Compare Averages: Determining if 4,4,4,4 Equals 1,4,5,7

To solve this problem, we'll calculate the average of each group and compare them.

• Step 1: Calculate the average of the first group $4, 4, 4, 4$:
  $\text{Sum of Group A} = 4 + 4 + 4 + 4 = 16$
  $\text{Number of elements in Group A} = 4$
  $\text{Average of Group A} = \frac{16}{4} = 4$
• Step 2: Calculate the average of the second group $1, 4, 5, 7$:
  $\text{Sum of Group B} = 1 + 4 + 5 + 7 = 17$
  $\text{Number of elements in Group B} = 4$
  $\text{Average of Group B} = \frac{17}{4} = 4.25$
• Step 3: Compare the two averages:
  $\text{Average of Group A} = 4$
  $\text{Average of Group B} = 4.25$
  Since $4 < 4.25$, the correct inequality is $4 < 4.25$.

Therefore, the appropriate sign to use is $<$.