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Properties of Mean, Standard Deviation

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Joined: 01 Aug 2013
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Schools: LBS '18 (S)
Properties of Mean, Standard Deviation [#permalink]

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New post 08 Apr 2014, 08:10
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Hi Guys,

Have my gmat in less than 36 hours and would appreciate help on the following:

Standard Deviation and Mean for a set of numbers

How does each change if:
a. a certain number is added to all the numbers
b. a certain number is subtracted from all the numbers
c. a certain number is multiplied with all the numbers
d. all the numbers are divided by a certain number

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Re: Properties of Mean, Standard Deviation [#permalink]

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New post 08 Apr 2014, 09:14
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brobeedle wrote:
Hi Guys,

Have my gmat in less than 36 hours and would appreciate help on the following:

Standard Deviation and Mean for a set of numbers

How does each change if:
a. a certain number is added to all the numbers
b. a certain number is subtracted from all the numbers
c. a certain number is multiplied with all the numbers
d. all the numbers are divided by a certain number


If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.

If we increase or decrease each term in a set by the same percent (multiply all terms by the constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

Questions on this concept to practice:
lately-many-questions-were-asked-about-the-standard-85896.html
ps-questions-about-standard-deviation-85897.html
if-q-is-a-set-of-consecutive-integers-what-is-the-standard-151794.html
in-the-last-two-years-each-of-jeremy-s-six-children-grew-in-130614.html
during-an-experiment-some-water-was-removed-from-each-of-94166.html
set-a-consists-of-all-even-integers-between-2-and-110876.html
if-d-is-the-standard-deviation-x-y-and-z-what-is-the-stan-93979.html
what-is-sd-of-given-set-of-numbers-whose-average-is-104000.html
there-is-a-set-of-consecutive-even-integers-what-is-the-98877.html

Theory on Statistics and Sets problems: math-standard-deviation-87905.html

All DS Statistics and Sets problems to practice: search.php?search_id=tag&tag_id=34
All PS Statistics and Sets problems to practice: search.php?search_id=tag&tag_id=55


Hope this helps.
_________________

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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Kudos [?]: 132526 [2], given: 12324

Manager
Manager
avatar
Joined: 01 Aug 2013
Posts: 93

Kudos [?]: 14 [0], given: 10

Schools: LBS '18 (S)
Re: Properties of Mean, Standard Deviation [#permalink]

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New post 09 Apr 2014, 00:27
Thanks Bunuel, so am I right to say that if all the terms are divided by the same constant, the effect is not linear - i.e., cannot be determined unless we calculate the st.dev of the new set as well?

Kudos [?]: 14 [0], given: 10

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42248

Kudos [?]: 132526 [0], given: 12324

Re: Properties of Mean, Standard Deviation [#permalink]

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New post 09 Apr 2014, 02:16
brobeedle wrote:
Thanks Bunuel, so am I right to say that if all the terms are divided by the same constant, the effect is not linear - i.e., cannot be determined unless we calculate the st.dev of the new set as well?


No.

Multiplying is the same as dividing: for example, dividing by 2 is the same as multiplying by 1/2.

If we increase or decrease each term in a set by the same percent (multiply all terms by the constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

Thus the above holds true for dividing as well.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 132526 [0], given: 12324

Manager
Manager
avatar
Joined: 01 Aug 2013
Posts: 93

Kudos [?]: 14 [0], given: 10

Schools: LBS '18 (S)
Re: Properties of Mean, Standard Deviation [#permalink]

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New post 09 Apr 2014, 20:10
Thank you! Clear now

Posted from my mobile device

Kudos [?]: 14 [0], given: 10

Re: Properties of Mean, Standard Deviation   [#permalink] 09 Apr 2014, 20:10
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