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The figure shows a square with a side length of 5m. A side of the squ

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New post 26 May 2020, 01:26
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[GMAT math practice question]

The figure shows a square with a side length of \(5m\). A side of the square is divided equally into \(5\) segments. The square is cut into \(5\) pieces, as the figure shows. What is the standard deviation of the areas of those \(5\) pieces?

Attachment:
5.26ps.png
5.26ps.png [ 11.37 KiB | Viewed 609 times ]


A. \(2\)

B. \(√5\)

C. \(√6\)

D. \(√7\)

E. \(2√2\)

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The figure shows a square with a side length of 5m. A side of the squ  [#permalink]

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New post 26 May 2020, 01:54
MathRevolution wrote:
[GMAT math practice question]

The figure shows a square with a side length of \(5m\). A side of the square is divided equally into \(5\) segments. The square is cut into \(5\) pieces, as the figure shows. What is the standard deviation of the areas of those \(5\) pieces?

Attachment:
5.26ps.png


A. \(2\)

B. \(√5\)

C. \(√6\)

D. \(√7\)

E. \(2√2\)


Ratio of sides of squares = 1:2:3:4:5
Ratio of Ateas of squares = 1:4:9:16:25

Ratio fo areas of 5 pieces = 1:(4-1):(9-4):(16-9):(25-16) = 1:3:5:7:9

i.e. Standard deviation will be slightly greater than 2 (because gaps between terms is 2)

We do NOT need to know the real calculation of standard deviation so I don't consider it a good question for GMAT question pool


Symbolic equation of DS \(= \frac{(5-1)+(5-3)+(5-5)+(7-5)+(9-5)}{5} = \frac{4+2+0+2+4}{5} = \frac{12}{5} = 2.4\)

√5 ≈ 2.2
√6 ≈ 2.5
√7 ≈ 2.7

therefore √6 seems the closest option so I would have gone for Option C

as per GMAT standard calculation



But exact calculation of SD is \(\frac{√∑(x_i - M)^2}{n}\) which gives actual standard deviation \(= 2√2 = 2.8\)

Answer: Option E
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Re: The figure shows a square with a side length of 5m. A side of the squ  [#permalink]

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New post 28 May 2020, 02:15
=>

Attachment:
5.26ps(a).png
5.26ps(a).png [ 22.7 KiB | Viewed 475 times ]


The areas of those \(5\) pieces are \(1, 3, 5, 7\), and \(9\), and their average is \(3.\)

The variance is \(\frac{[(1-5)^2 + (3-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2 ] }{ 5} = \frac{( 16 + 4 + 0 + 4 + 16 ) }{ 5} = \frac{40}{5} = 8.\)

Then, the standard deviation is \(√8 = 2√2.\)

Therefore, the answer is E.
Answer: E
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Re: The figure shows a square with a side length of 5m. A side of the squ  [#permalink]

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New post 01 Jun 2020, 13:58
GMATinsight wrote:
MathRevolution wrote:
[GMAT math practice question]

The figure shows a square with a side length of \(5m\). A side of the square is divided equally into \(5\) segments. The square is cut into \(5\) pieces, as the figure shows. What is the standard deviation of the areas of those \(5\) pieces?

Attachment:
5.26ps.png


A. \(2\)

B. \(√5\)

C. \(√6\)

D. \(√7\)

E. \(2√2\)


Ratio of sides of squares = 1:2:3:4:5
Ratio of Ateas of squares = 1:4:9:16:25

Ratio fo areas of 5 pieces = 1:(4-1):(9-4):(16-9):(25-16) = 1:3:5:7:9

i.e. Standard deviation will be slightly greater than 2 (because gaps between terms is 2)

We do NOT need to know the real calculation of standard deviation so I don't consider it a good question for GMAT question pool


Symbolic equation of DS \(= \frac{(5-1)+(5-3)+(5-5)+(7-5)+(9-5)}{5} = \frac{4+2+0+2+4}{5} = \frac{12}{5} = 2.4\)

√5 ≈ 2.2
√6 ≈ 2.5
√7 ≈ 2.7

therefore √6 seems the closest option so I would have gone for Option C

as per GMAT standard calculation



But exact calculation of SD is \(\frac{√∑(x_i - M)^2}{n}\) which gives actual standard deviation \(= 2√2 = 2.8\)

Answer: Option E


Agreed.
But, the formula for the standard deviation would be helpful for some of GMAT problems.
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Re: The figure shows a square with a side length of 5m. A side of the squ  [#permalink]

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New post 13 Jun 2020, 11:00
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MathRevolution wrote:
=>

Attachment:
5.26ps(a).png


The areas of those \(5\) pieces are \(1, 3, 5, 7\), and \(9\), and their average is \(3.\)

The variance is \(\frac{[(1-5)^2 + (3-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2 ] }{ 5} = \frac{( 16 + 4 + 0 + 4 + 16 ) }{ 5} = \frac{40}{5} = 8.\)

Then, the standard deviation is \(√8 = 2√2.\)

Therefore, the answer is E.
Answer: E



MathRevolution I guess you mean average is 5?
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Re: The figure shows a square with a side length of 5m. A side of the squ   [#permalink] 13 Jun 2020, 11:00

The figure shows a square with a side length of 5m. A side of the squ

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