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# Standard Deviation

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Intern
Status: GMAT on july 13.
Joined: 10 Feb 2017
Posts: 36
GMAT 1: 650 Q48 V30

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08 Jul 2017, 00:02
Could someone say,
1) What happens to S.D when a number is added/subtracted to all the numbers in the set?(set of consecutive integers)eg:{5,6,7,8,...}
2) What happens to S.D when a number is added/subtracted to all the numbers in the set?(set of different integers)eg{-4,9,2,-1..}
2) What happens to S.D when a number is added/subtracted to all the numbers in the set?(set of same integers) eg: {3,3,3,3,3,}
Similarly,

1) What happens to S.D when a number is multiplied/divided to all the numbers in the set?(set of consecutive integers)eg:{5,6,7,8,...}
2) What happens to S.D when a number is multiplied/divided to all the numbers in the set?(set of different integers)eg{-4,9,2,-1..}
2) What happens to S.D when a number is multiplied/divided to all the numbers in the set?(set of same integers) eg: {3,3,3,3,3,}
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1421

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08 Jul 2017, 04:31
2
The answer to your first three questions is the same -- if you add a constant to every value in a list, the standard deviation will not change. It doesn't matter what the list is. So the standard deviation of these two lists, for example:

2, 7, 10, 50

and

22, 27, 30, 70

is the same, because we can make the second list by adding 20 to every value in the first list. The reason the standard deviation does not change is because standard deviation is based on the distance between your elements, and when we add 20 to everything, the distances between our values don't change at all.

When you multiply every value in a list by a constant, the standard deviation will also be multiplied by that constant. So if you multiply every value in a list by 3, the standard deviation will be multiplied by 3. The standard deviation of the second list below is 3 times the s.d. of the first:

2, 7, 10, 50

6, 21, 30, 150

Notice that when we multiply by 3, we 'stretch out' the distances between values -- the distances between consecutive values in the second list are 3 times larger than in the first list. That's why the standard deviation changes when you multiply.

If instead you divide everything in a list by 3, then you're really just multiplying everything by 1/3, and so the standard deviation will be multiplied by 1/3.

These principles apply no matter what kind of list or set you're working with.
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Math Expert
Joined: 02 Sep 2009
Posts: 54436

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08 Jul 2017, 04:34
IanStewart wrote:
The answer to your first three questions is the same -- if you add a constant to every value in a list, the standard deviation will not change. It doesn't matter what the list is. So the standard deviation of these two lists, for example:

2, 7, 10, 50

and

22, 27, 30, 70

is the same, because we can make the second list by adding 20 to every value in the first list. The reason the standard deviation does not change is because standard deviation is based on the distance between your elements, and when we add 20 to everything, the distances between our values don't change at all.

When you multiply every value in a list by a constant, the standard deviation will also be multiplied by that constant. So if you multiply every value in a list by 3, the standard deviation will be multiplied by 3. The standard deviation of the second list below is 3 times the s.d. of the first:

2, 7, 10, 50

6, 21, 30, 150

Notice that when we multiply by 3, we 'stretch out' the distances between values -- the distances between consecutive values in the second list are 3 times larger than in the first list. That's why the standard deviation changes when you multiply.

If instead you divide everything in a list by 3, then you're really just multiplying everything by 1/3, and so the standard deviation will be multiplied by 1/3.

These principles apply no matter what kind of list or set you're working with.

Welcome back Ian. Good to see you!
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Math Expert
Joined: 02 Sep 2009
Posts: 54436

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08 Jul 2017, 04:36
1
1
Viserion99 wrote:
Could someone say,
1) What happens to S.D when a number is added/subtracted to all the numbers in the set?(set of consecutive integers)eg:{5,6,7,8,...}
2) What happens to S.D when a number is added/subtracted to all the numbers in the set?(set of different integers)eg{-4,9,2,-1..}
2) What happens to S.D when a number is added/subtracted to all the numbers in the set?(set of same integers) eg: {3,3,3,3,3,}
Similarly,

1) What happens to S.D when a number is multiplied/divided to all the numbers in the set?(set of consecutive integers)eg:{5,6,7,8,...}
2) What happens to S.D when a number is multiplied/divided to all the numbers in the set?(set of different integers)eg{-4,9,2,-1..}
2) What happens to S.D when a number is multiplied/divided to all the numbers in the set?(set of same integers) eg: {3,3,3,3,3,}

Fro more on the topics try the following links:

Statistics

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Joined: 24 Jun 2008
Posts: 1421

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08 Jul 2017, 06:12
Bunuel wrote:
Welcome back Ian. Good to see you!

Hi Bunuel - great to see you're still here! Hope you've been doing well.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Re: Standard Deviation   [#permalink] 08 Jul 2017, 06:12
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