• 6-8: 9B/M3. Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease, increase or decrease in steps, or do something different from any of these.
• 9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.

• 6-8: 9C/M4. The graphic display of numbers may help to show patterns such as trends, varying rates of change, gaps, or clusters that are useful when making predictions about the phenomena being graphed.

• 9-12: 11C/H9. It is not always easy to recognize meaningful patterns of change in a set of data. Data that appear to be completely irregular may be shown by statistical analysis to have underlying trends or cycles. On the other hand, trends or cycles that appear in data may sometimes be shown by statistical analysis to be easily explainable as being attributable only to randomness or coincidence.

• 9-12: 12D/H7. Use tables, charts, and graphs in making arguments and claims in oral, written, and visual presentations.

• 9-12: 12E/H1. Notice and criticize claims based on the faulty, incomplete, or misleading use of numbers, such as in instances when (1) average results are reported but not the amount of variation around the average, (2) a percentage or fraction is given but not the total sample size, (3) absolute and proportional quantities are mixed, or (4) results are reported with overstated precision.

• F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
• F-IF.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima.

• S-ID.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.
• S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
• S-ID.6.a Fit a function to the data; use functions fitted to data to solve problems in the context of the data.
• S-ID.6.b Informally assess the fit of a function by plotting and analyzing residuals.
• S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
• S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.

• S-IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
• S-IC.4 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.

• S-MD.1 (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
• S-MD.4 (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
• S-MD.7 (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

• 1. Write arguments focused on discipline-specific content. (WHST.9-10.1)
• 2. Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes. (WHST.9-10.2)

High school students can often record data and "plug & chug", but have more difficulty in fitting or interpreting data.  This exemplary two-week unit on data analysis introduces students to the statistical method known as least squares regression.  Using an online tool to plot data, students then calculate regression lines and fit the data to estimated parameters.

• Physics First Graphing Unit
• Conceptual Physics Graphing Unit
• Algebra-Based Physics Graphing Unit
• AP/Calculus-Based Physics Graphing Unit