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Set A={9, 13, 4, 2, 7} Set B={9, 13, 4, 2, 9} Set C={9, 13, 4, 2, 4}

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Aakash0101raj
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Set A={9, 13, 4, 2, 7} Set B={9, 13, 4, 2, 9} Set C={9, 13, 4, 2, 4} [#permalink] New post   14 Nov 2022, 07:55
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Set A={9, 13, 4, 2, 7}
Set B={9, 13, 4, 2, 9}
Set C={9, 13, 4, 2, 4}
Set D={9, 13, 4, 2, 6}

Which of the following statement illustrates the exact order of standard deviation of these sets of numbers from the lowest to the greatest?
A. A < B < C < D
B. A < B < D < C
C. D < B < C < A
D. C < B < D < A
E. A < D < B < C
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E
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r1smith
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Re: Set A={9, 13, 4, 2, 7} Set B={9, 13, 4, 2, 9} Set C={9, 13, 4, 2, 4} [#permalink] New post   14 Nov 2022, 08:55
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In order to solve this problem, I found the mean of each set and then took the absolute value of the variances of each value in the set in relation to the mean. Then I added them all together to give me an estimate of the standard deviation. That looked something like this:

Set A mean = 7 —> 2, 6, 5, 0 ==> 13

Set B mean = 7.4 —> 1.6, 5.6, 3.4, 5.4, 1.6 = 17.6

Set C mean = 6.4 —> 2.6 , 6.6, 2.4, 4.4, 2.4 = 18.4

Set D mean = 6.8 —> 2.2 , 6.2 , 2.8 , 4.8 , 0.8 = 16.8

13 < 16.8 < 17.6 < 18.4

A < D < B < C ------> Answer Choice E
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Aakash0101raj
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Re: Set A={9, 13, 4, 2, 7} Set B={9, 13, 4, 2, 9} Set C={9, 13, 4, 2, 4} [#permalink] New post   14 Nov 2022, 19:09
r1smith wrote:
In order to solve this problem, I found the mean of each set and then took the absolute value of the variances of each value in the set in relation to the mean. Then I added them all together to give me an estimate of the standard deviation. That looked something like this:

Set A mean = 7 —> 2, 6, 5, 0 ==> 13

Set B mean = 7.4 —> 1.6, 5.6, 3.4, 5.4, 1.6 = 17.6

Set C mean = 6.4 —> 2.6 , 6.6, 2.4, 4.4, 2.4 = 18.4

Set D mean = 6.8 —> 2.2 , 6.2 , 2.8 , 4.8 , 0.8 = 16.8

13 < 16.8 < 17.6 < 18.4

A < D < B < C ------> Answer Choice E


This is a standard approach that everyone would follow. I was hoping for something like estimation or any simplified methods.
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Re: Set A={9, 13, 4, 2, 7} Set B={9, 13, 4, 2, 9} Set C={9, 13, 4, 2, 4} [#permalink] New post   15 Nov 2022, 06:07
Aakash0101raj wrote:
r1smith wrote:
In order to solve this problem, I found the mean of each set and then took the absolute value of the variances of each value in the set in relation to the mean. Then I added them all together to give me an estimate of the standard deviation. That looked something like this:

Set A mean = 7 —> 2, 6, 5, 0 ==> 13

Set B mean = 7.4 —> 1.6, 5.6, 3.4, 5.4, 1.6 = 17.6

Set C mean = 6.4 —> 2.6 , 6.6, 2.4, 4.4, 2.4 = 18.4

Set D mean = 6.8 —> 2.2 , 6.2 , 2.8 , 4.8 , 0.8 = 16.8

13 < 16.8 < 17.6 < 18.4

A < D < B < C ------> Answer Choice E


This is a standard approach that everyone would follow. I was hoping for something like estimation or any simplified methods.


Then maybe pay for a tutor instead of complaining about free advice u got on the internet.
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asimovsalvador
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Set A={9, 13, 4, 2, 7} Set B={9, 13, 4, 2, 9} Set C={9, 13, 4, 2, 4} [#permalink] New post   12 May 2024, 00:55
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Aakash0101raj wrote:
Set A={9, 13, 4, 2, 7}
Set B={9, 13, 4, 2, 9}
Set C={9, 13, 4, 2, 4}
Set D={9, 13, 4, 2, 6}

Which of the following statement illustrates the exact order of standard deviation of these sets of numbers from the lowest to the greatest?
A. A < B < C < D
B. A < B < D < C
C. D < B < C < A
D. C < B < D < A
E. A < D < B < C


1. The common elements of all these sets are 2,4,9,13 whose average is = 28/4 =7
2. After that we check the absolute difference between the arithmatic mean (=7) and the numbers we are appending to the remaining sets i.e the last numbers in all the 5 sets.
3. The larger the difference, the larger the standard deviation.
That means, for Set A 7~7=0, Set B 9~7 =2 , Set C 4~7=3, Set D 6~7=1. (Normally we know if we append a value equal to the mean to the set, the standard deviation would decrease the most. So obviously A has the least standard deviation)
Therefore the answer would be, A<D<B<C (E)
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Set A={9, 13, 4, 2, 7} Set B={9, 13, 4, 2, 9} Set C={9, 13, 4, 2, 4} [#permalink]
12 May 2024, 00:55
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