Video Transcript
The average of four numbers is seven. The average of six other numbers is nine. What is the average of all 10 numbers?
First, let’s think about what the average is. The total of all values divided by the number of values equals the average. For the first average, the total of four numbers divided by four equals seven. Our second average is the total of six numbers divided by six and it equals nine. And we want to take the total of all 10 numbers, divide that by 10 to find our
average. If we combine the total of the four numbers and the total of the six numbers, we will
have the total of 10 numbers. To find the total of the four numbers, we multiply both sides of this equation by
four. Seven times four is 28. This means that the total of the four numbers plus 28. 28 divided by four is seven.
Following the same procedure with our total of six numbers, we multiply both sides of
the equation by six. Nine times six is 54. The total of the six numbers must be 54. 54 divided by six is nine. To find the average of all 10 of these numbers, we add 28 plus 54 and then divide by
10. 28 plus 54 is 82 and 82 divided by 10 is 8.2.
We need to be careful here. When you first read the question, you might be tempted to add seven plus nine
together and then divide that by two, which would give you 16 divided by two and
that’s eight. But this method is incorrect. We must find the total of all of 10 numbers and then divide that by 10. We can’t average these two averages.
The total of all 10 numbers divided by 10 is 8.2.
