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Standard Deviation?

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by Ahmed MS » Thu Jun 16, 2011 10:45 pm
If d is standard deviation of x, y, and z, what is standard deviation of x + 5, y + 5, and z + 5?

a. D
b. 3d
c. 15d
d. d + 5
e. d + 15

Answer is A. Can anyone help me to solve?

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by Frankenstein » Thu Jun 16, 2011 11:13 pm
Hi,
Let the series be x1,x2,...,xn
mean be m and standard deviation be d
If all the elements are added or subtracted by the same quantity(say a), new mean will be m+a
the deviations of each element will still be (x1+a)-(m+a),(x2+a)-(m+a),....(xn+a)-(m+a)i.e. same as (x1-m), (x2-m)...(xn-m). So S.D. will remain same irrespective of the value of quantity added(a).
Use he same principle here.
Hence, A
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by amit2k9 » Fri Jun 17, 2011 3:16 am
let the numbers be (1,2,3) changed numbers are (6,7,8).as you can see deviation from the mean has not changed,remaining the same 1 here in both the cases.Thus d it is.

Tips :

deviation for addition,subtraction never changes if the deviation is done by a constant quantity.

deviation increases if the constant (k) is positive integer, and each number is multiplied by that number.
d*k will be the value.

deviation decrease if a constant divides each number. d/k will be the value.
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by thephoenix » Fri Jun 17, 2011 5:27 am
since the set is inc by same constant the S.D will remain same.
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