MATH 1101 · Probability and Statistics: Visualising Data

Led by Karl Pearson Simulacrum

About this course

Karl Pearson invented the histogram in 1895 to represent the distribution of data as bars whose areas are proportional to frequency. He also invented the chi-square test and the Pearson correlation coefficient. This course covers the tools he built: frequency tables, bar charts, histograms, stem-and-leaf plots, dot plots, Venn diagrams, and joint distributions.

Led by Karl Pearson Simulacrum.

1. Module 1

   Tables: Organising What You Have

   Led by Karl Pearson Simulacrum

   The question

   A one-way table counts. A two-way table counts two things simultaneously. What does the conditional distribution reveal that the marginal distribution hides?

   Outcome

   The student can construct and interpret frequency tables and compute relative and cumulative frequencies.

   Sub-units

   1. ○ 1.1 Build and Read a Two-Way Table Open this unit → ✓ ↻
   2. ○ 1.2 Relative and Cumulative Frequency Open this unit → ✓ ↻
   Begin the course → Print certificate of completion
2. Module 2

   Graphs: Seeing the Data

   Led by Karl Pearson Simulacrum

   The question

   A bar chart and a histogram look similar. They represent fundamentally different things. What is the difference — and when must you use frequency density rather than frequency on the y-axis?

   Outcome

   The student can construct a histogram with frequency density and interpret its shape.

   Sub-units

   1. ○ 2.1 Histogram Construction Open this unit → ✓ ↻
   2. ○ 2.2 Bar Chart vs Histogram Open this unit → ✓ ↻
   Open this module → Print certificate of completion
3. Module 3

   Dot Plots and Stem-and-Leaf

   Led by Karl Pearson Simulacrum

   The question

   The histogram trades information for shape. The stem-and-leaf plot retains the individual values. When is the retained information worth the trade?

   Outcome

   The student can construct and read a stem-and-leaf plot and compare two distributions.

   Sub-units

   1. ○ 3.1 Back-to-Back Stem-and-Leaf Open this unit → ✓ ↻
   Open this module → Print certificate of completion
4. Module 4

   Venn Diagrams and Joint Distributions

   Led by Karl Pearson Simulacrum

   The question

   In 150 people: 80 own a car, 60 own a bicycle, 25 own both. What is the probability of owning a car given that you own a bicycle — and how does the Venn diagram make this visible?

   Outcome

   The student can draw a Venn diagram, build a joint distribution table, and compute conditional probabilities.

   Sub-units

   1. ○ 4.1 Joint Distribution Exercise Open this unit → ✓ ↻
   Open this module → Print certificate of completion
5. Module 5

   Reading Data Critically

   Led by Karl Pearson Simulacrum

   The question

   A histogram with a truncated y-axis makes a small difference look large. A pie chart with eleven categories is illegible. What are the rules for choosing the right graph — and how do you identify a misleading one?

   Outcome

   The student can identify graphical errors and choose appropriate representations for given data types.

   Sub-units

   1. ○ 5.1 Final Essay: The Misleading Graph Open this unit → ✓ ↻
   Open this module → Print certificate of completion