We are asked for the value closest to the average (arithmetic mean) of the 9 changes in the value of imports between consecutive years from 2000 to
2009.

This essentially means Yr 1–Yr 0 + Yr 2–Yr 1... + Yr 9–Yr 8.

Notice how all terms with the exception of Yr 0 and Yr 9 will cancel. This leaves us with 9–3.2/9 => 0.644bar*1000≈ 644 million.

Closest to this is E, 640 million.

Solution

Now the object is to find the average of 9 changes from 2000 to 2009. Which can also be defined as average change between 2000 to 2009.

So in year 2000: $3.3 Billion

and year 2009: $9 Billion.

Average change per year = \(\frac{($9 - $3.3)}{9}\) = $640 million Approx
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Hi, I was under the impression that we need to find the difference for each pair of consecutive years and then take the average of the 9 values, where does it mention that we have to only take the overall aggregate and not of each individual year difference?

Hi

if you read the stem, it is pretty clear.

I do not see any sort of pitfall.

Regards
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It mentions the average of the 9 changes in the imports values, so isn't the 9 differences to be taken into consideration? Then the average of these differences is asked, so we have to get the average of the differences in the import values between 2 consecutive years in the 2000 - 2009 decade period.
I am sorry, I am really confused because my interpretation of the question was this and I admit, this approach is much more convoluted and time consuming, but I am having a hard time in interpreting the question to get the answer specified, for the overall aggregate of the endpoint years 2000 and 2009, and not to consider the years within the range.

If you average out all 9 of the changes, you also get E for the answer. In my statistics courses I was told that this can be a more accurate way of calculating but it may not always be necessary. When I approximated the changes and took the average, I got around 700 million, which is closest to E.

This is a consecutive years series so we can use the formula (last - first) / 2. Can someone confirm if I am right?
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I'm guessing that because there are 9 values between the first and last, you need to divide by 9, not 2.

In a consecutive series we can use first+last/2 to get the average. This however isn't the case here since the values of the changes are not in a consecutive series.

The wording of the question is confusing.
It appears that the test maker got us by mentioning all "9 values" but had given a concession by saying approx.

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This is not a right way to solve the question.
Question states that we have to calculate the arithmetic mean (average) of changes in 9 years from 2000 to 2009.

2000-2001: 2.6 - 3.2= -0.6B
2001-2002: 3.2 - 2.6 = 0.6B
2002-2003: 3.9 - 3.2 = 0.7B
2003-2004: 4.0 - 3.9 = 0.1B
2004-2005: 5.0 - 4.0 = 1.0B
2005-2006: 5.9 - 5.0 = 0.9B
2006-2007: 7.0 - 5.9 = 1.1B
2007-2008: 5.0 - 7.0 = -2.0B
2008-2009: 9.0 - 5.0 = 4.0B

Now taking average of these changes:

mean = ( -0.6 + 0.6 + 0.7 + 0.1 + 1.0 + 0.9 + 1.1 - 2.0 + 4.0 ) / 9

= 0.644 B
= 644 M (close to 640 M)

So correct option is E.

Regards, Hamza Sharif

this indeed means [(2001-2000)+(2002-2001)+(2003-2002)+(2004-2003)+(2005-2004)+(2006-2005)+(2007-2006)+(2008-2007)+(2009-2008)]/9
but you will find out that numbers relating to 2001 to 2008 are all cancelled, leaving only (2009-2001)/9

if the term consecutive is mention, apply the simple formula = (final value-initial value)/(total no of terms-1).
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Why doesn't average of changes mean the average of "absolute changes"?
at this point: no year will be cancelled out.