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C
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Difficulty:
25%
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Question Stats:
68% (00:37) correct
32%
(00:36)
wrong
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Set A {3,3,3,4,5,5,5} has a standard deviation of 1. What will the standard deviation be if every number in the set is multiplied by 4?
A)1
B)2
C)4
D)8
E)16
A)1
B)2
C)4
D)8
E)16
02 Sep 2012, 21:38
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Smita04
Points to remember -
1. If one Add/Subtract the same amont from every term in a set, SD doesn't change.
2. If one Multiply/Divide every term by the same number in a set, SD changes by same number.
Hence the answer to the above question is C. Cheers!
General Discussion
Updated on: 30 Oct 2021, 11:15
Originally posted by BrushMyQuant on 02 Sep 2012, 21:16.
Last edited by BrushMyQuant on 30 Oct 2021, 11:15, edited 5 times in total.
Last edited by BrushMyQuant on 30 Oct 2021, 11:15, edited 5 times in total.
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Variance = (sum of (squares of difference of each number from mean )) / total number of numbers
Standard deviation = sqrt Variance
When we multiply all the numbers by something then while calculating the standard deviation we can take out that thing common and new standard deviation will be equal to value by which we multiplied all the number* old standard deviation.
Ex:
Suppose we have 4 entries a,b,c,d and suppose the mean is m
Then standard deviation = sqrt { { (a-m)^2 + (b-m)^2 + (c-m)^2 + (d-m)^2 } / 4 }
Now we multiply all the number by 4
so the new set will be 4a, 4b, 4c, 4d the new mean will be 4a + 4b+ 4c+ 4d /4 = 4 *( (a+b+c+d) /4 ) = 4m
Standard Deviation = sqrt { { (4a-4m)^2 + (4b-4m)^2 + (4c-4m)^2 + (4d-4m)^2 } / 4 }
sqrt {4^2} *sqrt { { (a-m)^2 + (b-m)^2 + (c-m)^2 + (d-m)^2 } / 4 }
= 4 * old standard deviation
So, Answer will be C
Hope it helps!
Watch the following video to Learn the Basics of Statistics
Standard deviation = sqrt Variance
When we multiply all the numbers by something then while calculating the standard deviation we can take out that thing common and new standard deviation will be equal to value by which we multiplied all the number* old standard deviation.
Ex:
Suppose we have 4 entries a,b,c,d and suppose the mean is m
Then standard deviation = sqrt { { (a-m)^2 + (b-m)^2 + (c-m)^2 + (d-m)^2 } / 4 }
Now we multiply all the number by 4
so the new set will be 4a, 4b, 4c, 4d the new mean will be 4a + 4b+ 4c+ 4d /4 = 4 *( (a+b+c+d) /4 ) = 4m
Standard Deviation = sqrt { { (4a-4m)^2 + (4b-4m)^2 + (4c-4m)^2 + (4d-4m)^2 } / 4 }
sqrt {4^2} *sqrt { { (a-m)^2 + (b-m)^2 + (c-m)^2 + (d-m)^2 } / 4 }
= 4 * old standard deviation
So, Answer will be C
Hope it helps!
Watch the following video to Learn the Basics of Statistics
