8.SP.4: Two-Way Tables
Also written as 8.SP.A.4 and CCSS.MATH.CONTENT.8.SP.A.4 · Cluster: Investigate patterns of association in bivariate data.
The Official Wording
Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
Common Core State Standards, Grade 8, Statistics & Probability · Read it at the source · Checked October 14, 2026
What 8.SP.4 Means in Plain English
Eighth graders sort yes-or-no answers to two questions into a two-way table with row and column totals. Then they compare percentages within rows: 32 of 40 library-card holders read weekly, 80%, against 18 of 60 without a card, 30%. A gap that wide suggests the two answers are linked.
Raw counts mislead when the groups differ in size, which is why relative frequency matters. High school adds joint, marginal and conditional relative frequencies (HSS-ID.5) and uses the same tables to decide whether events are independent (HSS-CP.4).
8.SP.4 I Can Statements
- I can build a two-way table from survey answers.
- I can find row and column relative frequencies as percentages.
- I can use those percentages to judge whether two variables are linked.
8.SP.4 Worked Example
One survey, two yes-or-no questions, and row percentages that show a link the raw counts blur.
A survey asked 100 eighth graders two questions: do you have a library card, and do you read for fun at least once a week? Of the 40 with a card, 32 read weekly. Of the 60 without one, 18 read weekly. Is there evidence that the two are linked?
- Put one question in the rows and the other in the columns, and fill the four cells.Card: 32 read weekly, 8 do not (40). No card: 18 read weekly, 42 do not (60).
- Add the column totals and the grand total, so every student is counted once.Read weekly 50, do not 50; total 100
- Compare within rows, not raw counts: what percent of each row reads weekly?Card: 32 ÷ 40 = 80%. No card: 18 ÷ 60 = 30%.
- Set the two row percentages side by side.80% against 30%: a gap of 50 percentage points
- State the association carefully: the table shows the answers go together, not which one causes the other.Card holders are much more likely to read weekly
Check it: With no association, both rows would match the overall rate, 50 ÷ 100 = 50%. The rows sit at 80% and 30%, far on either side of it.
Common Mistakes with 8.SP.4
Comparing counts instead of percentages
“32 card holders read weekly and 18 others do, so card holders read almost twice as much.”
Try this: Divide by each row total first: 32 of 40 is 80% and 18 of 60 is 30%, so compare 80% with 30%.
Dividing by the grand total
32 ÷ 100 = 32% and 18 ÷ 100 = 18%
Try this: Ask “percent of whom?” before dividing: of the card holders, so the denominator is the row total, 40.
Reading association as cause
“Getting a library card makes students read more.”
Try this: Write “tend to” instead of “makes”: the table shows the answers go together, not which one causes the other.
Where 8.SP.4 Fits
Practice 8.SP.4
Quick Check
- Of 25 students who play an instrument, 15 also sing in the choir. What is that row’s relative frequency?
- In one grade, 12 of 20 bus riders and 12 of 30 walkers buy school lunch. Compare the two groups.
- If 45% of dog owners and 46% of non-owners say they exercise daily, is there evidence of an association?