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Re: Which of the following sets of numbers has the greatest standard devia [#permalink]

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31 Mar 2015, 10:46

1

This post received KUDOS

Bunuel wrote:

Which of the following sets of numbers has the greatest standard deviation?

A. 10, 11, 12 B. -3, -4, -5 C. -2, 0, 2 D. 5.1, 5.2, 5.3 E. 20, 22, 22.5

Kudos for a correct solution.

Standard deviation is the deviation from the mean. Mean for set C is 0 and hence it's values have highest deviation from the mean in this set. Hence option (C).

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PSgreateststandarddeviation_text.PNG [ 18.17 KiB | Viewed 3102 times ]

FAQ: What about answer choice (E)?

This is definitely the trickiest of the wrong answers. If you chose (E), you're not alone!

Since these lists of numbers are very short and there's the same number of elements in each--only three in each answer choice--let's use the quick way to compare SDs: compare the ranges.

The range of (C) is 2 - (-2) = 4. The range of (E) is 22.5 - 20 = 2.5. Since the range of E is smaller (and these are such small lists), it's pretty safe to assume that the SD is also smaller

But if that's not convincing enough, we can find the exact SD of (E)

First, what's the mean of those three numbers? (20 + 22 + 22.5) / 3 64.5 / 3 21.5

Next, how far away is each number from the mean?

20 is 1.5 away from 21.5 22 is .5 away from 21.5 22.5 is 1 away from 21.5 This means the standard deviation is the average of .5, 1, and 1.5, which means SD = 1.

This is smaller than the average of 2, 0, and 2 from answer choice (C), which would be 4/3 = 1.33.
_________________

This is definitely the trickiest of the wrong answers. If you chose (E), you're not alone!

Since these lists of numbers are very short and there's the same number of elements in each--only three in each answer choice--let's use the quick way to compare SDs: compare the ranges.

The range of (C) is 2 - (-2) = 4. The range of (E) is 22.5 - 20 = 2.5. Since the range of E is smaller (and these are such small lists), it's pretty safe to assume that the SD is also smaller

But if that's not convincing enough, we can find the exact SD of (E)

First, what's the mean of those three numbers? (20 + 22 + 22.5) / 3 64.5 / 3 21.5

Next, how far away is each number from the mean?

20 is 1.5 away from 21.5 22 is .5 away from 21.5 22.5 is 1 away from 21.5 This means the standard deviation is the average of .5, 1, and 1.5, which means SD = 1.

This is smaller than the average of 2, 0, and 2 from answer choice (C), which would be 4/3 = 1.33.

How about this for The OG 2017 PS 47 qn? Same logic if u apply how will we get it?

As a general rule, it's not the best practice to ask about one question in the thread devoted to another. If people are curious about OG 2017, PS #47, they will not be likely to find a discussion of it here. Don't just think about getting an answer to your own personal question. Think about the impact you have on all the users of this forum. A responsible approach to question-asking benefits everyone.

Also, it's not the best practice to ask the same question in multiple places. I just gave you my answer to that question in this post. Asking the same question in two different places does not send the most respectful attitude to the experts whose help you solicited, and again, other users would not find the discussion of this new question here.

Every choice you make, every action you take, has impact on others, and thus impact on how you are perceived. Furthermore, how you do anything is how you do everything. Remember that this is a public forum and anyone reading this may one day be your boss, your employee, your customer, your supplier, your competitor, etc. etc. The rewards for deeply responsible behavior yield significant payoffs in life.

Does all this make sense? Mike :-)
_________________

Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

As a general rule, it's not the best practice to ask about one question in the thread devoted to another. If people are curious about OG 2017, PS #47, they will not be likely to find a discussion of it here. Don't just think about getting an answer to your own personal question. Think about the impact you have on all the users of this forum. A responsible approach to question-asking benefits everyone.

Also, it's not the best practice to ask the same question in multiple places. I just gave you my answer to that question in this post. Asking the same question in two different places does not send the most respectful attitude to the experts whose help you solicited, and again, other users would not find the discussion of this new question here.

Every choice you make, every action you take, has impact on others, and thus impact on how you are perceived. Furthermore, how you do anything is how you do everything. Remember that this is a public forum and anyone reading this may one day be your boss, your employee, your customer, your supplier, your competitor, etc. etc. The rewards for deeply responsible behavior yield significant payoffs in life.

Does all this make sense? Mike :-)

Thanks Mike I understand that > i was just trying to corelate the concepts in the two questions and how it can be applied > i wanted to check if the thinking is correct or if i am missing anything. All im checking is if the above snipet of lowest range= lowest std is a general rule and can be applied to all such questions?

As a general rule, it's not the best practice to ask about one question in the thread devoted to another. If people are curious about OG 2017, PS #47, they will not be likely to find a discussion of it here. Don't just think about getting an answer to your own personal question. Think about the impact you have on all the users of this forum. A responsible approach to question-asking benefits everyone.

Also, it's not the best practice to ask the same question in multiple places. I just gave you my answer to that question in this post. Asking the same question in two different places does not send the most respectful attitude to the experts whose help you solicited, and again, other users would not find the discussion of this new question here.

Every choice you make, every action you take, has impact on others, and thus impact on how you are perceived. Furthermore, how you do anything is how you do everything. Remember that this is a public forum and anyone reading this may one day be your boss, your employee, your customer, your supplier, your competitor, etc. etc. The rewards for deeply responsible behavior yield significant payoffs in life.

Does all this make sense? Mike :-)

Thanks Mike I understand that > i was just trying to corelate the concepts in the two questions and how it can be applied > i wanted to check if the thinking is correct or if i am missing anything. All im checking is if the above snipet of lowest range= lowest std is a general rule and can be applied to all such questions?

Thanks Mike I understand that > i was just trying to corelate the concepts in the two questions and how it can be applied > i wanted to check if the thinking is correct or if i am missing anything. All im checking is if the above snipet of lowest range= lowest std is a general rule and can be applied to all such questions?

With all due respect, you have pressed to have me ask your question, and it's far from clear to me that you read the blog article to which I linked. If you understood everything in that blog, you would have answered your own question.

As general rule, sets with larger ranges tend to have larger standard deviations. If we were to measure the range & S.D. for every single set that, for example, has ever appeared on the GMAT, I would expect the range and S.D. to be highly correlated. Nevertheless, as always, correlation is only a statement about a general pattern, and not a statement that is true in the granular sense. Thus, if Set A has a larger range than Set B, we can't necessarily say anything about the standard deviations of these two sets.

Consider these two example sets. Set A = {40, 40, 40, 40, 40, 60, 60, 60, 60, 60} ==> mean = median = 50, range = 20 Set B = {35, 50, 50, 50, 50, 50, 50, 50, 50, 65} ==> mean = median = 50, range = 30

Set B clearly has a much larger range. But look at how the numbers are distributed. All the numbers in Set A are at the extreme values, 10 units away from the mean, so S.D. = 10. Meanwhile, 8/10 of the numbers in Set B are at the mean, with a deviation of zero. Thus, it appears that Set B will have a much smaller S.D.

In Set A, every deviation has an absolute value of 10, so S.D. = 10 In Set B, one deviation is -15, one is +15, and other eight are zero. Sum of square deviations = 225 + 225 = 450. Average of square deviations = 45. S.D. = \(\sqrt{45}\) = \(3\sqrt{5}\) = 6.7082

Thus, Set B has a larger ranger and a smaller S.D.

Once again, I would strongly recommend reading this blog if you haven't do so already. Standard Deviation on the GMAT As a general rule, the way you show respect to an expert for providing help is to acknowledge explicitly everything you learned from what they already shared. If everything they shared has not answered your question, it's fine to present that as well, but to insist on what you want to know and to disregard everything else an expert tells you is relevant is disrespectful.

Does all this make sense? Mike
_________________

Mike McGarry Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Which of the following sets of numbers has the greatest standard devia [#permalink]

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21 Aug 2017, 18:25

mikemcgarry wrote:

AMsac123 wrote:

AMsac123 wrote:

Thanks Mike I understand that > i was just trying to corelate the concepts in the two questions and how it can be applied > i wanted to check if the thinking is correct or if i am missing anything. All im checking is if the above snipet of lowest range= lowest std is a general rule and can be applied to all such questions?

With all due respect, you have pressed to have me ask your question, and it's far from clear to me that you read the blog article to which I linked. If you understood everything in that blog, you would have answered your own question.

As general rule, sets with larger ranges tend to have larger standard deviations. If we were to measure the range & S.D. for every single set that, for example, has ever appeared on the GMAT, I would expect the range and S.D. to be highly correlated. Nevertheless, as always, correlation is only a statement about a general pattern, and not a statement that is true in the granular sense. Thus, if Set A has a larger range than Set B, we can't necessarily say anything about the standard deviations of these two sets.

Consider these two example sets. Set A = {40, 40, 40, 40, 40, 60, 60, 60, 60, 60} ==> mean = median = 50, range = 20 Set B = {35, 50, 50, 50, 50, 50, 50, 50, 50, 65} ==> mean = median = 50, range = 30

Set B clearly has a much larger range. But look at how the numbers are distributed. All the numbers in Set A are at the extreme values, 10 units away from the mean, so S.D. = 10. Meanwhile, 8/10 of the numbers in Set B are at the mean, with a deviation of zero. Thus, it appears that Set B will have a much smaller S.D.

In Set A, every deviation has an absolute value of 10, so S.D. = 10 In Set B, one deviation is -15, one is +15, and other eight are zero. Sum of square deviations = 225 + 225 = 450. Average of square deviations = 45. S.D. = \(\sqrt{45}\) = \(3\sqrt{5}\) = 6.7082

Thus, Set B has a larger ranger and a smaller S.D.

Once again, I would strongly recommend reading this blog if you haven't do so already. Standard Deviation on the GMAT As a general rule, the way you show respect to an expert for providing help is to acknowledge explicitly everything you learned from what they already shared. If everything they shared has not answered your question, it's fine to present that as well, but to insist on what you want to know and to disregard everything else an expert tells you is relevant is disrespectful.

Does all this make sense? Mike

Thanks Mike. I dint mean to be respectful. Just wanted to get a clarity if there is a corelation between range and STD. I am sorry if you felt that way ! Thanks again