or system and includes several criteria for success and constraints on materials, time, or cost.

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Use prior knowledge to describe problems that can be solved.

# data[].attributes.body
Identify scientific (testable) and non-scientific (non-testable) questions.

# data[].attributes.body
Ask questions about what would happen if a variable is changed.

# data[].attributes.body
1.A.1 Understand when a statistical investigation is appropriate

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Define a simple problem that can be solved through the development of a new or improved object or tool.

# data[].attributes.body
Ask and/or identify questions that can be answered by an investigation.

# data[].attributes.body
Asking questions and defining problems in K–2 builds on prior experiences and progresses to simple descriptive questions that can be tested.

# data[].attributes.body
Ask questions based on observations to find more information about the natural and/or designed world(s).

# data[].attributes.body
1.A.2 Pose statistical investigative questions of interest to students where the context is such that students can collect or have access to all required data

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HSS.IC.B.6

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CCSS.Math.Content.HSS.ID.A.2
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

CCSS.Math.Content.HSS.ID.A.3
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

CCSS.Math.Content.HSS.ID.A.4
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

CCSS.Math.Content.HSS.ID.B.5
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

CCSS.Math.Content.HSS.ID.B.6.a
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

CCSS.Math.Content.HSS.ID.C.7
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

# data[].attributes.attachment_link.title
High School: Statistics & Probability » Interpreting Categorical & Quantitative Data | Common Core State Standards Initiative

# data[].attributes.attachment_link.description
CCSS.Math.Content.HSS.ID.A.1Represent data with plots on the real number line (dot plots, histograms, and box plots).

# data[].attributes.body
HSS.ID.C.9

# data[].attributes.attachment_link.title
High School: Statistics & Probability " Interpreting Categorical & Quantitative Data " Interpret linear models " 9

# data[].attributes.attachment_link.description
Distinguish between correlation and causation.

# data[].attributes.body
HSS.IC.B.3

# data[].attributes.attachment_link.title
High School: Statistics & Probability " Making Inferences & Justifying Conclusions " Make inferences and justify conclusions from sample surveys, experiments, and observational studies " 3

# data[].attributes.attachment_link.description
Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

# data[].attributes.body
HSS.ID.A.3

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CCSS.Math.Content.HSS.ID.A.2
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

CCSS.Math.Content.HSS.ID.A.3
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

CCSS.Math.Content.HSS.ID.A.4
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

CCSS.Math.Content.HSS.ID.B.5
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

CCSS.Math.Content.HSS.ID.B.6.a
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

CCSS.Math.Content.HSS.ID.C.7
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

# data[].attributes.attachment_link.title
High School: Statistics & Probability " Interpreting Categorical & Quantitative Data

# data[].attributes.attachment_link.description
CCSS.Math.Content.HSS.ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. CCSS.Math.Content.HSS.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

# data[].attributes.body
HSS.ID.B.5

# data[].attributes.attachment_link.readable_text
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

# data[].attributes.attachment_link.title
High School: Statistics & Probability » Interpreting Categorical & Quantitative Data » Summarize, represent, and interpret data on two categorical and quantitative variables » 5 | Common Core State Standards Initiative

# data[].attributes.attachment_link.description
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

# data[].attributes.body
HSS.IC.B.5

# data[].attributes.attachment_link.title
High School: Statistics & Probability " Making Inferences & Justifying Conclusions

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CCSS.Math.Content.HSS.IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. CCSS.Math.Content.HSS.IC.A.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5.

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HSS.ID.A.2
HSS.ID.A.4

# data[].attributes.attachment_link.readable_text
CCSS.Math.Content.HSS.ID.A.2
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

CCSS.Math.Content.HSS.ID.A.3
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

CCSS.Math.Content.HSS.ID.A.4
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

CCSS.Math.Content.HSS.ID.B.5
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

CCSS.Math.Content.HSS.ID.B.6.a
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

CCSS.Math.Content.HSS.ID.C.7
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

# data[].attributes.attachment_link.title
High School: Statistics & Probability " Interpreting Categorical & Quantitative Data

# data[].attributes.attachment_link.description
CCSS.Math.Content.HSS.ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. CCSS.Math.Content.HSS.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

# data[].attributes.body
HSS.ID.A.1
HSS.ID.B.6

# data[].attributes.attachment_link.readable_text
CCSS.Math.Content.HSS.ID.A.2
Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

CCSS.Math.Content.HSS.ID.A.3
Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

CCSS.Math.Content.HSS.ID.A.4
Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

CCSS.Math.Content.HSS.ID.B.5
Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

CCSS.Math.Content.HSS.ID.B.6.a
Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

CCSS.Math.Content.HSS.ID.C.7
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

# data[].attributes.attachment_link.title
High School: Statistics & Probability " Interpreting Categorical & Quantitative Data

# data[].attributes.attachment_link.description
CCSS.Math.Content.HSS.ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. CCSS.Math.Content.HSS.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

# data[].attributes.body
HSS.IC.A.1

# data[].attributes.attachment_link.title
High School: Statistics & Probability » Making Inferences & Justifying Conclusions » Understand and evaluate random processes underlying statistical experiments » 1 | Common Core State Standards Initiative

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Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

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new standard

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[8.SP.A.3]

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Grade 8 " Statistics & Probability " Investigate patterns of association in bivariate data. " 3

# data[].attributes.attachment_link.description
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

# data[].attributes.body
HSS.IC.B.4

# data[].attributes.attachment_link.title
High School: Statistics & Probability » Making Inferences & Justifying Conclusions » Make inferences and justify conclusions from sample surveys, experiments, and observational studies » 4 | Common Core State Standards Initiative

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Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

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[7.SP.B.4]

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Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

# data[].attributes.attachment_link.title
Grade 7 " Statistics & Probability " Draw informal comparative inferences about two populations. " 4

# data[].attributes.attachment_link.description
Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

# data[].attributes.body
[HSS.ID.C.9]

# data[].attributes.attachment_link.title
High School: Statistics & Probability " Interpreting Categorical & Quantitative Data " Interpret linear models " 9

# data[].attributes.attachment_link.description
Distinguish between correlation and causation.

# data[].attributes.body
[6.SP.B.5]

# data[].attributes.attachment_link.readable_text
CCSS.Math.Content.6.SP.A.1
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.

CCSS.Math.Content.6.SP.A.2
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

CCSS.Math.Content.6.SP.A.3
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

CCSS.Math.Content.6.SP.B.5.b
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

CCSS.Math.Content.6.SP.B.5.c
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

CCSS.Math.Content.6.SP.B.5.d
Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

# data[].attributes.attachment_link.description
CCSS.Math.Content.6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.

# data[].attributes.body
[8.SP.A.1]

# data[].attributes.attachment_link.readable_text
Print this page

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

# data[].attributes.attachment_link.title
Grade 8 " Statistics & Probability " Investigate patterns of association in bivariate data. " 1

# data[].attributes.attachment_link.description
Print this page Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

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[7.SP.B.3]

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Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

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Grade 7 » Statistics & Probability » Draw informal comparative inferences about two populations. » 3 | Common Core State Standards Initiative

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Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than…

# data[].attributes.body
[8.SP.A.2]

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Print this page

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

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Grade 8 " Statistics & Probability " Investigate patterns of association in bivariate data. " 2

# data[].attributes.attachment_link.description
Print this page Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

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[7.SP.A.2]

# data[].attributes.attachment_link.title
Grade 7 " Statistics & Probability " Use random sampling to draw inferences about a population. " 2

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Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

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[6.SP.A.2]

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Grade 6 " Statistics & Probability " Develop understanding of statistical variability. " 2

# data[].attributes.attachment_link.description
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

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[6.SP.B.4]

# data[].attributes.attachment_link.title
Grade 6 " Statistics & Probability " Summarize and describe distributions. " 4

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Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

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[6.SP.A.3]

# data[].attributes.attachment_link.title
Grade 6 " Statistics & Probability " Develop understanding of statistical variability. " 3

# data[].attributes.attachment_link.description
Print this page Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

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[8.SP.A.4]

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Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

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Grade 8 » Statistics & Probability » Investigate patterns of association in bivariate data. » 4 | Common Core State Standards Initiative

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Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequenci…

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[7.SP.A.1]

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Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

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Grade 7 " Statistics & Probability " Use random sampling to draw inferences about a population. " 1

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Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

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[6.SP.A.1]

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Grade 6 " Statistics & Probability " Develop understanding of statistical variability. " 1 | Common Core State Standards Initiative

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Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.

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[5.MD.B.2]

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Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

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Grade 5 " Measurement & Data " Represent and interpret data. " 2

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Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

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[4.MD.B.4]

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Grade 4 » Measurement & Data » Represent and interpret data. » 4 | Common Core State Standards Initiative

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Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest an…

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[3.MD.B.3]

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Grade 3 " Measurement & Data " Represent and interpret data. " 3

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Print this page Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

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[2.MD.D.10]

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Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems ¹ using information presented in a bar graph.

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Grade 2 " Measurement & Data " Represent and interpret data. " 10

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Print this page Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems 1 using information presented in a bar graph.

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[1.MD.C.4]

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Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

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Grade 1 " Measurement & Data " Represent and interpret data. " 4

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Print this page Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

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[K.MD.B.3]

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Kindergarten " Measurement & Data " Classify objects and count the number of objects in each category. " 3

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Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. 1