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# National Standards for Grade 12 - Mathematics (page 5)

#### Data Analysis and Probability

Students in grade 12 will be expected to use a wide variety of statistical techniques for all phases of the data analysis process, including a more formal understanding of statistical inference (but still with simulation as the main inferential analysis tool). In addition to comparing univariate data sets, students at this level should be able to recognize and describe possible associations between two variables by looking at two-way tables for categorical variables or scatter plots for measurement variables. Association between variables is related to the concepts of independence and dependence, and an understanding of these ideas requires knowledge of conditional probability. These students should be able to use statistical models (linear and non-linear equations) to describe possible associations between measurement variables and should be familiar with techniques for fitting models to data.

 GRADE 12 1) Data representation Histograms, line graphs, scatter plots, box plots, circle graphs, stem and leaf plots, frequency distributions, and tables. a) Read or interpret data, including interpolating or extrapolating from data. b) For a given set of data, complete a graph and then solve a problem using the data in the graph (histograms, scatter plots, line graphs). c) Solve problems by estimating and computing with univariate or bivariate data (including scatter plots and two-way tables). d) Given a graph or a set of data, determine whether information is represented effectively and appropriately (bar graphs, box plots, histograms, scatter plots, line graphs). e) Compare and contrast the effectiveness of different representations of the same data. 2) Characteristics of data sets a) Calculate, interpret, or use mean, median, mode, range, interquartile range, or standard deviation. b) Recognize how linear transfor­mations of one-variable data affect mean, median, mode, and range (e.g., effect on the mean by adding a constant to each data point). c) Determine the effect of outliers on mean, median, mode, range, interquartile range, or standard deviation. d) Compare two or more data sets using mean, median, mode, range, interquartile range, or standard deviation describing the same characteristic for two different populations or subsets of the same population. e) Given a set of data or a scatter plot, visually choose the line of best fit and explain the meaning of the line. Use the line to make predictions. f) Use or interpret a normal distri­bution as a mathematical model appropriate for summarizing certain sets of data. g) Given a scatter plot, make decisions or predictions involving a line or curve of best fit. h) Given a scatter plot, estimate the correlation coefficient (e.g., Given a scatter plot, is the cor­relation closer to 0, .5, or 1.0? Is it a positive or negative correlation?). 3) Experiments and samples a) Identify possible sources of bias in data collection methods and describe how such bias can be controlled and reduced. b) Recognize and describe a method to select a simple random sample. c) Make inferences from sample results. d) Identify or evaluate the charac­teristics of a good survey or of a well-designed experiment. 4) Probability a) Analyze a situation that involves probability of independent or dependent events. b) Determine the theoretical probability of simple and compound events in familiar or unfamiliar contexts. c) Given the results of an experiment or simulation, estimate the probability of simple or compound events in familiar or unfamiliar contexts. d) Use theoretical probability to evaluate or predict experimental outcomes. e) Determine the number of ways an event can occur using tree diagrams, formulas for combinations and permutations, or other counting techniques. f) Determine the probability of the possible outcomes of an event. g) Determine the probability of independent and dependent events. h) Determine conditional probabil­ity using two-way tables. i) Interpret probabilities within a given context.

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