Calculate Average to Compare: Are (7,8,4,3,6,5) = (3,7,8,5)?

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

• Step 1: Calculate the average of the first group $(7, 8, 4, 3, 6, 5)$.
• Step 2: Calculate the average of the second group $(3, 7, 8, 5)$.
• Step 3: Compare the two averages.

Let's complete each step in detail:

Step 1: Calculate the average of the first group.

The numbers in the first group are $7, 8, 4, 3, 6, 5$. First, find the sum:

$7 + 8 + 4 + 3 + 6 + 5 = 33$.

There are 6 numbers in this group, so the average is:

$\text{Average} = \frac{33}{6} = 5.5$.

Step 2: Calculate the average of the second group.

The numbers in the second group are $3, 7, 8, 5$. First, find the sum:

$3 + 7 + 8 + 5 = 23$.

There are 4 numbers in this group, so the average is:

$\text{Average} = \frac{23}{4} = 5.75$.

Step 3: Compare the two averages.

The average of the first group is $5.5$ and the average of the second group is $5.75$.

Therefore, $5.5$ is less than $5.75$.

We choose the sign $<$ indicating that the average of the first group is less than the average of the second group.

The correct answer is $<$.