Two-way Tables Worksheet Answer Key – Grade 8

Problem 1 Find the totals

Row totals: 18 + 12 = 30 and 14 + 26 = 40.

Column totals: 18 + 14 = 32 and 12 + 26 = 38.

Grand total: 30 + 40 = 70.

Rows 30 and 40; columns 32 and 38; total 70

Problem 2 Read one cell

Find the row for pet owners and the column for students who like hiking.

18 students

Problem 3 Marginal count

Add the column: 12 + 26 = 38.

38 students

Problem 4 From a list to a table

Count each pair: (Y, Y) appears 3 times, (Y, N) 3 times, (N, Y) once, and (N, N) 3 times.

3, 3, 1, 3 with row totals 6 and 4 and column totals 4 and 6

Problem 5 Share of the whole

18 ÷ 70 ≈ 0.2571.

About 25.7%

Problem 6 Row percents

Pet owners: 18 ÷ 30 = 60% like hiking and 12 ÷ 30 = 40% do not.

No pet: 14 ÷ 40 = 35% like hiking and 26 ÷ 40 = 65% do not.

Pet owners: 60% and 40%; no pet: 35% and 65%

Problem 7 Column percents

Likes hiking (total 32): 18 ÷ 32 = 56.25% and 14 ÷ 32 = 43.75%.

Does not like hiking (total 38): 12 ÷ 38 ≈ 31.6% and 26 ÷ 38 ≈ 68.4%.

Likes hiking: 56.3% and 43.8%; does not: 31.6% and 68.4%

Problem 8 Row percents from a table

7th grade: 21 ÷ 50 = 42% and 29 ÷ 50 = 58%.

8th grade: 33 ÷ 50 = 66% and 17 ÷ 50 = 34%.

7th: 42% soccer, 58% basketball; 8th: 66% soccer, 34% basketball

Problem 9 Compare the groups

Soccer is chosen by 66% of eighth graders and 42% of seventh graders, a gap of 24 percentage points.

Eighth graders; yes, grade and favorite sport appear to be associated

Problem 10 Read the bars

The streaming share is 80% for the younger group and 45% for the older group. The percents differ a lot.

Yes, there is an association: younger people are more likely to use streaming

Problem 11 Missing entries

Row 1: 40 − 25 = 15. Row 2: 50 − 20 = 30.

Column totals: 25 + 30 = 55 and 15 + 20 = 35. Check: 55 + 35 = 90.

Blanks 15 and 30; column totals 55 and 35

Problem 12 A table with no pattern

Plays games: 17 ÷ 24 ≈ 71% passed and 7 ÷ 24 ≈ 29% did not.

Does not play: 11 ÷ 16 ≈ 69% passed and 5 ÷ 16 ≈ 31% did not.

The rows are almost the same (71% and 69%), so there is little or no association

Problem 13 Explain a percent

A row relative frequency divides by the row total, so it compares within the group of eighth graders.

60% of the eighth graders in the survey bring a bag lunch

Problem 14 Big and small groups

Seventh graders: 54 ÷ 300 = 18%. Eighth graders: 36 ÷ 150 = 24%.

Although most members are seventh graders, they are a much bigger group.

Eighth graders are more likely to join (24% versus 18%)

Problem 15 Three grades

Sixth: 18 ÷ 60 = 30%. Seventh: 22 ÷ 60 ≈ 36.7%. Eighth: 35 ÷ 60 ≈ 58.3%.

The percent who walk rises with grade (30%, 36.7%, 58.3%), so older students are more likely to walk

Problem 16 Chess and math

Members: 9 qualified, 3 did not. Non-members: 7 qualified, 21 did not. Totals: 16 qualified, 24 did not, 40 students.

Members: 9 ÷ 12 = 75%. Non-members: 7 ÷ 28 = 25%.

75% versus 25%: club members are much more likely to qualify, a strong association

Problem 17 Tea or coffee

Adults: 0.60 · 200 = 120. Tea: 0.25 · 120 = 30; coffee: 90.

Children: 75% of 80 = 60 prefer tea; 20 prefer coffee.

Adults: 30 tea, 90 coffee; children: 60 tea, 20 coffee. Children prefer tea far more often (75% versus 25%), so age group and drink are associated

Problem 18 Check a claim

40 of 70 members are eighth graders, about 57.1%, but that compares members with each other.

Row percents: eighth grade 40 ÷ 200 = 20%; seventh grade 30 ÷ 100 = 30%.

Mia is not right: seventh graders are more likely to join (30% versus 20%)

Problem 19 Smartwatches

Under 30: 105 ÷ 150 = 70%. 30 or older: 100 ÷ 250 = 40%.

Overall: (105 + 100) ÷ 400 = 205 ÷ 400 = 51.25%.

70% and 40%; overall about 51.3%; younger people are more likely to own a smartwatch

Problem 20 Which percent?

Compare the honor-roll percent within each group, which means row relative frequencies when the rows are the sports groups.

In sports: 36 ÷ 90 = 40%. Not in sports: 24 ÷ 110 ≈ 21.8%.

Compare 40% and 21.8%; students in sports are more likely to be on the honor roll