MDM4U – Mathematics of Data Management – Grade 12
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; solve problems involving probability and statistics; and carry out a culminating investigation that integrates statistical concepts and skills. Students will also refine their use of the mathematical processes necessary for success in senior mathematics.
$450.00
*Course outline is subject to change
Overall Curriculum Expectations
By the end of this course, students will :
Counting and Probability
- A1 – Solve problems involving the probability of an event or a combination of events for discrete sample spaces
- A2 – Solve problems involving the application of permutation and combinations to determine the probability of an event
Probability Distributions
- B1 – Demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications
- B2 – Demonstrate an understanding of continuous probability distributions, make connections to discrete probability distributions, determine standard deviations, describe key features of the normal distribution, and solve related problems from a variety of applications
Organization of Data for Analysis
- C1 – Demonstrate an understanding of the role of data in statistical studies and the variability inherent in data, and distinguish different types of data
- C2 – Describe the characteristics of a good sample, some sampling techniques, and principles of primary data collection and organize data to solve a problem
Statistical Analysis
- D1 – Analyse, interpret, and draw conclusions from one-variable data using numerical and graphical summaries
- D2 – Analyze, interpret, and draw conclusions from two-variable data using numerical, graphical, and algebraic summaries
- D3 – Demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations
Culminating Data Management Investigation
- E1 – Design and carry out a culminating investigation that requires the integration and application of the knowledge and skills related to the expectation of this course
- E2 – Communicate the findings of a culminated investigation and provide constructive critiques of the investigation of others
Outline of Course Content
In this unit students will demonstrate an understanding of the role of data in statistical studies and the variability inherent in data, and distinguish different types of data; 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; demonstrate an understanding of the applications of data management used by the media and the advertising industry and in various occupations. To summarize data and recognize the trends, we use tables and graphs. Another way of representing data is by using indices. Students will analyze, interpret, and draw conclusions from one-variable data using numerical and graphical summaries as well as draw conclusions from two-variable data using numerical, graphical, and algebraic summaries.
In this unit students will demonstrate an understanding of the role of data in statistical studies and the variability inherent in data, and distinguish different types of data; 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. This unit will also introduce students to a type of diagram that helps them organize data about groups of items when the order of the items is not important. These are called Venn diagrams and they show all possible relationships between sets. In this unit students will demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications. Students are now ready to solve problems for which order does not matter. This is the branch of combinatorics called Combinations. For example, in many card games, what is in your hand is important, but the order in which it was dealt is not. In Combinations the number of ways of choosing r objects from n objects with no order involved is calculated. In this unit students will solve problems involving the probability of an event or a combination of events for discrete sample spaces; solve problems involving the application of permutations and combinations to determine the probability of an event. The Binomial Theorem is an important formula giving the expansion of powers of sums. This formula and the triangular arrangement of the binomial coefficients are often attributed to Pascal who described them in the 17th century. This triangle is referred to as Pascal’s 21 hours Triangle. Pascal’s method for building his triangle is a simple iterative process similar to those described in Unit 1. Pascal made the triangle famous by finding many applications for it. In this unit students will demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications using the Binomial theorem and Pascal’s triangle.
n this unit students will solve problems involving the probability of an event or a combination of events for discrete sample spaces; solve problems involving the application of permutations and combinations to determine the probability of an event; demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications; demonstrate an understanding of continuous probability distributions, make connections to discrete probability distributions, determine standard deviations, describe key features of the normal distribution, and solve related problems from a variety of applications.
In this unit students will solve problems involving the probability of an event or a combination of events for discrete sample spaces; solve problems involving the application of permutations and combinations to determine the probability of an event; demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications; demonstrate an understanding of continuous probability distributions, make connections to discrete probability distributions, determine standard deviations, describe key features of the normal distribution, and solve related problems from a variety of applications. Students will also solve problems involving the probability of an event or a combination of events for discrete sample spaces; solve problems involving the application of permutations and combinations to determine the probability of an event; demonstrate an understanding of discrete probability distributions, represent them numerically, graphically, and algebraically, determine expected values, and solve related problems from a variety of applications; demonstrate an understanding of continuous probability distributions, make connections to discrete probability distributions, determine standard deviations, describe key features of the normal distribution, and solve related problems from a variety of applications.
It is not enough to understand the mathematics of statistics. One must also 15 hours 5 learn how to use statistics to put forward arguments, and how others might use statistics to tell – or distort- the truth. In this section, students will build upon their knowledge and skills from the first four units to investigate the statistical validity of sample literature.
The final assessment task is a proctored exam worth 20% and a presentation worth 10%