Calculate Average Change: Adding 6 to the Sequence 9,6,7,2

To solve this problem, we'll first calculate the average of the original set of numbers and then calculate the average of the new set with the added number. Finally, we compare both averages to see if they differ.

• Step 1: Calculate the average of the original set (9, 6, 7, 2).

First, find the sum of the original numbers:
$9 + 6 + 7 + 2 = 24$

Next, compute the average by dividing the sum by the number of elements:
$\text{Average} = \frac{24}{4} = 6$

• Step 2: Calculate the average of the new set (9, 6, 7, 2, 6).

First, find the sum of the new numbers:
$9 + 6 + 7 + 2 + 6 = 30$

Now, compute the average by dividing the sum by the number of elements:
$\text{Average} = \frac{30}{5} = 6$

• Step 3: Compare the two averages.

Both averages are 6. Therefore, adding the number 6 to the group does not change the average.

Thus, the conclusion is that the average does not change, confirming:

No, the average will not change when adding the number 6 to this set of numbers.