A combined mean gives each person’s score equal weight. When the groups have different sizes, multiply each group mean by its size to recover the group’s total before combining the scores.
If one group size is missing, call it n. Write the total score in two ways, once by adding the group totals and once by multiplying the combined mean by the combined size.
- Multiply the known group’s mean by its size.
- Use n for the missing group size and include it in the combined size.
- Check that the answer gives the stated combined mean.
Worked example | How many students are in Group B?
Group A has 12 students with a mean score of 60. Group B has a mean of 75. Together their mean is 66. Let n be the number of students in Group B.
Group A contributes 12 × 60 = 720 marks and Group B contributes 75n. The combined total is also 66(12 + n). Therefore 720 + 75n = 792 + 66n. This gives 9n = 72, so Group B has eight students.
Check with the original totals. Group B contributes 8 × 75 = 600 marks. The combined mean is (720 + 600) ÷ 20 = 66.
A second way to see why the answer is eight
Compared with the combined mean of 66, Group A is six marks below per student. That makes 12 × 6 = 72 marks below across the group. Group B is nine marks above per student, so eight students supply the 72 marks needed to balance that difference.
The combined mean is closer to Group A’s mean because Group A has more students. This gives you a quick check on the relative sizes before you solve for n.
Try a smaller group with a lower mean
Group A has 15 students and a mean of 72. Group B has a mean of 52. The combined mean is 67. Find the number of students in Group B.
Answer. Group A is 5 × 15 = 75 marks above the combined mean. Group B is 15 marks below per student, so it has five students.
Frequently asked questions
Can I just average 60 and 75?
The simple mean of the two group means gives each group equal weight. Use that shortcut when the two groups have equal sizes.
What if the reported means were rounded?
Treat the calculation as an estimate unless the question supplies exact totals or enough precision to determine a unique whole-number size.
Official information
SEAB, 2027 SEC G3 Mathematics syllabus (K310), Data Analysis, mean and its uses. Syllabus checked 11 November 2026. The examples are original.