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9 changes in the value of imports between consecutive

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9 changes in the value of imports between consecutive [#permalink] New post 10 Jan 2016, 15:49
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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 ?

A $260 million
B $320 million
C $400 million
D $480 million
E $640 million


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Page: 163
Difficulty: medium
[Reveal] Spoiler: OA

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Re: 9 changes in the value of imports between consecutive [#permalink] New post 10 Jan 2016, 16:16
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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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Re: 9 changes in the value of imports between consecutive [#permalink] New post 25 Apr 2020, 09:16
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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?
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Re: 9 changes in the value of imports between consecutive [#permalink] New post 25 Apr 2020, 09:35
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Hi

if you read the stem, it is pretty clear.

I do not see any sort of pitfall.

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Re: 9 changes in the value of imports between consecutive [#permalink] New post 25 Apr 2020, 10:58
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Quote:
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 ?

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.
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Re: 9 changes in the value of imports between consecutive [#permalink] New post 25 Apr 2020, 19:32
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Zohair123 wrote:
Quote:
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 ?

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.
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Re: 9 changes in the value of imports between consecutive [#permalink] New post 07 May 2020, 12:48
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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Re: 9 changes in the value of imports between consecutive [#permalink] New post 07 May 2020, 13:23
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Farina wrote:
This is a consecutive years series so we can use the formula (last - first) / 2. Can someone confirm if I am right?



I'm guessing that because there are 9 values between the first and last, you need to divide by 9, not 2.
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Re: 9 changes in the value of imports between consecutive [#permalink] New post 11 May 2020, 22:33
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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.
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Re: 9 changes in the value of imports between consecutive [#permalink] New post 11 May 2020, 22:35
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Farina wrote:
This is a consecutive years series so we can use the formula (last - first) / 2. Can someone confirm if I am right?


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.
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Re: 9 changes in the value of imports between consecutive [#permalink] New post 23 Jun 2020, 09:05
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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