A two-way table (contingency table) displays the frequency of data categorized by two different categorical variables simultaneously, with one variable in rows and the other in columns, allowing comparison of distributions across groups.
A two-way table is like a spreadsheet that shows how two questions relate. 'Do you like pizza?' and 'Are you a kid or adult?' becomes a 2×2 grid showing how many kid pizza-lovers, adult pizza-lovers, etc.
Showing a random 20 of 76 problems.
Example 1
medium
100 students were surveyed: 70 play sports; among those, 49 also play music. Among non-sport students, 9 play music. Build the table and find the percent of music players overall.
Example 2
hard
In a 2×2 table, the four conditional row distributions read: Row 1 has 60% Yes, 40% No; Row 2 has 60% Yes, 40% No. Is there an association?
Example 3
medium
A 2×2 table with grand total 200: a=60, b=40, c=30. Find d and the column 2 marginal total.Find d and the column 2 marginal total.
Example 4
easy
In a two-way table, the totals on the bottom and right edges are called what?
Example 5
easy
Boys total 35, Girls total 45, soccer total 45, basketball total 35. What is the grand total?What is the grand total?
Example 6
medium
Movie Genre (Action/Comedy) by Age (Teen/Adult): Teens: 24 Action, 6 Comedy; Adults: 10 Action, 20 Comedy. Among Teens, what percent prefer Comedy?Among Teens, what percent prefer Comedy?
Example 7
easy
A survey records 30 students. The two-way table has rows Kid/Adult and columns Likes Pizza/Dislikes Pizza. Kids: 12 like, 3 dislike. Adults: 9 like, 6 dislike. How many people are in the survey total?Grand total = ?
Example 8
challenge
A table reports that a+ba=0.6 for row 1 and the row-1 total a+b=50. Cell a is also 41 of the grand total. Find the grand total.
Example 9
medium
Table cells: a=18, b=12 (row 1), c=6, d=24 (row 2). What proportion of the data is in cell d (joint relative frequency)?What is the joint relative frequency of cell d?
Example 10
medium
From the Pass/Fail table (Studied-Yes: 28 Pass, 4 Fail; Studied-No: 6 Pass, 12 Fail), what fraction of ALL students both studied and passed?What fraction of ALL students both studied and passed?
Example 11
hard
A two-way table cross-classifies 300 patients by Treatment (A/B) and Outcome (Cured/Not). Treatment A: 90 cured, 30 not. Treatment B: 60 cured, 120 not. Compute the cure rate for each treatment.Compute the cure rate for each treatment.
Example 12
hard
Two variables have joint relative frequency 0.3 in a cell and the row marginal proportion is 0.5. What is the conditional relative frequency within that row?
Example 13
medium
Survey of 80 people by Coffee (Yes/No) and Tea (Yes/No). Coffee-Yes/Tea-Yes =30, Coffee-Yes/Tea-No =20, Coffee-No/Tea-Yes =18, Coffee-No/Tea-No =12. How many drink coffee?How many people drink coffee?
Example 14
medium
In a 2×2 table the row 1 marginal is 40, row 2 is 60, column 1 is 50. If cell a (row 1, col 1) is 25, fill in the rest.Fill in cells b, c, and d.
Example 15
medium
In the same Action/Comedy table, among Adults, what percent prefer Action?Among Adults, what percent prefer Action?
Example 16
medium
If the two categorical variables in a two-way table are independent, conditional distributions of one given the other are all ____.
Example 17
medium
In a 2×3 table, the three column totals are 15, 25, and 20, and one row total is 36. What is the other row total?
Example 18
hard
From a 2×2 table with cells a=18,b=12,c=12,d=8, is there an association between the row and column variables?Is there an association between the row and column variables?
Example 19
medium
Joint distribution: (P(A∩X),P(A∩Y),P(B∩X),P(B∩Y))=(0.25,0.15,0.10,0.50). Find P(A), the marginal probability for row A.
Example 20
easy
Adults: 9 like pizza, 6 dislike. What is the marginal total of Adults?