Mathematics of Data Management, Grade 12 (University)

Unit 1: Counting and Probability

Understanding theoretical and experimental probability for discrete sample spaces, and using permutations, combinations, and counting principles to solve probability problems.

• Probabilities represent the likelihood of a result
• Discrete versus continuous sample spaces
• Theoretical probability and the probability distribution summing to 1
• Experimental probability approaching theoretical probability
• Complements and mutually exclusive events
• Independent, dependent, and conditional events

• Permutations vs. combinations: when order matters
• Calculating permutations and combinations and connecting them
• Solving counting problems with standard combinatorial notation
• The additive and multiplicative counting principles
• Connecting combinations and Pascal's triangle
• Solving probability problems using counting principles

Unit 2: Probability Distributions

Understanding discrete probability distributions including binomial and hypergeometric, and continuous probability distributions including the normal distribution, and solving related problems.

• Discrete random variables and generating a probability distribution
• Calculating and interpreting expected value
• Representing a distribution with a probability histogram
• The binomial probability distribution
• The hypergeometric probability distribution
• Comparing discrete probability distributions
• Solving real-world problems with probability distributions

• Continuous random variables and discrete vs. continuous frequency distributions
• Standard deviation as a measure of spread
• Representing continuous data with frequency tables, histograms, and polygons
• Challenges in determining a continuous frequency distribution
• Theoretical probability over a range for a continuous variable
• Properties of the normal distribution
• Connecting the normal distribution to binomial and hypergeometric distributions
• Using z-scores to solve normal distribution problems

Unit 3: Organization of Data for Analysis

Understanding the role and variability of data in statistical studies, distinguishing types of data, and designing sampling and data-collection methods.

• The role of data in statistical studies
• Why variability is inherent in data, and one-variable vs. multi-variable situations
• Distinguishing types of statistical data

• Principles of primary data collection
• Population vs. sample, and sampling techniques
• How sample bias affects study results
• Designing effective surveys and experiments
• Collecting and organizing data from primary and secondary sources

Unit 4: Statistical Analysis

Analysing, interpreting, and drawing conclusions from one-variable and two-variable data, and evaluating the validity of statistics presented in the media.

• Numerical summaries of one-variable data
• Positions within a data set using quartiles, percentiles, and z-scores
• Graphical summaries of one-variable data
• Margin of error and confidence level
• Interpreting, comparing, and concluding from one-variable statistical summaries

• Two-variable data, correlation coefficient, and numerical summaries
• Types of relationships between two variables
• Graphical summaries of two-variable data
• Linear regression and the fit of an individual data point
• Interpreting, comparing, and concluding from two-variable statistical summaries

• How the media and advertising use and misuse statistics
• Assessing the validity of conclusions presented in the media
• Applications of data management in occupations and university programs

Unit 5: Culminating Data Management Investigation

A staged capstone research investigation — posing a problem, planning, gathering data, analysing, concluding, reporting, presenting, and responding to critique — that draws together everything learned in the course.

• Stage 1 — Posing a significant problem and doing background research
• Stage 2 — Designing a plan to study the problem
• Stage 3 — Gathering and organizing investigation data
• Stage 4 — Interpreting, analysing, and summarizing the data
• Stage 5 — Drawing conclusions and evaluating the strength of the evidence
• Stage 6 — Compiling a clear, well-organized, detailed report

• Stage 7 — Presenting the investigation summary to peers
• Stage 8 — Answering questions and responding to critiques
• Stage 9 — Critiquing the mathematical work of others constructively