Cross
Use rows for one category and columns for another, so each inside cell names one exact subgroup.
Lesson 2.2 · Simple Statistics
Build and Check Two-Way Tables
A two-way table crosses two kinds of information. Each inside cell answers two questions at once—and every total can help check the others.
Cross the categories. Add across. Add down. Meet at the grand total.
Total
Add across rows and down columns to find row totals, column totals, and the grand total. These totals at the edges of a table are called margins.
Check
Confirm that row totals and column totals reach the same grand total—and investigate when they do not.
two-way table
row
column
cell
row total
column total
grand total
1
The table’s map · Two questions at once
Cross two categories
In the book’s combined table, the rows describe gender and the columns describe school teams. An inside cell belongs to one row and one column. Each number counts memberships in one team. If a student belongs to two teams, that student appears in two cells. Adding across teams therefore counts memberships, not necessarily different students.
Which kind of information labels the rows on the left?
Which kind of information labels the columns across the top?
| TeamGender | Choir | Orchestra | Dance |
|---|---|---|---|
| Boys | |||
| Girls |
2
Book Example 3
Transfer the six inside counts
The worked example gives three separate team tables. Move the boys’ and girls’ counts into one larger table. Do not calculate yet—this step is about placing each fact at the correct intersection.
Choir
| Total | 52 |
|---|---|
| Boys | 23 |
| Girls | 29 |
Orchestra
| Total | 59 |
|---|---|
| Boys | 32 |
| Girls | 27 |
Dance
| Total | 38 |
|---|---|
| Boys | 15 |
| Girls | 23 |
| TeamGender | Choir | Orchestra | Dance |
|---|---|---|---|
| Boys | |||
| Girls |
3
Column totals · Add down
Check each team total
A column keeps the team fixed while the gender changes. Add boys and girls down each team column and compare with the total printed in its small original table.
Choir
23 + 29 =
Orchestra
32 + 27 =
Dance
15 + 23 =
Column question: “How many people are in this team altogether?” Keep the column fixed; combine its rows.
4
Row totals · Add across
Build the gender totals and grand total
A row keeps the gender fixed while the team changes. Add across the row, then combine the two row totals.
Boys
23 + 32 + 15 =
Girls
29 + 27 + 23 =
All team memberships
boys total + girls total =
5
The double-entry check · Two paths, one total
Make the totals meet
The grand total can be reached by adding the team columns or by adding the gender rows. Both paths must arrive at the same number because they add the same six inside cells. Matching totals are a useful check, but cannot prove that every copied count is correct: two errors could cancel each other out. Compare the inside cells with the original counts too.
Add team totals
52 + 59 + 38
Add gender totals
70 + 79
Why is this useful?
6
Read before calculating · Follow row and column labels
Interrogate the completed table
Point to a number, tap it, or focus it with the Tab key to highlight its row and column. Then answer four questions that use cells, row totals, column totals, and comparisons.
| TeamGender | Total | Choir | Orchestra | Dance |
|---|---|---|---|---|
| Total | 149 | 52 | 59 | 38 |
| Boys | 70 | 23 | 32 | 15 |
| Girls | 79 | 29 | 27 | 23 |
1. Girls in dance
How many girls are in the dance team? Enter the number in that cell.
2. All boys
How many team memberships are held by boys across the three teams?
3. Compare gender totals
How many more team memberships are held by girls than by boys?
4. Largest team
Which team has the largest column total?
7
Error Detective · Totals are clues, not decorations
Find the entry that breaks two checks
A student copied one inside value incorrectly. The printed row and column totals are correct. Use both a row and a column to locate the suspicious cell.
| Gender / Team | Total | Choir | Orchestra | Dance |
|---|---|---|---|---|
| Total | 149 | 52 | 59 | 38 |
| Boys | 70 | 23 | 32 | 15 |
| Girls | 79 | 29 | 29 | 23 |
Which intersection is suspicious?
What should its value be?
Which checks expose the error?
8
Book Exercise 7 · Turn prose into a table
Build the extracurricular-activity table
The six given counts are displayed below. First place those facts inside the table. Then calculate row and column totals and compare the three groups. The grand total counts activity memberships; a student in two groups counts once in each group.
Sports
Boys98
Girls80
Arts
Boys120
Girls180
Technology
Boys144
Girls78
| Gender / Group | Total | Sports | Arts | Technology |
|---|---|---|---|---|
| Total | ||||
| Boys | ||||
| Girls |
Largest group
Smallest group
9
Book Exercise 11 · Read a second two-way table
Sports-event table lab
The worked example lists boys’ and girls’ entries in five events. It asks students to make a graph; here we first use the same table to practice row totals, column totals, and careful interpretation.
| Gender / Event | 800 m | Jump rope | High jump | Throwing | 60 m | Row total |
|---|---|---|---|---|---|---|
| Boys | 8 | 7 | 5 | 6 | 4 | |
| Girls | 6 | 9 | 4 | 3 | 6 | |
| Column total |
Careful with meaning: adding all cells gives the number of event entries. The worked example does not say that each student entered exactly one event, so the table alone does not prove that there were 58 different students.
What can the grand total safely mean?
| Gender / Club | Total | Chess | Art | Coding |
|---|---|---|---|---|
| Total | 30 | 9 | 12 | 9 |
| Boys | 15 | 6 | 4 | 5 |
| Girls | 15 | 3 | 8 | 4 |
Solved: 0 of 6. Reach 4 to pass the workshop.
10
Mastery check · Work without lesson hints
Exit Ticket
Earn at least 4 of 5 to unlock the Two-Way Table Architect certificate.
1. Interpret a cell
In the school-team table used in Missions 1–7, what does the inside count 32 mean?
2. Row total
Girls: 29 choir, 27 orchestra, 23 dance. Find the row total.
3. Grand total
Add the worked example team totals: 52 + 59 + 38.
4. Exercise 7 column total
Arts has 120 boys and 180 girls. Find its total.
5. Explain the double check
How can adding across rows and down columns help you detect an error?
Part A. What should happen when you add all row totals and when you add all column totals?
Part B. What does it mean if the two grand totals do not match?
Question 5 is scored from Parts A and B. The optional explanation is for reflection or teacher/parent review.
Mastery result
Certificate of Mastery
Two-Way Table Architect
This certifies that
can cross categories, build row and column totals, read intersections, and use a two-direction check to find errors.
Add across = Add down = Grand total