Find Numbers with Mean = 5½: Reverse Average Problem

To solve this problem, we'll evaluate the average (mean) of each group's numbers provided in the options and find out which one equals $5\frac{1}{2}$.

• Step 1: Calculate the mean for each group.

Let's start with the options:

Option 1: $4, 4, 5$

Sum: $4 + 4 + 5 = 13$
Number of terms: 3
Average: $\frac{13}{3} = 4.33$ (not $5\frac{1}{2}$)

Option 2: $2, 9$

Sum: $2 + 9 = 11$
Number of terms: 2
Average: $\frac{11}{2} = 5.5$ (This matches $5\frac{1}{2}$)

Option 3: $4, 5, 6, 9$

Sum: $4 + 5 + 6 + 9 = 24$
Number of terms: 4
Average: $\frac{24}{4} = 6$ (not $5\frac{1}{2}$)

Option 4: $2, 9, 1$

Sum: $2 + 9 + 1 = 12$
Number of terms: 3
Average: $\frac{12}{3} = 4$ (not $5\frac{1}{2}$)

Therefore, the correct choice is the group of numbers $2, 9$. This group has an average of $5\frac{1}{2}$.