Representing a Categorical Variable with Tables - AP Statistics

1. Identify the parts of a two-way table.

   Rows, columns, and cells. Rows show one variable's categories, columns show the other's, cells show counts.

2. Calculate the relative frequency for a count of 9 out of 45.

   $0.2$. Divide count by total: $\frac{9}{45} = 0.2$.

3. Calculate the percentage for a category with count 5 out of 25.

   20%. Convert to percentage: $\frac{5}{25} \times 100\% = 20\%$.

4. What does a column in a two-way table represent?

   A category of one of the two variables. Columns organize data by the levels of one categorical variable.

5. What does a cell in a two-way table with 0 indicate?

   No observations for that category combination. Zero means no cases have that particular combination of characteristics.

6. Find the cumulative frequency for counts: 2, 3, 5.

   10. Add frequencies progressively: $2 + 3 + 5 = 10$.

7. What is a cross-tabulation table?

   Another name for a two-way table. Cross-tabulation and two-way tables are identical concepts.

8. Find the percentage of a category with count 10 out of 50.

   20%. Convert to percentage: $\frac{10}{50} \times 100\% = 20\%$.

9. Identify the table type: displays counts for two variables.

   Two-way table. Two-way tables cross-classify observations by two categorical variables.

10. What is a contingency table?

    Another name for a two-way table. Both terms describe tables organizing data by two categorical variables.

11. Which table type includes cumulative frequency?

    Cumulative frequency table. Shows running totals as you move through categories in order.

12. Find the total frequency in a table with counts: 5, 10, 15.

    30. Add all individual counts: $5 + 10 + 15 = 30$.

13. Define conditional distribution.

    Distribution of one variable given a specific condition. Shows how one variable behaves when the other is held constant.

14. What does a total row or column in a two-way table show?

    Marginal totals. These show the overall frequency for each level of one variable.

15. Identify an example of a categorical variable.

    Color of a car. Car color sorts objects into distinct groups like red, blue, green.

16. Which table shows data for one categorical variable?

    Frequency table. Simple frequency tables display one variable's category counts.

17. Calculate the cumulative frequency for 3, 7, 10.

    20. Sum all values: $3 + 7 + 10 = 20$.

18. Find the relative frequency for a count of 15 out of 60.

    $0.25$. Divide count by total: $\frac{15}{60} = 0.25$.

19. What does a two-way table display?

    Counts for combinations of two categorical variables. Shows how two categorical variables relate by displaying joint frequencies.

20. What is a categorical variable?

    A variable that describes categories or groups. These variables classify data into distinct groups rather than measuring quantities.

21. Find the marginal total for a category with counts: 4, 6, 10.

    20. Sum the counts: $4 + 6 + 10 = 20$.

22. What is a frequency table?

    A table showing counts of observations in each category. Displays raw counts for each category of a categorical variable.

23. What is the sum of all cell counts in a table?

    The total number of observations. The grand total represents the entire sample size.

24. Calculate the relative frequency for a count of 8 out of 40.

    $0.2$. Divide count by total: $\frac{8}{40} = 0.2$.

25. Identify the difference between frequency and relative frequency.

    Frequency is count; relative frequency is proportion. Frequency counts observations; relative frequency shows their proportion.

26. How is relative frequency calculated?

    Relative frequency = $\frac{\text{Frequency}}{\text{Total observations}}$. Divide the count in each category by the total number of observations.

27. What type of table shows cumulative totals?

    Cumulative frequency table. Displays running totals that accumulate through ordered categories.

28. What does a contingency table allow you to analyze?

    The relationship between two categorical variables. Shows patterns of association between two categorical variables.

29. What does a row represent in a one-way table?

    A category with its frequency. Each row displays one category and its corresponding count.

30. How is a conditional distribution found in a two-way table?

    By focusing on a row or column's data. Fix one variable and examine how the other varies within that subset.

31. What is a percentage frequency table?

    A table showing percentages for each category. Multiplies relative frequencies by 100 to show data as percentages.

32. Which variable types are best represented by tables?

    Categorical variables. Tables organize categorical data into countable groups or categories.

33. What does each cell in a two-way table represent?

    A count for a specific combination of categories. Each cell shows how many observations have that row-column combination.

34. How are marginal totals used in a two-way table?

    To find the total counts for each variable. Marginal totals show the overall distribution of each variable separately.

35. What type of table shows proportions of counts?

    Relative frequency table. Converts raw counts to proportions of the total sample.

36. What is a relative frequency table?

    A table showing proportions of observations in each category. Shows the fraction or percentage each category represents of the total.

37. What is a marginal distribution?

    Distribution of totals for one variable in a two-way table. Found in the margins by totaling across rows or down columns.

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