Learning Domain: Statistics and Probability

Standard: Summarize and describe distributions

Indicator: 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 was gathered.

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Learning Domain: Statistics and Probability

Standard: Summarize and describe distributions

Indicator: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

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Learning Domain: Statistics and Probability

Standard: Summarize and describe distributions

Indicator: Reporting the number of observations.

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Learning Domain: Statistics and Probability

Standard: Develop understanding of statistical variability

Indicator: 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?"ť is not a statistical question, but "How old are the students in my school?"ť is a statistical question because one anticipates variability in students' ages.

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Learning Domain: Statistics and Probability

Standard: Develop understanding of statistical variability

Indicator: 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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Learning Domain: Statistics and Probability

Standard: Develop understanding of statistical variability

Indicator: 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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Learning Domain: Statistics and Probability

Standard: Summarize and describe distributions

Indicator: Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.

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Learning Domain: Statistics and Probability

Standard: Summarize and describe distributions

Indicator: Summarize and describe distributions. Summarize numerical data sets in relation to their context, such as by:

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Learning Domain: Statistics and Probability

Standard: Summarize and describe distributions

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

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Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

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Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Reason abstractly and quantitatively. Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize"Óto abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents"Óand the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

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Learning Domain: Mathematical Practices

Standard: Mathematical practices

Indicator: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?"ť They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

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