ARM 10.53.520. CORE DATA REASONING AND PROBABILITY STANDARDS

(1) The quantitative literacy content standards for high school are to: (a) distinguish between quantitative and categorical data and use representations and analysis techniques that are appropriate for each type; (b) ask a statistical question to determine whether there appears to be an association between two variables, design and carry out an investigation, and write a persuasive argument based on the results of the investigation; and (c) distinguish between association and causation. (2) The visualizing, summarizing, and interpreting data content standards for high school are to: (a) use technology to organize data, including very large data sets, into a useful and manageable structure; (b) represent the distribution of univariate quantitative data with plots on the real number line, choosing a format most appropriate to the data set, and representing the distribution of bivariate quantitative data with a scatter plot; (c) understand that standard deviation measures the variability of a data distribution, and calculate standard deviation using technology; (d) interpret differences in the shape, center, and spread of quantitative data distributions, in context, accounting for possible effects of outliers on measures of central tendency and variability; (e) compare and contrast two or more quantitative data distributions, using shape, center, and spread in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities; (f) analyze the relationship between two quantitative data distributions in context that have a linear association. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by: (i) using technology strategically, represent two quantitative data distributions on scatter plots; (ii) describing verbally how the variables are related; (iii) using technology to find the least-squares regression line (line of best) fit for two quantitative variables; (iv) understanding that the line of best fit minimizes the square of the residuals; and (v) understanding correlation as a measure of linear association and using technology, compute the correlation coefficient of a linear relationship; (g) analyze the relationship between two categorical variables in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by: (i) summarizing categorical data for two categories in two-way frequency tables and visual representations; (ii) interpreting relative frequencies for categorical data in context; and (iii) identifying possible associations and trends in categorical data. (3) The probability content standards for high school are to: (a) understand the concept of a sample space and describe events as subsets of a sample space; and (b) understand the concepts of conditional probability and independence in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by: (i) determining whether two events, A and B, are independent by using two-way tables, tree diagrams, and/or Venn diagrams, and interpreting the answer in context; and (ii) computing the conditional probability of event A given event B by using two-way tables, tree diagrams, and/or Venn diagrams, and interpreting the answer in context.