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The average (arithmetic mean) population in town X was recor

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The average (arithmetic mean) population in town X was recor [#permalink] New post 29 Aug 2018, 16:29
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The average (arithmetic mean) population in town X was recorded as 22,455 during the years 2000–2010, inclusive. However, an error was later uncovered: the figure for 2009 was erroneously recorded as 22,478, but should have been correctly recorded as 22,500. What was the average population in town X during the years 2000–2010, inclusive, once the error was corrected?

[Reveal] Spoiler: OA
22457

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Re: The average (arithmetic mean) population in town X was recor [#permalink] New post 31 Aug 2018, 20:59
Please tell the method of solving it.
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Re: The average (arithmetic mean) population in town X was recor [#permalink] New post 02 Sep 2018, 05:05
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total sum for 11 year (2000 - 2010) inclusive = 11 * 22455 = X(say)

Now 22478 needs to be replace with 22500 , since their difference is 22

or

X - 22478 + 22500 = Sum after correction

Divide X - 22 by 11 years = 22457.
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Re: The average (arithmetic mean) population in town X was recor [#permalink] New post 15 Oct 2018, 10:15
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22,457. There is a simple shortcut for a change to an average. The figure for 2009 was recorded
as 22,478, but actually should have been recorded as 22,500, meaning 22 people in that year were not
counted. Thus, the sum should have been 22 higher when the average was originally calculated.
2000–2010, inclusive, is 11 years (subtract low from high and then add 1 to count an inclusive list of
consecutive numbers). When taking an average, divide the sum by the number of things being
averaged (in this case, 11). So the shortcut is to take the change to the sum and “spread it out” over all
of the values being averaged by dividing the change by the number of things being averaged.
Divide 22 by 11 to get 2. The average should have been 2 greater. Thus, the correct average for the
11-year period is 22,457.
Alternatively, use the traditional method: 22,455 × 11 years = 247,005, the sum of all 11 years’
recorded populations. Add the 22 uncounted people, making the corrected sum 247,027. Divide by 11
to get the corrected average: 22,457. (Note that while the traditional method is faster to explain, the
shortcut is faster to actually execute!)
Re: The average (arithmetic mean) population in town X was recor   [#permalink] 15 Oct 2018, 10:15
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The average (arithmetic mean) population in town X was recor

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