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17 Jul 2020, 20:06
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VeritasKarishma
Hi VeritasKarishma - if i understand your method, it is
Whenever you add a new number to a set -- check how far this new number (in this case 100) is to the pre-existing mean to compare how much the SD will change.
Question : When you add a new number to the set (Set A / Set B or Set C), won't all of them have new averages ?
Thus, shouldn't you be re-calculating all of the absolute distances from this new mean (post addition of 100) to determine the change in SD ? It's quite possible that this new mean may be closer to other elements in the set
Yes, the mean will change when we add a number (if we do not add it at the mean) but the impact of one number on the mean will be little (assuming a big set of numbers).
Say we add the number at the mean - then mean doesn't change, there is no extra dispersion of data, but the number of observations increases so SD will actually reduce.
If we add a number far away from the mean, the mean will change slightly, a lot of extra dispersion will be added and the number of observations will increase by 1. Overall impact would be increased mean.
Check out this video: https://youtu.be/0E6FQMzQVj0
GMAT will not give you a situation in which you cannot differentiate appropriately without calculating.
28 Oct 2024, 02:52
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KarishmaB
Notice that the denominator in the calculation of SD will be the same in the case of all the 3 sets (since they all have 5 elements each). When you add 100 to each one of them, they will have 6 elements each and hence the denominator will still stay the same.
In case of set B, the numerator increases by 100^2 (before you take the root)
In case of set C, the numerator increases by 60^2 (before you take the root)
In case of set A, the numerator increases by 30^2 (before you take the root)
So in absolute terms, B will see the most effect and A will see the least. You can look at the actual calculation to understand exactly why this happens. The formula for SD is discussed in the first post below.[/quote]
