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Standard deviation

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by liferocks » Mon May 31, 2010 1:32 am
standard deviation is difference of the values from the mean.If all values change by same amount difference of the values with mean does not change or standard deviation remains same.hence standard deviation of x+5,y+5,z+5 is d.

To show it algebraically,let m be the mean of x,y and z
then d=sqrt{1/3 * [(m-x)^2+(m-y)^2+(m-z)^2]}

mean of x+5,y+5,z+5=(x+5+y+5+z+5)/3=d+3

so standard deviation= sqrt{1/3 * [(m+5-x-5)^2+(m+5-y-5)^2+(m+5-z-5)^2]}=sqrt{1/3 * [(m-x)^2+(m-y)^2+(m-z)^2]}=d
Last edited by liferocks on Mon May 31, 2010 2:40 am, edited 1 time in total.
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by gmatmachoman » Mon May 31, 2010 2:12 am
liferocks wrote:standard deviation is difference of the values from the mean.If all values change by same amount difference of the values with mean does not change or standard deviation remains same.hence standard deviation of x+5,y+5,z+5 is d.

To show it algebraically,let m be the mean of x,y and z
then d=sqrt{1/3 * [(d-x)^2+(d-y)^2+(d-z)^2]}

mean of x+5,y+5,z+5=(x+5+y+5+z+5)/3=d+3

so standard deviation= sqrt{1/3 * [(d+5-x-5)^2+(d+5-y-5)^2+(d+5-z-5)^2]}=sqrt{1/3 * [(d-x)^2+(d-y)^2+(d-z)^2]}=d
LR U missed using "m" .Plz replace d by "m" in RHS
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by liferocks » Mon May 31, 2010 2:41 am
gmatmachoman wrote: LR U missed using "m" .Plz replace d by "m" in RHS
edited.Thnx!
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by karthikpandian19 » Mon May 14, 2012 12:24 am
By avoiding the formula, is there a logical way to get the result.

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by aneesh.kg » Mon May 14, 2012 12:46 am
There is no need to calculate anything in this problem if you understand the meaning of Standard Deviation.

Standard Deviation is a representation of how much the terms are separated from the mean. It does not depend on mean, it only depends on how much the separation is.

Example 1:
(2,4,6) and (3,4,5) have the same mean (of 4) but the terms in (2,4,6) have a greater separation from the mean than in (3,4,5)
so
SD(2,4,6) > SD(3,4,5)

Example 2:
(2,4,6) and (13,15,17) have different means (4 and 15 respectively) but the separation of the terms from the mean is the same.
so
SD(2,4,6) = SD(13,15,17)

Now, let's look at the problem given here.
We have to compare (x,y,z) and (x+5,y+5,z+5), which have different means. But the separation is the same.

Let's plot them on a number line and understand better.

Image

SD(X,Y,Z) = SD(X+5,Y+5,Z+5)
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