Question

Fill in the blank with an integer so that the given list has an average of 12.

13, 15, 9, 5, 10, ...

Answer 1

We can use the formula for the average (arithmetic mean) of a set of numbers to solve this problem:

average = (sum of numbers) / (number of numbers)

Let's call the missing number x. Then the sum of the numbers in the list is:

• 13 + 15 + 9 + 5 + 10 + x

We want the average of this list to be 12, so we can set up the following equation:

• 12 = (13 + 15 + 9 + 5 + 10 + x) / 6

Multiplying both sides by 6, we get:

• 72 = 52 + x

Subtracting 52 from both sides, we get:

• x = 20

Therefore, the missing number is 20, and the complete list is:

• 13, 15, 9, 5, 10, 20

The average of this list is:

• average = (13 + 15 + 9 + 5 + 10 + 20) / 6

• average = 72 / 6

• average = 12

So the list now has an average of 12.