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Set A {300,400,500,700,900} Set B {100,200,300,500,900}

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Set A {300,400,500,700,900} Set B {100,200,300,500,900} [#permalink] New post 05 Dec 2018, 09:32
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Set A {300,400,500,700,900}
Set B {100,200,300,500,900}

Quantity A
Quantity B
Standard deviation of Set A
Standard deviation of Set B


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given
[Reveal] Spoiler: OA
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Re: Set A {300,400,500,700,900} Set B {100,200,300,500,900} [#permalink] New post 05 Dec 2018, 10:22
Expert's post
Arun1992 wrote:
Set A {300,400,500,700,900}
Set B {100,200,300,500,900}

Quantity A
Quantity B
Standard deviation of Set A
Standard deviation of Set B


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given


The standard deviation is dependent on the spread of the elements.
Although it is highly unlikely that we will be required to calculate a standard deviation, but we should be able to relate the spread of elements in sets.

Set A {300,400,500,700,900}... Mean = \(\frac{2800}{5}=580\)
Set B {100,200,300,500,900}....Mean = \(\frac{2000}{5}=400\)
we can see that set B has more spread around its mean, thus B>A

B
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: Set A {300,400,500,700,900} Set B {100,200,300,500,900} [#permalink] New post 06 Dec 2018, 08:12
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Expert's post
Arun1992 wrote:
Set A {300,400,500,700,900}
Set B {100,200,300,500,900}

Quantity A
Quantity B
Standard deviation of Set A
Standard deviation of Set B


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given


For many standard deviation questions on the GRE, we can often just "eyeball" the numbers in each set to get a feel for which set has the greatest dispersion (aka deviation).

If we do so, we can see that the numbers in Set B are more dispersed, which means Set B has the greater standard deviation

Answer: B

---------------------------------
Alternatively, we can apply the informal definition of standard deviation (covered in the video below) to conclude that Set B has the greater standard deviation.

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CAT Tests
Re: Set A {300,400,500,700,900} Set B {100,200,300,500,900} [#permalink] New post 12 Dec 2018, 14:34
Answer: B
In the informal way of standard deviation, we just compare different elements difference from the mean in each set.
A: Mean equals (300+400+500+700+900)/ 5 = 2800/5 = 560
Difference from mean for each element:
260, 160, 60, 140, 440

B: Mean equals (100+200+300+500+900)/5= 2000/5=400
Difference from mean for each element:
300, 200, 100, 100, 500

We see in B numbers in the set differ more from the difference of A’s numbers from the mean in A. So B’s standard deviation is more than A’s. The answer is B.
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Re: Set A {300,400,500,700,900} Set B {100,200,300,500,900}   [#permalink] 12 Dec 2018, 14:34
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