Data+Analysis+and+Probability

__**Data Analysis and Probability Standard**__ **Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and** **arguments that are based on data.**

**By the end of the 3-4 program:**
 * A. Gather and organize data from surveys and classroom experiments, including data collected over a period of time.
 * B. Read and interpret tables, charts, graphs (bar, picture, line, line plot), and timelines as sources of information, identify main idea, draw conclusions, and make predictions.
 * C. Construct charts, tables and graphs to represent data, including picture graphs, bar graphs, line graphs, line plots and Venn diagrams.
 * D. Read, interpret and construct graphs in which icons represent more than a single unit or intervals greater than one; e.g., each = 10 bicycles or the intervals on an axis are multiples of 10.
 * E. Describe data using mode, median and range.
 * F. Conduct a simple probability experiment and draw conclusions about the likelihood of possible outcomes.
 * G. Identify and represent possible outcomes, such as arrangements of a set of up to four members and possible combinations from several sets, each containing 2 or 3 members.
 * H. Use the set of possible outcomes to describe and predict events.

**By the end of the 5-7 program:**
 * A. Read, create and use line graphs, histograms, circle graphs, box-and-whisker plots, stem-and-leaf plots, and other representations when appropriate.
 * B. Interpret data by looking for patterns and relationships, draw and justify conclusions, and answer related questions.
 * C. Evaluate interpretations and conclusions as additional data are collected, modify conclusions and predictions, and justify new findings.
 * D. Compare increasingly complex displays of data, such as multiple sets of data on the same graph.
 * E. Collect, organize, display and interpret data for a specific purpose or need.
 * F. Determine and use the range, mean, median and mode to analyze and compare data, and explain what each indicates about the data.
 * G. Evaluate conjectures and predictions based upon data presented in tables and graphs, and identify misuses of statistical data and displays.
 * H. Find all possible outcomes of simple experiments or problem situations, using methods such as lists, arrays and tree diagrams.
 * I. Describe the probability of an event using ratios, including fractional notation.
 * J. Compare experimental and theoretical results for a variety of simple experiments.
 * K. Make and justify predictions based on experimental and theoretical probabilities.

**By the end of the 8-10 program:**
 * A. Create, interpret and use graphical displays and statistical measures to describe data; e.g., box-and-whisker plots, histograms, scatterplots, measures of center and variability.
 * B. Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose.
 * C. Compare the characteristics of the mean, median and mode for a given set of data, and explain which measure of center best represents the data.
 * D. Find, use and interpret measures of center and spread, such as mean and quartiles, and use those measures to compare and draw conclusions about sets of data.
 * E. Evaluate the validity of claims and predictions that are based on data by examining the appropriateness of the data collection and analysis.
 * F. Construct convincing arguments based on analysis of data and interpretation of graphs.
 * G. Describe sampling methods and analyze the effects of method chosen on how well the resulting sample represents the population.
 * H. Use counting techniques, such as permutations and combinations, to determine the total number of options and possible outcomes.
 * I. Design an experiment to test a theoretical probability, and record and explain results.
 * J. Compute probabilities of compound events, independent events, and simple dependent events.
 * K. Make predictions based on theoretical probabilities and experimental results.

__**Examples:**__ 3rd Grade/Creating a Bar Graph http://nces.ed.gov/nceskids/createagraph/

8th Grade/Creating Box and Whisker Graph http://ellerbruch.nmu.edu/cs255/jnord/boxplot.html