Compare Averages: Does 9,0 Equal the Mean of 9,0,0?

To solve this problem, we'll follow these steps:

• Step 1: Calculate the average of each group.
• Step 2: Compare the averages using the appropriate sign.

Now, let's work through each step:

Step 1: The first group is $(9,0)$. To find the average:

$\text{Average of (9,0)} = \frac{9 + 0}{2} = \frac{9}{2} = 4.5$

Step 2: The second group is $(9,0,0)$. To find the average:

$\text{Average of (9,0,0)} = \frac{9 + 0 + 0}{3} = \frac{9}{3} = 3$

Now, we compare the two averages:

$4.5$ compared to $3$.

Since $4.5$ is greater than $3$, we mark the appropriate sign as $\gt$.

Therefore, the solution to the problem is $9,0 \gt 9,0,0$.