atul.kakkar Wrote:so to summarize, the standard deviation will not change if:
1) You add or subtract a constant to each term
correct.
2) Increase or decrease each term in a set of terms by the same percentage
incorrect. if you do this, then the standard deviation will change by the same percentage.
i.e., if you cut every number in half (a 50% reduction), then the standard deviation will also become half of what it was.
you can see this perhaps most easily on a number line. if you cut all the numbers in half, then all the gaps between the numbers become half their previous size.
standard deviation is essentially a measure of how far away things are from the average. therefore, if you shrink all those gaps by 50%, then the SD will also shrink by 50%.
same goes for shrinking or expanding by any other percentage factor.
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the point of my previous post was that
increasing/decreasing by a PERCENTAGE and increasing/decreasing by a CONSTANT NUMBER are different. the poster to whom i was replying was treating these two things as identical. they aren't.
the difference is further underscored by your question: one of these changes leads to changes in the standard deviation, while the other leaves the standard deviation invariant.