Which of the following is closest to the average (arithmetic mean) of the 9 changes in the value of imports between consecutive years from 2000 to 2009?
$260 million, $320 million, $400 million, $480 million, $640 million

2 Explanations

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barak rosen

I understood "changes" as absolute difference. Can you advise me how not to do this mistake again?

The question asks us for the average of "the 9 changes in the value of imports between consecutive years from 2000 to 2009." So the questions tells us that we need to look at each of the 9 changes (separately), and then find the average.

If we were simply told to look at the change in the value of imports "from 2000 to 2009," then we we could simply consider these two values (imports in 2009 vs. imports in 2000).

Maybe I didn't explained myself properly. I thought that we should find the average difference, meaning that if it went up by 3 one year, and then went down the next year by 6, then the average of these two years is 4.5. How should I understand that changes in difference direction cancel one another?

Ah, I see what you mean now. In these kinds of situations, keep in mind that increasing by 3 is not the same as decreasing by 3. Those are two very different changes! So we need to note this by saying that a decrease of 3 would be -3, and an increase of 3 would be +3.

If we don't do this, and simply take the absolute value of each change in order to calculate the average change, we would misrepresent the total change between 2000 and 2009.

For example, imagine that we were looking at imports from 2000 to 2002. In 2000 imports were $5 million, in 2001 imports were $0, and in 2002 imports were back at $5 million. The average yearly change for this period is 0. However, if we said that the average change is (5+5)/2 = 5, that would suggest that we started at $5 million in 2000 and ended up at $15 million in 2002.

## 2 Explanations