Mathematics of Data Management - 12

Course Description:

This course broadens students' understanding of mathematics as it relates to managing data. Students will apply methods for organizing and analyzing large amounts of information; apply counting techniques, probability, and statistics in modelling and solving problems; and carry out a data management investigation that integrates the expectations of the course and encourages perseverance and independence. Students planning to pursue university programs in business, the social sciences, or the humanities will find this course of particular interest.

Prerequisite: MCR3U - Functions Grade 11 or MCF3M - Functions and Applications Grade 11

Course Outline

Unit 1: Counting and Probability (26 hours)

In this unit, you will demonstrate an understanding of how to solve problems involving permutations and combinations to determine the probability of an event. You will also demonstrate an understanding of solving counting problems using counting principles and solve related problems from a variety of applications using the Binomial theorem and Pascal's triangle.

1-1 Organized Counting
1-2 Permutations          
1-3 Pascal's Triangle and its Applications
1-4 Venn Diagrams and Sets
1-5 Combinations                                                                    
1-6 The Binomial Theorem and the General Term


Unit 2: Organization of Data for Analysis (20 hours)

In this unit, you will demonstrate an understanding of the role of data in statistical studies, describe the characteristics of some sampling techniques and principles of primary data collection.  You will design and describe the characteristics of an effective survey and collect data from primary sources, through experimentation. You will also explore how to organize data with one or more attributes using a variety of data management tools.

2-1 Constructing & Interpreting Visual Display of Data
2-2 Sampling Techniques
2-3 Bias & Surveys
2-4 Collecting Data using Technology
2-5 Careers Involving Statistics


Unit 3: Statistical Analysis (28 hours)

This unit will introduce statistical techniques for measuring relationships between two variables. We will explore two variables statistics that has an enormous range of applications including industrial processes, medical studies, and environmental issues - in fact, almost any field where you need to determine if a change in one variable affects another.

3-1 Measures of Central Tendency & Standard Deviation   
3-2 Scatter Plots and Linear Correlation
3-3 The Correlation Coefficient
3-4 Linear Regression
3-5 Cause and Effect
3-6 Measures of Dispersion
3-7 Validity of Data


Unit 4: Probability Distribution (20 hours)

In this unit, we will learn methods that we can use to calculate probabilities from the samples and to make predictions about the population. We will also develop the principles of probability theory and apply them to such situations as games of chance, learning patterns and sports.

4-1 Basic Probability Concepts
4-2 General Probabilities Distributions
4-3 The Binomial Distribution
4-4 The Hypergeometric Distribution
4-5 Continuous Probability and the Normal Distribution      


Unit 5: Culminating Data Management Investigation (16 hours)

In this unit, you will work on the Culminating Project. It is a research assignment on statistics in which you will collect data, analyze the data and present a report on their findings. It requires the integration and application of the knowledge and skills related to the expectations of the previous units. 

5-1 Choosing a Topic and Finding Data                             
5-2 Conducting Data Analysis
5-3 Written Report
5-4 Final Presentation