8th grade · Math · Unit 17 of 17
Two-Way Tables
Data in rows and columns
What your child practices
Reading two-way tables of survey data, finding relative frequencies (percents) in a row, and deciding whether two things seem to be linked.
Arizona Academic Standards learning standard: 8.SP.A.4 · looking for patterns of association in two-way tables of categorical data
How we explain it
Children can open this short lesson before they practice.
- A two-way table sorts data by two questions at once.
- Find a row, then read across to the column.
- Compare row percents to look for an association.
Example: 20 students play sports; 15 of them have a pet. What percent of them have a pet? 15 ÷ 20 = 0.75. 0.75 = 75%. Answer: 75%
Two-Way Tables in Arizona
In the Arizona Academic Standards, this is unit 17 of 17 in 8th grade Math, after Slope & Rate of Change.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Source: Arizona Department of Education
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
How many in all are "Felt rested"?
Morning survey Felt rested Felt tired Total Ate breakfast 28 22 50 No breakfast 15 10 25 Total ? 32 75 - 44
- 28
- 50
- 43
43
Hint: Add down the column.
Question 2
Compare the percent of each row that is "Has a pet". Is there evidence of an association?
Sports and pets Has a pet No pet Total Plays sports 45 5 50 No sports 14 26 40 Total 59 31 90 - Not much, the percents are close
- You can't tell from a two-way table
- Yes, the percents are very different
Yes, the percents are very different
Hint: Plays sports: 90%. No sports: 35%.
Question 3
How many in the "No sports" row are in the "No pet" column?
Sports and pets Has a pet No pet Total Plays sports 3 47 50 No sports 18 7 25 Total 21 54 75 - 7
- 18
- 47
- 25
7
Hint: Find the row, then move across to the column.
Question 4
What percent of the "Grade 8" row are "Walks to school"?
Getting to school Walks to school Rides to school Total Grade 8 2 48 50 Grade 9 17 3 20 Total 19 51 70 - 14%
- 10.5%
- 2.9%
- 4%
4%
Hint: 2 out of 50 = 2 ÷ 50 × 100.
Question 5
How many in the "Doesn't like reading" row are in the "No library card" column?
Reading survey Has a library card No library card Total Likes reading 7 13 20 Doesn't like reading 9 11 20 Total 16 24 40 - 9
- 20
- 13
- 11
11
Hint: Find the row, then move across to the column.
Question 6
What percent of the "Ate breakfast" row are "Felt rested"?
Morning survey Felt rested Felt tired Total Ate breakfast 31 19 50 No breakfast 28 12 40 Total 59 31 90 - 34.4%
- 52.5%
- 62%
- 72%
62%
Hint: 31 out of 50 = 31 ÷ 50 × 100.