Card 1 of 20
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Prompt
What is categorical data?
Answer
Data that classify observations into labels or groups rather than measuring a numerical quantity.
MathChapter 9: Categorical Data and Probability
Flashcards
Categorical Data and Conditional Probabilities Flashcards
Twenty concise cards on contingency tables, marginal and joint probabilities, conditional denominators, relative frequencies, and table validation.
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Card 2 of 20
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Prompt
What does a two-way contingency table display?
Answer
Counts or relative frequencies for combinations of two categorical variables.
Card 3 of 20
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Prompt
What is an interior cell frequency?
Answer
The count satisfying one row category AND one column category.
Card 4 of 20
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Prompt
What is a marginal frequency?
Answer
A row total or column total shown at the margin of a contingency table.
Card 5 of 20
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Prompt
What is the grand total?
Answer
The total number of observations, equal to the sum of all row totals and also all column totals.
Card 6 of 20
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Prompt
How do you find a marginal probability?
Answer
Divide the relevant row or column total by the grand total.
Card 7 of 20
MediumStudy card 7
Prompt
How do you find a joint probability from a count table?
Answer
Divide the appropriate intersection cell by the grand total.
Formula
\[P(A\text{ and }B)=\frac{\text{intersection count}}{\text{grand total}}\]
Card 8 of 20
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Prompt
What does 'given B' do to the sample space?
Answer
It restricts the denominator to observations satisfying B.
Card 9 of 20
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Prompt
What is the conditional-probability formula?
Answer
\(P(A\mid B)=\frac{P(A\text{ and }B)}{P(B)}\)
Formula
\[P(A\mid B)=\frac{P(A\text{ and }B)}{P(B)}\]
Card 10 of 20
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Prompt
In count form, what is the denominator of \(P(A\mid B)\)?
Answer
The total count satisfying B, the condition after the vertical bar.
Card 11 of 20
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Prompt
Are \(P(A\mid B)\) and \(P(B\mid A)\) generally equal?
Answer
No. Reversing the condition usually changes the denominator.
Card 12 of 20
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Prompt
What denominator does an overall relative frequency use?
Answer
The grand total.
Card 13 of 20
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Prompt
What denominator does a within-row percentage use?
Answer
That row's total, because the row is the reference group.
Card 14 of 20
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Prompt
How can you recover a missing cell from a row total?
Answer
Subtract the other known cells in that row from the row total.
Card 15 of 20
HardStudy card 15
Prompt
Why should two groups be compared using conditional rates rather than raw counts?
Answer
Different group sizes can make a larger count represent a smaller within-group proportion.
Card 16 of 20
EasyStudy card 16
Prompt
A question names category A AND category B. Which table value is the numerator?
Answer
The interior cell at the intersection of A and B.
Card 17 of 20
EasyStudy card 17
Prompt
A question names only one category. Which table value is usually the numerator?
Answer
The corresponding row or column total.
Card 18 of 20
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Prompt
What table check confirms the grand total?
Answer
The sum of row totals and the sum of column totals must both equal it.
Card 19 of 20
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Prompt
What common denominator error occurs in conditional probability?
Answer
Using the grand total instead of the total for the group named after 'given.'
Card 20 of 20
HardStudy card 20
Prompt
What four steps reliably evaluate \(P(A\mid B)\) from a table?
Answer
Locate B, use B's total as denominator, find the A-and-B intersection, then divide and simplify.
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