Compare Group Averages: Is (5,5,5) = (20,0,0,0)?

To solve this problem, we will follow these steps:

• Step 1: Calculate the average of the first group (5, 5, 5).
• Step 2: Calculate the average of the second group (20, 0, 0, 0).
• Step 3: Compare the two averages to choose the appropriate sign.

Now, let's work through each step:

Step 1: Calculate the average of Group 1.
The sum of Group 1 is $5 + 5 + 5 = 15$.
The number of terms in Group 1 is 3.
Thus, the average of Group 1 is $\frac{15}{3} = 5$.

Step 2: Calculate the average of Group 2.
The sum of Group 2 is $20 + 0 + 0 + 0 = 20$.
The number of terms in Group 2 is 4.
Thus, the average of Group 2 is $\frac{20}{4} = 5$.

Step 3: Compare the averages.
The average of Group 1 is 5, and the average of Group 2 is also 5.
Since the averages are equal, the appropriate mathematical sign is '='.

Therefore, the correct comparison is $5, 5, 5 \stackrel{=}{=} 20, 0, 0, 0$.

The appropriate sign is =.