8th Grade Math Flashcards: Construct And Interpret Two Way Tables

What this deck covers

This deck focuses on Construct And Interpret Two Way Tables, giving you a quick way to review the definitions, rules, and examples that matter most for 8th Grade Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is a row total in a two-way table?

Answer: The sum of all frequencies across one row. Shows how many subjects are in that row's category.

Flashcard 2: Decide if there is association: $P(A\mid B)=0.52$ and $P(A\mid \text{not }B)=0.51$.

Answer: No clear association; the conditional relative frequencies are nearly equal. Similar conditional probabilities (0.52 vs 0.51) suggest independence.

Flashcard 3: What does the term frequency mean in a two-way table?

Answer: The number of subjects in a cell (a count). Each cell contains how many subjects fall in that category combination.

Flashcard 4: What does the term relative frequency mean in a two-way table?

Answer: A proportion: cell count$ divided by a total (row, column, or grand). Shows what fraction of a total each cell represents.

Flashcard 5: What is the grand total in a two-way table?

Answer: The total number of subjects in the entire table. Sum of all cells; represents all subjects surveyed.

Flashcard 6: What is a column total in a two-way table?

Answer: The sum of all frequencies down one column. Shows how many subjects are in that column's category.

Flashcard 7: What formula gives a row relative frequency for a cell?

Answer: $\frac{\text{cell count}}{\text{row total}}$. Shows what fraction of that row the cell represents.

Flashcard 8: Identify the correct step to construct a two-way table from paired survey responses.

Answer: Tally each subject once in the cell matching both category choices. Each subject goes in exactly one cell based on their two responses.

Flashcard 9: Choose the correct conclusion if row relative frequencies are the same in every row.

Answer: No association is suggested between the two categorical variables. Equal row proportions mean the variables are independent.

Flashcard 10: Decide if there is association: $P(\text{Chores}\mid\text{Curfew})=0.70$ and $P(\text{Chores}\mid\text{No Curfew})=0.30$.

Answer: Yes; the conditional relative frequencies are different. Different conditional probabilities (0.70 vs 0.30) indicate association.

Flashcard 11: In a $2\times 2$ table, identify the cell for “Curfew: Yes” and “Chores: No.”

Answer: The intersection of the “Curfew: Yes” row and “Chores: No” column. Find where the row and column categories meet.

Flashcard 12: Find the joint relative frequency: cell count $18$, grand total $60$.

Answer: $\frac{18}{60}=0.3$. Divide cell count by grand total: $\frac{18}{60}=\frac{3}{10}=0.3$.

Flashcard 13: Find the column relative frequency: cell count $9$, column total $36$.

Answer: $\frac{9}{36}=0.25$. Divide cell count by column total: $\frac{9}{36}=\frac{1}{4}=0.25$.

Flashcard 14: Find the row relative frequency: cell count $12$, row total $30$.

Answer: $\frac{12}{30}=0.4$. Divide cell count by row total: $\frac{12}{30}=\frac{2}{5}=0.4$.

Flashcard 15: Which comparison best checks association: row relative frequencies or only raw counts?

Answer: Row or column relative frequencies (not raw counts alone). Relative frequencies reveal patterns; counts alone can mislead.

Flashcard 16: Identify the meaning of the conditional relative frequency $P(A\mid B)$ in a two-way table.

Answer: The relative frequency of $A$ within the group that has $B$. Conditional probability: proportion of $A$ given $B$ occurred.

Flashcard 17: What formula gives a marginal relative frequency for a row or column total?

Answer: $\frac{\text{row or column total}}{\text{grand total}}$. Shows what fraction of all subjects are in that category.

Flashcard 18: What is a two-way table used for in bivariate categorical data?

Answer: A table that shows counts for two categorical variables at once. Displays frequencies for two variables simultaneously.

Flashcard 19: What formula gives a joint relative frequency for a cell?

Answer: $\frac{\text{cell count}}{\text{grand total}}$. Shows what fraction of all subjects the cell represents.

Flashcard 20: What formula gives a column relative frequency for a cell?

Answer: $\frac{\text{cell count}}{\text{column total}}$. Shows what fraction of that column the cell represents.

Flashcard 21: Which relative frequencies help you compare groups: row relative or overall relative?

Answer: Row or column relative frequencies (conditional relative frequencies). Conditional frequencies reveal group differences.

Flashcard 22: Decide association: $P(\text{chores}|\text{curfew})=0.70$ and $P(\text{chores}|\text{no curfew})=0.30$.

Answer: Yes, there is evidence of association. Large difference (0.70 vs 0.30) indicates association.

Flashcard 23: Find the overall relative frequency: cell = $9$, grand total = $60$.

Answer: $\frac{9}{60}=0.15$. Divide cell count by grand total.

Flashcard 24: What is the meaning of a column relative frequency in words?

Answer: The percent of a column category that falls in a row category. Given the column, what percent is in this row.

Flashcard 25: Compute $P(\text{chores}|\text{curfew})$: chores and curfew $=24$, curfew total $=40$.

Answer: $\frac{24}{40}=0.6$. Divide joint count by curfew total.

Flashcard 26: What is the meaning of a row relative frequency in words?

Answer: The percent of a row category that falls in a column category. Given the row, what percent is in this column.

Flashcard 27: Which comparison tests if curfew is associated with chores: $P(\text{chores}|\text{curfew})$ vs $P(\text{chores}|\text{no curfew})$?

Answer: Compare $P(\text{chores}|\text{curfew})$ and $P(\text{chores}|\text{no curfew})$. Compares chore rates between curfew groups.

Flashcard 28: Find the row relative frequency: cell $=18$, row total $=30$.

Answer: $\frac{18}{30}=0.6$. Divide cell count by row total.

Flashcard 29: What is a column total (marginal frequency) in a two-way table?

Answer: The total count down a column for one category. Sums all values in that column.

Flashcard 30: What is a relative frequency in a two-way table?

Answer: A proportion: rac{\text{part}}{\text{whole}}. Converts counts to proportions for comparison.