Compare two data sets in one graph

2.MD.D.103.MD.B.3 · take · grade 3

Archetype: Read and Scale a Data Graph · step in a 21-type progression

The number of students in each group of Ethan's class was surveyed and shown in a graph. Find the total number of students in the group where the difference between the number of girls and the number of boys is the greatest.

The graph is titled "Number of students by group." The horizontal axis shows the groups $1$ , $2$ , $3$ , and $4$ , and the vertical axis shows the number of students from $1$ to $5$ . For each group, the open circles ○ (girls) and the filled circles ● (boys) are stacked separately.

Group $1$ : girls (○) $3$ , boys (●) $4$
Group $2$ : girls (○) $3$ , boys (●) $3$
Group $3$ : girls (○) $3$ , boys (●) $1$
Group $4$ : girls (○) $2$ , boys (●) $5$

Show solution

Understand

A graph shows the number of girls and boys in each of four groups. Find the group where the gap between girls and boys is the largest, then report the total number of students in that group.

Givens

Group 1: 3 girls, 4 boys.
Group 2: 3 girls, 3 boys.
Group 3: 3 girls, 1 boy.
Group 4: 2 girls, 5 boys.

Unknowns

The total number of students in the group with the greatest difference between girls and boys.

Constraints

The difference is how many more of one group there are than the other (a non-negative number).
The total of a group is girls plus boys.

Plan

#2 Make a Systematic List · also uses: #7 Identify Subproblems

There are only four groups, so I list each group's girl-boy difference one at a time (a subproblem per group), pick the biggest difference, then add that group's girls and boys for the total.

Execute

#2 Make a Systematic List 2.MD.D.10

For each group subtract the smaller count from the larger: Group 1 is 4-3=1, Group 2 is 3-3=0, Group 3 is 3-1=2, Group 4 is 5-2=3.

4-3=1,\ 3-3=0,\ 3-1=2,\ 5-2=3

Reading two stacked columns per group from the graph lets you compare girls and boys directly by subtracting.

#7 Identify Subproblems 3.MD.B.3

Comparing the four differences 1, 0, 2, 3, the largest is 3, which belongs to Group 4.

\max(1,0,2,3)=3

Interpreting the graph means comparing the bars; the tallest gap wins.

#7 Identify Subproblems 2.MD.D.10

Group 4 has 2 girls and 5 boys, so its total is 2+5=7 students.

2+5=7

The total of a group is just the two columns added together.

Answer: 7 students

Review

Each group has at most 5+3=8 students, and 7 fits within that range. Group 4 indeed has the most lopsided split (5 vs 2), matching the largest difference.

You could read off both columns for every group, write each total and each difference in a small two-column table, and scan the difference column for its maximum.

Standards · min grade 3

2.MD.D.10 Draw and interpret picture graphs and bar graphs — Reading each group's girl and boy counts from the stacked graph.
3.MD.B.3 Draw and interpret scaled picture graphs and bar graphs — Comparing the differences across groups to find the greatest one.

💡 Just read each pair off the graph, subtract to find the biggest gap, then add that pair up!