Two-Way Tables — Practice
Two yes-or-no questions, four boxes, and a set of totals that must agree. Then turn counts into percentages.
What these questions cover
These questions use 3 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Percent — Parts per hundred. 37% = 37100 = 0.37.
- Association — A pattern linking the two variables.
- Two-way table — A table of counts sorted by two categorical variables at once.
Problem 1
A table has row totals 18 and 22. Find the grand total.
Worked answer
40
18 + 22 = 40
Problem 2
A row totals 30 and one cell in it is 11. Find the other cell.
Worked answer
19
30 - 11 = 19
Problem 3
In a table, 14 of 50 students walk to school. What percent walk?
Worked answer
28
1450 = 0.28
28%
Problem 4
A column totals 25 and holds cells 9 and x. Find x.
Worked answer
16
25 - 9 = 16
Problem 5
A table records 12 students who both bike and bring lunch. This count is called
Worked answer
a joint frequency
Inner cells are joint frequencies
Row and column totals are marginal
Problem 6
Of 40 walkers, 16 bring lunch. What percent of walkers bring lunch?
Worked answer
40
1640 = 0.4
40%
Problem 7
Of the 25 lunch-bringers, 16 walk. What percent of lunch-bringers walk?
Worked answer
64
1625 = 0.64
64%
Same cell, different denominator
Problem 8
60 people: 35 own a dog, 20 of those also own a cat, and 30 own a cat altogether. How many own neither?
Worked answer
15
Dog only: 35 - 20 = 15
Cat only: 30 - 20 = 10
At least one: 20 + 15 + 10 = 45
Neither: 60 - 45 = 15
Problem 9
The four inner cells of a table are x, 17, 23 and 12, with a grand total of 70. Find x.
Worked answer
18
x + 17 + 23 + 12 = 70
x + 52 = 70
x = 18
Problem 10
20 of 40 boys and 24 of 60 girls joined the club. Which is true?
- A larger share of boys joined
- A larger share of girls joined
- The shares are equal
- More boys joined than girls
Worked answer
A larger share of boys joined
Boys: 2040 = 50%
Girls: 2460 = 40%
So a larger share of boys
Problem 11
45 of 180 surveyed prefer tea. What percent is that?
Worked answer
25
45180 = 0.25
25%
Problem 12
In a two-way table, the total at the end of a row is called
Worked answer
a marginal frequency
Row and column totals are marginal frequencies
Problem 13
80 students: 48 take Spanish, 30 take art, 18 take both. How many take neither?
Worked answer
20
Spanish only: 48 - 18 = 30
Art only: 30 - 18 = 12
At least one: 18 + 30 + 12 = 60
Neither: 80 - 60 = 20
Problem 14
30 of 50 athletes and 18 of 60 non-athletes eat breakfast. Is there an association? Answer yes or no.
Worked answer
yes
Athletes: 3050 = 60%
Non-athletes: 1860 = 30%
A 30-point gap, so yes
Problem 15
In a table, 21 of the 28 people in a row answered yes. What percent of that row said no?
Worked answer
25
No: 28 - 21 = 7
728 = 0.25
25%
Problem 16
A table shows: total 150; 90 are female; 60 of the males said yes; 110 said yes altogether. How many females said no?
Worked answer
40
Males: 150 - 90 = 60
All 60 males said yes
Females who said yes: 110 - 60 = 50
Females who said no: 90 - 50 = 40