Data & Graphs

Problem

Compare two data sets in one graph

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.
Number of students by group 1 2 3 4 5 Count Group Group 1 Group 2 Group 3 Group 4 Girls Boys
Measurement & data
Your answer
How to solve
Strategy Make a Systematic List — 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.
1STEP 1

Find each group's difference

Subtract each group's smaller count from its larger: G1 4-3=1, G2 3-3=0, G3 3-1=2, G4 5-2=3.

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

Pick the greatest difference

Among the four gaps 1, 0, 2, 3 the largest is 3, which belongs to Group 4.

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

Total the winning group

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

2+5=7
Answer
7 students
2+5=7
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.
Takeaway

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

  • Find each group's difference
  • Pick the greatest difference
  • Total the winning group
Where next?
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▶ Practice — 8 problems