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

Video Solution

Solution Steps

00:00 Calculate the average of each group and choose the appropriate sign:

00:05 To calculate the average, we need to divide the sum by the number of occurrences

00:32 This is the average, now let's use the same method for the second group

01:02 Let's compare and match the sign

01:09 And this is the solution to the question

Step-by-Step Solution

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 $<$ .