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23 Feb 2016, 15:17
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Say set A is (1,2,3) and set B is (1,2,2,3) is the standard deviation the same?
Say Set C is (1, 5, 6) and say Set D is (1, 5, 5, 6) is the standard deviation the same in set C and D?
Say Set C is (1, 5, 6) and say Set D is (1, 5, 5, 6) is the standard deviation the same in set C and D?
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23 Feb 2016, 20:03
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jasonfodor
No the standard deviation for both of these will not be the same.
In general standard deviation is the square root of sum of squares of the distance of the terms from the mean.
In these sets, the mean is different and so is the distance of elements from the mean.
24 Feb 2016, 21:26
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A good general rule of thumb is that the closer the elements of the set are to that set's mean, on average, the lower the standard deviation. When you go from {1,2,3} to {1,2,2,3} you're adding a fourth element that's exactly on the mean, which makes the average distance from the mean lower. When you go from {1,2,3} to {1,2,2,2,2,2,2,2,2,2,2...,2,2,2,3}, almost all of the elements are equal to the mean, and there are a lot of elements, so the average distance from the mean is very low. So, the standard deviation is very small.
Mathematically, this happens because the standard deviation formula includes an 'average' step - to find the standard deviation, you average the squared distances from the mean over all of the data points. It might be worthwhile to practice a bit with the actual standard deviation formula (although you probably shouldn't use it on the GMAT), just to get a feeling for what happens when the set changes in different ways.
Mathematically, this happens because the standard deviation formula includes an 'average' step - to find the standard deviation, you average the squared distances from the mean over all of the data points. It might be worthwhile to practice a bit with the actual standard deviation formula (although you probably shouldn't use it on the GMAT), just to get a feeling for what happens when the set changes in different ways.
