California Draft Standards: Statistics, Data Analysis, Probability
Students display, analyze, compare and interpret different data sets, including data sets that are not the same size, 1) analyzing data to determine measures and appropriate uses of central tendencies (mean, median and mode), and explain why these measures are the same or different; 2) organizing and displaying single-variable data in appropriate graphs and representations (e.g., histogram, line graphs, circle graphs) and explaining which types of graphs are appropriate for different kinds of data sets; 3) using fractions and percentages to compare data sets of different size; and 4) identifying ordered pairs of data from a graph and interpreting the meaning of the data in terms of the situation depicted by the graph. Sample tasks: Use information on bedtimes to determine the truth of various statements, using the mean, median and mode.
Read California's final Grade Five Mathematics Content Standards
Students collect data using samples of a population and describe the characteristics and limitations of the samples, 1) comparing different samples from a population with the data from the entire population and explaining when it makes sense to use a sample; 2) identifying different ways of selecting a sample (e.g., convenience sampling, those who respond to a survey, random sampling) and which makes a sample more representative for a population; 3) analyzing data displays and explaining how the way the question was asked might have influenced the results obtained, and/or how the way the results were displayed might have influenced the conclusions reached; 4) identifying data displayed in the media that represent sampling and explain why the sample (and the display) may be biased; 5) identifying claims based on statistical data and, in simple cases, evaluating the validity of the claims; 6) explaining which measure of central tendency (mean, median, mode) is most representative for a given sample.
Read California's final Grade Six Mathematics Content Standards
Students collect, organize and represent data sets that have one or more variables and identify relationships among variables within a data set, 1) using a stem-and-leaf plot or box-and-whisker plot to display a single set of data or compare two sets of data; and 2) representing two numerical variables on a scatter plot and informally describing how the data points are distributed and whether there is an apparent relationship between the two variables (e.g., time spent on homework and grade level).
Read California's final Grade Seven Mathematics Content Standards
Students analyze the trends in sets of bi-variate data, 1) summarizing trends in bi-variate data by informally fitting lines to data that appears to have a linear trend; and 2) evaluating the "goodness of fit" of a line for a set of data, assessing its usefulness as a model for the data and using the line to make predictions. Students also critique the conclusions and uses of statistics in both school materials and public documents, 1) using information displayed in graphs (line, bar, circle, and picture graphs and histograms) to make comparisons, predictions and inferences, and critique the conclusions drawn by others; and 2) explaining and critiquing the process of a survey or experiment, how that might have contributed to or influenced the results (e.g., reliability of sampling procedures, bias, missing or incorrect information), and describing misuses of statistical or numerical data.
Read California's final Probability/Statistics-Grades Eight Through Twelve Standards