Anonymous Wrote:Ron, please see the link below where this question has been discussed previously. One of the comments (from Emily) is
http://www.manhattangmat.com/forums/dur ... -t819.htmlHarish, the source of your confusion is your statement "I know that the standard deviation of the sample doesn't change if we add or subtract the same constant value to the sample values." That is only true if all of the samples have the same quantity to begin with (std. dev. = 0)!
The more accurate statement would have been "The standard deviation of the sample changes by a known factor if we add or subtract the same percentage to each of the sample values." If the samples each decrease by 30%, the mean decreases by 30%, and the (X - mean) decreases by 30% for each term. You don't really have to complete the calculation to see that the resulting std. dev. will be smaller than the original 10 by some factor (I believe the result would be 7, but you can check my math).
Applying your explanation and emily's explanation to this, does this mean the option A is sufficient or actually not
Not too clear about the context.
ah, whoa, no, the first statement is incorrect.
here are the correct statements:
* if you
ADD OR SUBTRACT A CONSTANT to/from all the values in a set, then the
standard deviation will remain exactly the same.
visual equivalent: imagine sliding all the data points along a number line, by exactly the same amount, to the right or left. if you do this, then the average spread obviously won't change, because, in fact,
none of the spreads
anywhere in the set changes at all.
this is where the referenced post went wrong: even if you have a set in which the values are wildly different from one another, the standard deviation will not change if a constant is added to or subtracted from all the values.
* if you
INCREASE OR DECREASE ALL THE VALUES BY A FIXED FACTOR / PERCENTAGE, then the
standard deviation will increase or decrease by the same percentage.
visual equivalent: imagine drawing a number line with the set on an elastic band, and stretching or contracting the elastic band to mimic the % increase / decrease applied to the set. if you do this, then the average spread must increase / decrease by the same %, because
all the spreads will increase / decrease by that %.