Explanation 1
Marginal: A row or column total divided by the grand total.
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Lesson 10 of 16
Turn a frequency table into validated marginal, joint, and conditional probabilities.
Theory
Turn a frequency table into validated marginal, joint, and conditional probabilities.
Explanation 1
Marginal: A row or column total divided by the grand total.
Explanation 2
Joint: One interior cell divided by the grand total.
Explanation 3
Conditional: One cell divided by its conditioned row or column total.
Terminology
A row or column total divided by the grand total.
All volunteers over all alumni.
One interior cell divided by the grand total.
Degree and volunteer.
One cell divided by its conditioned row or column total.
Volunteer given Degree.
Notation and formulas
joint = cell / grand total; conditional = cell / conditioned total
Define every event before substituting values, then validate the result and denominator.
Interactive Mission
| Row total: 50 | ||
|---|---|---|
| Row total: 50 | ||
| Grand total: 100 | ||
Cell (1,1) joint
0.32
32 / 100
First-row marginal
0.5
50 / 100
Column 1 given row 1
0.64
32 / highlighted row total 50
Worked example
Scenario
An educator cross-tabulates program type and volunteer status.
Every table percentage needs an explicit denominator.
R connection
Run and edit the code, inspect intermediate output, and use the movable R Code Guide while practising.
Live R Lab
Calculate marginal, joint, row-conditional, and column-conditional probabilities from counts.
Ready to run
Dataset provenance
Original synthetic data generated for STATLAB Academy. No textbook data used.
Interpretation safeguard
A conditional percentage must use the total of the conditioned row or column, not the grand total.
Reflection
Name the event, denominator, probability interpretation, and one operational limitation.
Assistant
Help me reason through Marginal, Joint, and Conditional Probabilities in Contingency Tables by asking questions about my event definitions, denominator, formula choice, assumptions, and interpretation. Do not give a quiz answer before I submit.
Exit check
Use a hint before submitting if needed. Full calculations and interpretations appear after submission.
Checkpoint
Question 1 of 2. Answered 0/2. Passing score: 70%.
Resource
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