CH-13-001 · Combined means and an unknown group size
Group A contains 17 students and has mean score 35. Group B has mean score 55. The mean score for the two groups together is 50. Find the number of students in group B. Then explain why averaging 35 and 55 does not give the combined mean.
Averages: 'Mean' Mean ("TiMoNe" Table with Algebra)
Booklet p. 10 & p. 56
Method
1) Set up TiMoNe table (Mean | Number | Total) with unknown b in Group B
2) Equate Total_A + Total_B = Combined Mean × (n + b) and solve
Worked Example (CH-13-001)
1)
| Group | Mean | Number | Total |
|---|---|---|---|
| A | 35 | 17 | 595 |
| B | 55 | x | |
| Combined | 50 |
2)
Add totals and numbers, never means: .
3)
4)
The two groups have different numbers of students. The combined mean weights each group by its size, so averaging the two means equally would be wrong.
Ans =
51 students; the groups have different sizes, so their means need different weights.