Two-Way Frequency Tables
A two-way frequency table sorts the same group of people by two categories at once — grade level and favorite pet, gender and favorite sport. Each cell holds a count: the number of people who fit that row and that column at the same time.
Every question about these tables comes down to two skills: finding the cell where a row meets a column, and using the totals to work out a number the table doesn't show. Both are quick once you know where to look.
How the table is built
One category runs across the columns and the other runs down the rows. The cell where the “Boys” row meets the “Tennis” column counts the students who are both — boys who chose tennis.
The last row and last column are usually totals. Each row adds up to its row total, each column adds up to its column total, and the bottom-right corner is the grand total — the number of people surveyed in all. In the table below, grade level runs down the rows and favorite pet runs across the columns, with the totals along the shaded edges.
Reading a cell
To answer “how many 7th graders chose dogs,” put one finger on the “7th grade” row and one on the “Dogs” column. Slide them together — the number where they meet is the answer.
Watch which count the question wants. “How many 7th graders chose dogs” is one cell. “How many students chose dogs” is the whole Dogs column total. “How many 7th graders were surveyed” is the whole row total.
Finding a missing value
Because every row and column adds to its total, one missing cell is always recoverable. Find a row or column that contains the missing cell and has everything else filled in, then subtract the known entries from the total.
If the missing cell sits in a row reading , , , then . Check your answer against the column it sits in — it has to make that total work too.
Worked examples
Example 1: reading one cell
A table sorts students by grade (rows: 6th grade, 7th grade) and favorite pet (columns: Dogs, Cats). The 6th grade row reads , and the 7th grade row reads , . How many 7th graders chose dogs?
Answer: seventh graders chose dogs
Example 2: filling in a missing value
In a table of how students get to school, the “Boys” row shows ride the bus, an unknown number walk, and the row total is . How many boys walk?
Answer: boys walk to school
Example 3: how many were surveyed in all
A table's row totals are sixth graders and seventh graders. How many students were surveyed?
Answer: students were surveyed
Try one yourself
Common questions
How do I know which number the question is asking for?
Count the conditions. Two conditions (“boys who chose tennis”) means one inner cell. One condition (“students who chose tennis”) means a total row or column. No conditions (“students surveyed”) means the grand total in the corner.
What if two cells in the same row are missing?
Use a column instead. A missing cell only needs one line — row or column — where everything else is known. Fill in whichever cells you can, and the new numbers unlock the rest one at a time.
Why don't my row totals match the grand total?
Either an inner cell is wrong or an addition slipped. The built-in check on every two-way table: row totals and column totals must add to the same grand total. If they disagree, redo the smaller sums first.
Is a two-way table the same as a scatter plot?
No. A scatter plot shows two number measurements per person, so it can show a trend. A two-way table counts people in categories — there's no and to trend, just counts to compare.
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