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The standard deviation of x1, x2, …, x5 is 2√2. What is the standard d

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The standard deviation of x1, x2, …, x5 is 2√2. What is the standard d [#permalink] New post   07 Apr 2020, 04:25
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[GMAT math practice question]

The standard deviation of x1, x2, …, x5 is \(2√2\). What is the standard deviation of √2x1, √2x2, …, √2x5?

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B. 1
C. 2
D. 3
E. 4
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Re: The standard deviation of x1, x2, …, x5 is 2√2. What is the standard d [#permalink] New post   07 Apr 2020, 06:04
Standard deviation
when each element is multiplied by constant - Standard deviation also gets multiplies by same constant
when each element is divided by constant - Standard deviation also gets divided by same constant
when each element is added or subtracted by constant - Standard deviation remain unchanged

when each element is multiplied by constant - Standard deviation also gets multiplies by same constant
So here, new standard deviation is \(old*\sqrt{2}\)
\(2*\sqrt{2}*\sqrt{2} = 4\)
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Re: The standard deviation of x1, x2, …, x5 is 2√2. What is the standard d [#permalink] New post   07 Apr 2020, 07:26
if,Y = BX + A
then, sd(Y)= B *sd(X)
The standard deviation of x1, x2, …, x5 is 2√2.
the standard deviation of √2x1, √2x2, …, √2x5 will be = √2*2√2 = 4
correct answer is E
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Re: The standard deviation of x1, x2, …, x5 is 2√2. What is the standard d [#permalink] New post   09 Apr 2020, 19:10
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Remind the property that \(S(aX+b) = |a|S(X)\) where \(S(X)\) is the standard deviation of set \(X\) and \(X\) is a data set.

S(√2x1, √2x2, …, √2x5) = √2S(x1,x2,x3,x4,x5) =√2*(2√2) = 4.

Therefore, E is the answer.
Answer: E
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Re: The standard deviation of x1, x2, …, x5 is 2√2. What is the standard d [#permalink]
09 Apr 2020, 19:10
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