Two-way tables worksheet

Grade 8 math, Common Core 8.SP.A.4. 6 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

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Two-way tables

Grade 8 math, Common Core 8.SP.A.4

Use each two-way table to answer the question. Round percents to the nearest whole percent.

1.
Fill in the missing numbers (?) in the table.
Likes math Doesn’t like math Total
Plays an instrument 38 ? 78
Doesn’t play ? 26 42
Total 54 66 ?
2.
What percent of the students who skipped breakfast felt tired?
Felt rested Felt tired Total
Ate breakfast 17 9 26
Skipped breakfast 28 15 43
Total 45 24 69
3.
Of the students who felt tired, what fraction ate breakfast?
Felt rested Felt tired Total
Ate breakfast 9 19 28
Skipped breakfast 36 30 66
Total 45 49 94
4.
Is there an association between eating breakfast and feeling rested? Compare the row percents.
Felt rested Felt tired Total
Ate breakfast 22 9 31
Skipped breakfast 11 36 47
Total 33 45 78
5.
Fill in the missing numbers (?) in the table.
Likes math Doesn’t like math Total
Plays an instrument 35 33 ?
Doesn’t play 18 ? 44
Total ? 59 112
6.
What percent of the students with a pet walk to school?
Walks to school Rides to school Total
Has a pet 23 15 38
No pet 12 38 50
Total 35 53 88

	Likes math	Doesn’t like math	Total
Plays an instrument	38	?	78
Doesn’t play	?	26	42
Total	54	66	?

	Felt rested	Felt tired	Total
Ate breakfast	17	9	26
Skipped breakfast	28	15	43
Total	45	24	69

	Felt rested	Felt tired	Total
Ate breakfast	9	19	28
Skipped breakfast	36	30	66
Total	45	49	94

	Felt rested	Felt tired	Total
Ate breakfast	22	9	31
Skipped breakfast	11	36	47
Total	33	45	78

	Likes math	Doesn’t like math	Total
Plays an instrument	35	33	?
Doesn’t play	18	?	44
Total	?	59	112

	Walks to school	Rides to school	Total
Has a pet	23	15	38
No pet	12	38	50
Total	35	53	88

Answer key: Two-way tables

Grade 8 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. Plays an instrument and Doesn’t like math: 40. Doesn’t play and Likes math: 16. Grand total: 120
78 − 38 = 4054 − 38 = 1678 + 42 = 120
2. 35%
15 ÷ 43 ≈ 0.349
3. 1949
19 out of 49
4. Yes. 71% of the students who ate breakfast felt rested, but only 23% of the students who skipped breakfast did.
22 ÷ 31 ≈ 71%11 ÷ 47 ≈ 23%
5. Doesn’t play and Doesn’t like math: 26. Plays an instrument total: 68. Likes math total: 53
44 − 18 = 2635 + 33 = 6835 + 18 = 53
6. 61%
23 ÷ 38 ≈ 0.605

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About two-way tables

A two-way table counts data in two categories at once, like grade and favorite sport. Each cell counts the data that fits both its row and its column, and the totals are at the ends. Divide a cell by its row or column total to find a relative frequency, which helps you spot an association between the two categories.

Worked example 1

What percent of the 8th graders chose soccer?

	Soccer	Basketball	Total
Grade 7	12	8	20
Grade 8	31	10	41
Total	43	18	61

Step 1.31 ÷ 41 ≈ 0.756

Answer: 76%

Worked example 2

Of the students who chose basketball, what fraction are 8th graders?

	Soccer	Basketball	Total
Grade 7	20	29	49
Grade 8	15	21	36
Total	35	50	85

Step 1.21 out of 50

Answer: 2150

Worked example 3

Is there an association between playing an instrument and liking math? Compare the row percents.

	Likes math	Doesn’t like math	Total
Plays an instrument	37	17	54
Doesn’t play	33	14	47
Total	70	31	101

Step 1.37 ÷ 54 ≈ 69%
Step 2.33 ÷ 47 ≈ 70%

Answer: No. 69% of the students who play an instrument and 70% of the students who don’t play an instrument like math, which is about the same.

Watch out for

Read the question carefully: “of the 8th graders” means divide by the 8th grade row total.
Check that the row totals and column totals add up to the same grand total.
Relative frequencies can be written as fractions, decimals or percents.

Practice two-way tables online

On StudyWiz, your kid can practice two-way tables with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

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