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Set A {3,3,3,4,5,5,5} has a standard deviation of 1.

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Set A {3,3,3,4,5,5,5} has a standard deviation of 1. [#permalink] New post 02 Sep 2012, 17:19
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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
[Reveal] Spoiler: OA

Last edited by Smita04 on 03 Sep 2012, 19:04, edited 1 time in total.
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Re: Set A {3,3,3,4,5,5,5} has a standard deviation of 1. [#permalink] New post 02 Sep 2012, 20:16
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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 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!
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Last edited by nktdotgupta on 13 Dec 2012, 04:55, edited 3 times in total.
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Re: Set A {3,3,3,4,5,5,5} has a standard deviation of 1. [#permalink] New post 02 Sep 2012, 20:38
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Smita04 wrote:
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


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!
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Re: Set A {3,3,3,4,5,5,5} has a standard deviation of 1. [#permalink] New post 03 Oct 2014, 06:09
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Re: Set A {3,3,3,4,5,5,5} has a standard deviation of 1.   [#permalink] 03 Oct 2014, 06:09
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Set A {3,3,3,4,5,5,5} has a standard deviation of 1.

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