Mathematics

D. STATISTICAL ANALYSISTHE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics Grade 12, University PreparationOVERALL EXPECTATIONSBy the end of this course, students will:1. analyse, interpret, and draw conclusions from one-variable data using numerical and graphicalsummaries;2. analyse, interpret, and draw conclusions from two-variable data using numerical, graphical, andalgebraic summaries;3. demonstrate an understanding of the applications of data management used by the media and theadvertising industry and in various occupations.SPECIFIC EXPECTATIONS1. Analysing One-Variable DataBy the end of this course, students will:1.1 recognize that the analysis of one-variabledata involves the frequencies associated withone attribute, and determine, using technology,the relevant numerical summaries (i.e.,mean, median, mode, range, interquartilerange, variance, and standard deviation)1.2 determine the positions of individual datapoints within a one-variable data set usingquartiles, percentiles, and z-scores, use thenormal distribution to model suitable onevariabledata sets, and recognize theseprocesses as strategies for one-variabledata analysis1.3 generate, using technology, the relevantgraphical summaries of one-variable data(e.g., circle graphs, bar graphs, histograms,stem-and-leaf plots, boxplots) based on thetype of data provided (e.g., categorical,ordinal, quantitative)1.4 interpret, for a normally distributed population,the meaning of a statistic qualified by astatement describing the margin of error andthe confidence level (e.g., the meaning of astatistic that is accurate to within 3 percentagepoints, 19 times out of 20), and make connections,through investigation using technology(e.g., dynamic statistical software), betweenthe sample size, the margin of error, and theconfidence level (e.g., larger sample sizescreate higher confidence levels for a givenmargin of error)Sample problem: Use census data fromStatistics Canada to investigate, usingdynamic statistical software, the minimumsample size such that the proportion of thesample opting for a particular consumer orvoting choice is within 3 percentage points ofthe proportion of the population, 95% of thetime (i.e., 19 times out of 20).1.5 interpret statistical summaries (e.g., graphical,numerical) to describe the characteristics of aone-variable data set and to compare tworelated one-variable data sets (e.g., comparethe lengths of different species of trout;compare annual incomes in Canada and in athird-world country; compare Aboriginal andnon-Aboriginal incomes); describe how statisticalsummaries (e.g., graphs, measures ofcentral tendency) can be used to misrepresentone-variable data; and make inferences, andmake and justify conclusions, from statisticalsummaries of one-variable data orally and inwriting, using convincing arguments2. Analysing Two-Variable DataBy the end of this course, students will:2.1 recognize that the analysis of two-variabledata involves the relationship between twoattributes, recognize the correlation coefficient120