Nee wrote:Hi Ian, Can you please explain how the answer to this question is A ??
hi -
in general, you won't actually need to
calculate standard deviations on this exam, so, if you understand the
properties of the standard deviation, then you should be fine. if that understanding includes a fair amount of memorization, then so be it.
in general:
you can CONCEPTUALIZE standard deviation as the average distance from the mean. this is not quite the way the SD is defined, but, as a conceptual approximation, it will justify all important properties of the standard deviation.
for instance:
* if you
add or subtract the same number to/from all points in a data set, this is like "sliding" the entire set a constant distance up or down the number line. if you do that, then none of the distances within the set (including the mean) will change; therefore,
the standard deviation will not change.
(this is not what is happening in this problem)
* if you
multiply all points in a data set by the same constant, this is like "shrinking" or "expanding" the data set by that factor, as you would with a
pantograph.
if you "shrink" or "expand" the data set in this manner, then ALL of the distances - including those involving the mean - will shrink or expand by the same factor. therefore,
the standard deviation will be multiplied by the same factor.
the latter of these is what is happening in statement (1).
so, the standard deviation will just be 30% less than 10, or 7.
therefore (a)
Ron has been teaching various standardized tests for 20 years.
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