Data Analysis, Probability, and Statistics 1

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(K-4) Elementary School Learning Targets	(5-8) Middle School Learning Targets	(9-12) High School Learning Targets
DPS-1 Gather and interpret data to answer questions related to a particular/single context. Formulate questions, gather data, and build representations; Identify and describe variation in data, and describe and compare shapes of distributions and measures of central tendency.	DPS-1 Design investigations and gather data to answer questions about multiple populations. Formulate questions, gather data, and build representations; Compare populations by analyzing distributions in terms of variability and measures of central tendency.	DPS-1 Design and conduct statistical studies: Use appropriate statistical measures for analysis; Develop the concepts of statistical inference and statistical significance, especially in relation to probability principles and sampling distributions.

Grade Differentiation

Elementary School Progress Indicators

Progress Indicator: E.DPS.1a posing questions of interest that can be answered by counting or collecting data (e.g., concrete comparisons about students, classroom materials, science topics) with teacher guidance
Core Content Connectors: K	CCSS Domain/Cluster	Common Core State Standard
K.DPS.1a1 Select a question that is answered by collected data	Counting and Cardinality K CC Count to tell the number of objects.	K.CC.B.5 Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.

Progress Indicator: E.DPS.1a posing questions of interest that can be answered by counting or collecting data (e.g., concrete comparisons about students, classroom materials, science topics) with teacher guidance
Core Content Connectors: 1	CCSS Domain/Cluster	Common Core State Standard
1.DPS.1a2 Select questions that ask about "How many" and represent up to three categories that can be concretely represented	Measurement and Data 1 MD Represent and interpret data.	1.MD.C.4 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.
1.DPS.1a3 Identify 2 categories resulting from a selected question	Measurement and Data 1 MD Represent and interpret data.	1.MD.C.4 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.
1.DPS.1a4 Analyze data by sorting into 2 categories; answer questions about the total number of data points and how many in each category	Measurement and Data 1 MD Represent and interpret data.	1.MD.C.4 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.
Progress Indicator: E.DPS.1c collecting and organizing/representing data (e.g., picture graphs, tally charts, bar graphs)
Core Content Connectors: 1	CCSS Domain/Cluster	Common Core State Standard
1.DPS.1c1 Using a picture graph, represent each object/person counted on the graph (1:1 correspondence) for 2 or more categories	Measurement and Data 1 MD Represent and interpret data.	1.MD.C.4 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.
Progress Indicator: E.DPS.1d recognizing that data can take on different values
Core Content Connectors: 1	CCSS Domain/Cluster	Common Core State Standard
1.DPS.1d1 Interpret a picture graph to answer questions about how many in each category	Measurement and Data 1 MD Represent and interpret data.	1.MD.C.4 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.
Progress Indicator: E.DPS.1e describing and comparing data and beginning to identify what the data do or do not show (e.g., bar graphs, line plots, picture graphs)
Core Content Connectors: 1	CCSS Domain/Cluster	Common Core State Standard
1.DPS.1e1 Compare the values of the 2 categories of data in terms of more or less	Measurement and Data 1 MD Represent and interpret data.	1.MD.C.4 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.

Progress Indicator: E.DPS.1a posing questions of interest that can be answered by counting or collecting data (e.g., concrete comparisons about students, classroom materials, science topics) with teacher guidance
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
2.DPS.1a5 Select a question about 3 attributes that can be concretely represented	Measurement and Data 1 MD Represent and interpret data.	1.MD.C.4 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.
2.DPS.1a6 Identify up to 3 categories resulting from a selected question	Measurement and Data 1 MD Represent and interpret data.	1.MD.C.4 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.
2.DPS.1a7 Analyze data by sorting into categories established by each question	Measurement and Data 2 MD Represent and interpret data.	2.MD.D.10 Draw a picture graph and a bar graph to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph.
2.DPS.1a8 Interpret the number of points in each category		No CCSS linked
Progress Indicator: E.DPS.1c collecting and organizing/representing data (e.g., picture graphs, tally charts, bar graphs)
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
2.DPS.1c2 Organize data by representing categorical data on a pictorial graph or bar graph	Measurement and Data 2 MD Represent and interpret data.	2.MD.D.10 Draw a picture graph and a bar graph to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph.
2.DPS.1c3 Organize data by representing continuous data on a line plot	Measurement and Data 2 MD Represent and interpret data.	2.MD.D.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.
Progress Indicator: E.DPS.1d recognizing that data can take on different values
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
2.DPS.1d2 Identify the value of each category represented on picture graph and bar graph or each point on a line plot	Measurement and Data 2 MD Represent and interpret data.	2.MD.D.10 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 using information presented in a bar graph.
Progress Indicator: E.DPS.1e describing and comparing data and beginning to identify what the data do or do not show (e.g., bar graphs, line plots, picture graphs)
Core Content Connectors: 2	CCSS Domain/Cluster	Common Core State Standard
2.DPS.1e2 Compare the information shown in a bar graph or picture graph with up to 4 categories. Solve simple comparisons of how many more or how many less	Measurement and Data 2 MD Represent and interpret data.	2.MD.D.10 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 using information presented in a bar graph.

Progress Indicator: E.DPS.1f formulating questions and designing investigations (defining measures and variables)
Core Content Connectors: 3	CCSS Domain/Cluster	Common Core State Standard
3.DPS.1f1 Develop questions, make a plan for data collection		No CCSS linked
Progress Indicator: E.DPS.1g collecting data and representing data (e.g., bar graphs, frequency tables, line plots)
Core Content Connectors: 3	CCSS Domain/Cluster	Common Core State Standard
3.DPS.1g1 Collect data, organize into picture or bar graph	Measurement and Data 3 MD Represent and interpret data.	3.MD.B.3 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.
3.DPS.1g2 Organize measurement data into a line plot	Measurement and Data 3 MD Represent and interpret data.	3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.
Progress Indicator: E.DPS.1i describing data shapes and what the data representations do and do not show (bar graphs, picture graphs, frequency tables, line plots, circle graphs) including the attributes used
Core Content Connectors: 3	CCSS Domain/Cluster	Common Core State Standard
3.DPS.1i1 Select the appropriate statement that describes the data representations based on a given graph (picture, bar, line plots)	Measurement and Data 3 MD Represent and interpret data.	3.MD.B.3 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.
Progress Indicator: E.DPS.1k using data to make and support claims and interpretations (e.g., making comparisons among individuals, between individuals and the group, and among groups)
Core Content Connectors: 3	CCSS Domain/Cluster	Common Core State Standard
3.DPS.1k1 Apply results of data to a real world situation		No CCSS linked

Progress Indicator: E.DPS.1f formulating questions and designing investigations (defining measures and variables)
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.DPS.1f2 Develop questions, make a plan for data collection		No CCSS linked
Progress Indicator: E.DPS.1g collecting data and representing data (e.g., bar graphs, frequency tables, line plots)
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.DPS.1g3 Collect data, organize in graph (e.g., picture graph, line plot, bar graph)	Measurement and Data 3 MD Represent and interpret data. 4 MD Represent and interpret data.	3.MD.B.3 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. 4.MD.B.4 Make a line plot to display a data set of measurements in fractions of a unit. 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 and shortest specimens in an insect collection.
Progress Indicator: E.DPS.1i describing data shapes and what the data representations do and do not show (bar graphs, picture graphs, frequency tables, line plots, circle graphs) including the attributes used
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.DPS.1i1 Select the appropriate statement that describes the data representations based on a given graph (picture, bar, line plots)	Measurement and Data 3 MD Represent and interpret data.	3.MD.B.3 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.
Progress Indicator: E.DPS.1j identifying clumps, gaps, trends, or central tendency (mode, median) in the data
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.DPS.1j1 Select an appropriate statement that describes the most frequent or the least frequent data point using a line plot, picture graph, or bar graph	Measurement and Data 3 MD Represent and interpret data.	3.MD.B.3 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. 3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.
Progress Indicator: E.DPS.1k using data to make and support claims and interpretations (e.g., making comparisons among individuals, between individuals and the group, and among groups)
Core Content Connectors: 4	CCSS Domain/Cluster	Common Core State Standard
4.DPS.1k2 Apply results of data to a real world situation	Measurement and Data 3 MD Represent and interpret data.	3.MD.B.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.

Progress Indicator: M.DPS.1c using representations (e.g., dot plots, scatter plots, line plots) to display data from investigations to describe the shapes of the data
Core Content Connectors: 5	CCSS Domain/Cluster	Common Core State Standard
5.DPS.1c1 Collect and graph data: bar graph, line plots, picture graph (e.g., average height among 3 classrooms, # of boys and girls)	Measurement and Data 3 MD Represent and interpret data. 5 MD Represent and interpret data.	3.MD.B.3 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. 5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (½, ¼, ⅛). 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.
Progress Indicator: M.DPS.1d identifying the range, three common measures of central tendency (mean, median, and mode) and interpreting the mean as a fair share and a center of balance
Core Content Connectors: 5	CCSS Domain/Cluster	Common Core State Standard
5.DPS.1d1 Select an appropriate statement about the range of the data for a given graph (bar graph, line plot) (i.e., range of data) up to 10 points	Statistics and Probability 6 SP Develop understanding of statistical variability.	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.
Progress Indicator: M.DPS.1e making claims about populations from data distributions, supporting interpretations on the basis of mean, median, or mode, and the shape of the distribution
Core Content Connectors: 5	CCSS Domain/Cluster	Common Core State Standard
5.DPS.1e1 Use measures of central tendency to interpret data including overall patterns in the data	Statistics and Probability 6 SP Develop understanding of statistical variability.	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.

Middle School Progress Indicators

Progress Indicator: M.DPS.1a formulating questions about groups larger than classroom groups and comparing different populations or samples
Core Content Connectors: 6	CCSS Domain/Cluster	Common Core State Standard
6.DPS.1a2 Identify statistical questions and make a plan for data collection	Statistics and Probability 6 SP Develop understanding of statistical variability.	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.
Progress Indicator: M.DPS.1c using representations (e.g., dot plots, scatter plots, line plots) to display data from investigations to describe the shapes of the data
Core Content Connectors: 6	CCSS Domain/Cluster	Common Core State Standard
6.DPS.1c2 Collect and graph data: bar graph, line plots, dot plots, histograms	Statistics and Probability 6 SP Summarize and describe distributions.	6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Progress Indicator: M.DPS.1d identifying the range, three common measures of central tendency (mean, median, and mode) and interpreting the mean as a fair share and a center of balance
Core Content Connectors: 6	CCSS Domain/Cluster	Common Core State Standard
6.DPS.1d2 Solve for mean of a given data set	Statistics and Probability 6 SP Develop understanding of statistical variability.	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.
6.DPS.1d3 Select statement that matches mean, mode, and spread of data for 1 measure of central tendency for a given data set	Statistics and Probability 6 SP Summarize and describe distributions.	6.SP.B.5 Summarize numerical data sets in relation to their context such as by: c) Giving quantitative measures of center (median and/or mean) and variability as well as describing any overall pattern and striking deviations from the overall pattern with reference to the context in which the data were gathered.
6.DPS.1d4 Find the range of a given data set	Statistics and Probability 6 SP Develop understanding of statistical variability.	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.
6.DPS.1d5 Explain or identify what the mean represents in a set of data	Statistics and Probability 6 SP Develop understanding of statistical variability.	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.
6.DPS.1d6 Explain or identify what the mode represents in a set of data	Statistics and Probability 6 SP Develop understanding of statistical variability.	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.
6.DPS.1d7 Explain or identify what the median represents in a set of data	Statistics and Probability 6 SP Summarize and describe distributions.	6.SP.B.5 Summarize numerical data sets in relation to their context such as by: c) Giving quantitative measures of center (median and/or mean) and variability as well as describing any overall pattern and striking deviations from the overall pattern with reference to the context in which the data were gathered.
Progress Indicator: M.DPS.1e making claims about populations from data distributions, supporting interpretations on the basis of mean, median, or mode, and the shape of the distribution
Core Content Connectors: 6	CCSS Domain/Cluster	Common Core State Standard
6.DPS.1e2 Use measures of central tendency to interpret data including overall patterns in the data	Statistics and Probability 6 SP Summarize and describe distributions.	6.SP.B.5 Summarize numerical data sets in relation to their context such as by: c) Giving quantitative measures of center (median and/or mean) and variability as well as describing any overall pattern and striking deviations from the overall pattern with reference to the context in which the data were gathered.

Progress Indicator: M.DPS.1b distinguishing among populations, censuses, and sampling
Core Content Connectors: 7	CCSS Domain/Cluster	Common Core State Standard
7.DPS.1b1 Determine sample size to answer a given question	Statistics and Probability 7 SP Use random sampling to draw inferences about a population.	7.SP.A.1 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.
Progress Indicator: M.DPS.1g displaying and interpreting univariate data using dot plots, histograms, and circle graphs
Core Content Connectors: 7	CCSS Domain/Cluster	Common Core State Standard
7.DPS.1g1 Graph continuous data using line graphs, histograms, or dot plots	Statistics and Probability 6 SP Summarize and describe distributions.	6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Progress Indicator: M.DPS.1i using box plots, interquartile range, mean absolute deviation, range, and the concept of outliers to characterize the distribution (variability) of univariate data
Core Content Connectors: 7	CCSS Domain/Cluster	Common Core State Standard
7.DPS.1i1 Solve for the median of a given data set	Statistics and Probability 6 SP Summarize and describe distributions.	6.SP.B.5 Summarize numerical data sets in relations to their context such as by: c) Giving quantitative measures of center (median and/or mean) and variability as well as describing any overall pattern and striking deviations from the overall pattern with reference to the context in which the data were gathered.
7.DPS.1i2 Identify the range (high/low), median (middle), mean, or mode of a given data set	Statistics and Probability 7 SP Draw informal comparative inferences about two populations.	7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about the 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.
Progress Indicator: M.DPS.1j comparing two unequal distributions of data using number of data points, measures of central tendency, shape, and variability (numerical data), and two-way tables (categorical variables)
Core Content Connectors: 7	CCSS Domain/Cluster	Common Core State Standard
7.DPS.1j1 Make or select a statement to compare the distribution of 2 data sets	Statistics and Probability 7 SP Draw informal comparative inferences about two populations.	7.SP.B.3 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.
Progress Indicator: M.DPS.1k supporting claims about the results of investigations (e.g., coordinating among the measures of central tendency and variability)
Core Content Connectors: 7	CCSS Domain/Cluster	Common Core State Standard
7.DPS.1k1 Analyze graphs to determine or select appropriate comparative inferences about two samples or populations	Statistics and Probability 7 SP Draw informal comparative inferences about two populations.	7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about the 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.

Progress Indicator: M.DPS.1f formulating questions about groups larger than classroom groups, comparing different populations or samples, and involving two variables
Core Content Connectors: 8	CCSS Domain/Cluster	Common Core State Standard
8.DPS.1f1 Formulate a research question to study		No CCSS linked
8.DPS.1f2 Identify two variables to study in a given a research question		No CCSS linked
8.DPS.1f3 Construct a two-way table summarizing data on two categorical variables collected from the same subjects; identify possible association between the two variables	Statistics and Probability 8 SP Investigate patterns of association in bivariate data.	8.SP.A.4. 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?
Progress Indicator: M.DPS.1g displaying and interpreting univariate data using dot plots, histograms, and circle graphs
Core Content Connectors: 8	CCSS Domain/Cluster	Common Core State Standard
8.DPS.1g2 Graph data using line graphs, histograms, or box plots	Statistics and Probability 8 SP Investigate patterns of association in bivariate data.	8.SP.A.1 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 non linear association.
Progress Indicator: M.DPS.1h displaying data in scatter plots and investigating the association between the variables
Core Content Connectors: 8	CCSS Domain/Cluster	Common Core State Standard
8.DPS.1h1 Graph bivariate data using scatter plots and identify possible associations between the variables	Statistics and Probability 8 SP Investigate patterns of association in bivariate data.	8.SP.A.1 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 non linear association.
Progress Indicator: M.DPS.1i using box plots, interquartile range, mean absolute deviation, range, and the concept of outliers to characterize the distribution (variability) of univariate data
Core Content Connectors: 8	CCSS Domain/Cluster	Common Core State Standard
8.DPS.1i3 Using box plots and scatter plots, identify data points that appear to be outliers	Statistics and Probability 8 SP Investigate patterns of association in bivariate data.	8.SP.A.1 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 non linear association.
8.DPS.1i4 Identify outliers, range, mean, median, and mode	Statistics and Probability 6 SP Summarize and describe distributions.	6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: 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.
Progress Indicator: M.DPS.1j comparing two unequal distributions of data using number of data points, measures of central tendency, shape, and variability (numerical data), and two-way tables (categorical variables)
Core Content Connectors: 8	CCSS Domain/Cluster	Common Core State Standard
8.DPS.1j2 Make or select an appropriate statement based upon two unequal data sets using measure of central tendency and shape	Statistics and Probability 7 SP Draw informal comparative inferences about two populations.	7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about the 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.
Progress Indicator: M.DPS.1k supporting claims about the results of investigations (e.g., coordinating among the measures of central tendency and variability)
Core Content Connectors: 8	CCSS Domain/Cluster	Common Core State Standard
8.DPS.1k2 Analyze displays of bivariate data to develop or select appropriate claims about those data	Statistics and Probability 8 SP Investigate patterns of association in bivariate data.	8.SP.A.4 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?

High School Progress Indicators

Progress Indicator: H.DPS.1a designing and conducting different kinds of studies using categorical and numerical data, explain results, and use data to estimate a population mean or proportion: a. observational studies (e.g., traffic patterns at an intersection near the school); b. sample surveys (a survey of student nutritional habits); c. simple comparative experiments (e.g., comparisons of water and fertilizer treatments in a plant growth experiment)
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.DPS.1a1 Design study using categorical and continuous data, including creating a question, identifying a sample, and making a plan for data collection	Interpreting Categorical and Quantitative Data S ID Summarize, represent and interpret data on two categorical and quantitative variables.	HSS.ID.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data. Recognize possible associations and trends in the data.
Progress Indicator: H.DPS.1b representing data with plots on the real number line (dot plots, histograms, box plots)
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.DPS.1b1 Complete a graph given the data, using dot plots, histograms, or box plots	Interpreting Categorical and Quantitative Data S ID Summarize, represent, and interpret data on a single count or measurement variable.	HSS.ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
Progress Indicator: H.DPS.1c analyzing and summarizing the data resulting from studies using statistical measures appropriate to shape of the data (median, mean) and spread (interquartile range, standard deviation), and using data to support inferences (population parameters, sample size) or explain possible outliers
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.DPS.1c1 Use descriptive stats; range, median, mode, mean, outliers/gaps to describe the data set	Interpreting Categorical and Quantitative Data S ID Summarize, represent, and interpret data on a single count or measurement variable. S ID Summarize, represent and interpret data on two categorical and quantitative variables.	HSS.ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets. 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. HSS.ID.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data. Recognize possible associations and trends in the data.
H.DPS.1c2 Compare means, median, and range of 2 sets of data	Interpreting Categorical and Quantitative Data S ID Summarize, represent and interpret data on two categorical and quantitative variables.	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.
H.DPS.1c3 Determine what inferences can be made from statistics	Making Inferences and Justifying Conclusions S IC Understand and evaluate random processes underlying statistical experiments.	HSS.IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Progress Indicator: H.DPS.1d representing and interpreting data (graphs, scatter plots) to explain how variables are related, or to fit a function to the data
Core Content Connectors: 9-12	CCSS Domain/Cluster	Common Core State Standard
H.DPS.1d1 Represent data on a scatter plot to describe and predict	Interpreting Categorical and Quantitative Data S ID Summarize, represent and interpret data on two categorical and quantitative variables.	HSS.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
H.DPS.1d2 Select an appropriate statement that describes the relationship between variables	Interpreting Categorical and Quantitative Data S ID Summarize, represent and interpret data on two categorical and quantitative variables.	HSS.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
H.DPS.1d3 Make or select an appropriate statement(s) about findings	Making Inferences and Justifying Conclusions S IC Make inferences and justify conclusions from sample surveys, experiments, and observational studies.	HSS.ID.B.6 Evaluate reports based on data.
H.DPS.1d4 Apply the results of the data to a real world situation	Making Inferences and Justifying Conclusions S IC Make inferences and justify conclusions from sample surveys, experiments, and observational studies.	HSS.ID.B.6 Evaluate reports based on data.