Page 120 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

Grade 12, University Preparation
1. demonstrate an understanding of the role of data in statistical studies and the variability inherent in data, and distinguish different types of data;
2. describe the characteristics of a good sample, some sampling techniques, and principles of primary data collection, and collect and organize data to solve a problem.
1. Understanding Data Concepts
2. Collecting and Organizing Data
THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics
OVERALL EXPECTATIONS
By the end of this course, students will:
SPECIFIC EXPECTATIONS
By the end of this course, students will:
1.1 recognize and describe the role of data in statistical studies (e.g., the use of statistical techniques to extract or mine knowledge of relationships from data), describe examples
of applications of statistical studies (e.g., in medical research, political decision making, market research), and recognize that conclu- sions drawn from statistical studies of the same relationship may differ (e.g., conclusions about the effect of increasing jail sentences on crime rates)
1.2 recognize and explain reasons why variability is inherent in data (e.g., arising from limited accuracy in measurement or from variations in the conditions of an experiment; arising from differences in samples in a survey), and distinguish between situations that involve one variable and situations that involve more than one variable
Sample problem: Use the Census at School database to investigate variability in the median and mean of, or a proportion esti-
mated from, equal-sized random samples of data on a topic such as the percentage of students who do not smoke or who walk to school, or the average height of people of a particular age. Compare the median and mean of, or a proportion estimated from, samples of increasing size with the median and mean of the population or the popula- tion proportion.
1.3 distinguish different types of statistical data (i.e., discrete from continuous, qualitative from quantitative, categorical from numerical, nominal from ordinal, primary from secondary, experimental from observational, microdata from aggregate data) and give examples
(e.g., distinguish experimental data used to compare the effectiveness of medical treat- ments from observational data used to exam- ine the relationship between obesity and
type 2 diabetes or between ethnicity and type 2 diabetes)
By the end of this course, students will:
2.1 determine and describe principles of primary data collection (e.g., the need for randomiza- tion, replication, and control in experimental studies; the need for randomization in sample surveys) and criteria that should be consid- ered in order to collect reliable primary data (e.g., the appropriateness of survey questions; potential sources of bias; sample size)
2.2 explain the distinction between the terms population and sample, describe the character- istics of a good sample, explain why sampling is necessary (e.g., time, cost, or physical con- straints), and describe and compare some sampling techniques (e.g., simple random, systematic, stratified, convenience, voluntary)
Sample problem: What are some factors that a manufacturer should consider when deter- mining whether to test a sample or the entire population to ensure the quality of a product?
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C. ORGANIZATION OF DATA FOR ANALYSIS