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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Standard Deviation?
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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
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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- amit2k9
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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.
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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- thephoenix
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since the set is inc by same constant the S.D will remain same.
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