MATH 1102 · Probability and Statistics: Describing Data

Led by Carl Friedrich Gauss Simulacrum

Central tendency, spread, box plots, the normal distribution and z-scores, Chebyshev's theorem — taught by the mathematician behind the bell curve.

1. Module 1

   Measures of Central Tendency

   Led by Carl Friedrich Gauss Simulacrum

   The question

   Mean, median, mode — three different answers to "what is the typical value?" The commute dataset has a mean of 34 minutes and a median of 30.5 minutes. One person commutes 95 minutes. Which measure should a transport planner use — and why does the choice matter?

   Outcome

   The student can compute mean, median, and weighted mean, and choose the appropriate measure for a given dataset.

   Sub-units

   1. ○ 1.1 Central Tendency Calculations Open this unit → ✓ ↻
   Begin the course → Print certificate of completion
2. Module 2

   Measures of Spread

   Led by Carl Friedrich Gauss Simulacrum

   The question

   Two classes both average 65% on a test. Class A has a standard deviation of 5; Class B has a standard deviation of 22. Why does this difference matter — and why do we divide by n-1, not n, for the sample variance?

   Outcome

   The student can compute variance, SD, and IQR, apply Bessel's correction, and choose between SD and IQR for skewed data.

   Sub-units

   1. ○ 2.1 Variance and Standard Deviation Open this unit → ✓ ↻
   Open this module → Print certificate of completion
3. Module 3

   Outliers and Box-and-Whisker Plots

   Led by Carl Friedrich Gauss Simulacrum

   The question

   The 1.5 × IQR rule identifies outliers visually. Group A has one outlier; Group B does not. What does the box plot reveal about distributional shape, spread, and typical performance that a mean and SD alone cannot?

   Outcome

   The student can construct a box-and-whisker plot, apply the 1.5 × IQR rule, and read shape from a box plot.

   Sub-units

   1. ○ 3.1 Box Plot Construction and Comparison Open this unit → ✓ ↻
   Open this module → Print certificate of completion
4. Module 4

   The Normal Distribution and Z-Scores

   Led by Carl Friedrich Gauss Simulacrum

   The question

   Heights are normally distributed: mean 178 cm, SD 8 cm. What proportion of men are taller than 190 cm? What height marks the 90th percentile? How many standard deviations from the mean is "unusually tall"?

   Outcome

   The student can compute z-scores and use the standard normal table to find probabilities and percentiles.

   Sub-units

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

   Chebyshev's Theorem, Weighted Means, and Distributions

   Led by Carl Friedrich Gauss Simulacrum

   The question

   Household incomes: mean £45,000, median £32,000, SD £28,000. What does the mean-median gap tell you about the distribution shape? Using Chebyshev's theorem, what can you assert about the range containing at least 75% of incomes?

   Outcome

   The student can apply Chebyshev's theorem and fully describe a distribution in terms of centre, spread, and shape.

   Sub-units

   1. ○ 5.1 Final Essay: Describing a Distribution Open this unit → ✓ ↻
   Open this module → Print certificate of completion