X is the set of n natural numbers (x1,x2.......xn) and Y is another set of n natural numbers (y1,y2.......yn), such that ax+by+c=0. If the standard deviation of set X is 'M', what is the standard deviation of set Y?
I think I've asked you this a few times in other threads, but where are these questions from?MBA.Aspirant wrote:X is the set of n natural numbers (x1,x2.......xn) and Y is another set of n natural numbers (y1,y2.......yn), such that ax+by+c=0. If the standard deviation of set X is 'M', what is the standard deviation of set Y?
The wording here is pretty bad. What they mean to say is that, for each value y_k in the second set, b*y_k = -a*x_k - c, so y_k = (-a/b)*x_k - c. That is, to get the values in the second set, we take each value in the first set, multiply it by -a/b, and subtract c.
Now, adding or subtracting some constant to every value in a set has no effect on the distances between the elements in your set, so has no effect on the standard deviation. So c is irrelevant here. If we multiply everything in a set by some positive value r, all of the distances within the set get multiplied by r as well, so the standard deviation is multiplied by r. Here, we are multiplying every value by -a/b. This quantity could be positive or negative, so we don't know if the standard deviation is multiplied by -a/b or by a/b, but we can be certain it's multiplied by | -a/b | , or more simply, by |a/b|.
