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The highest term in a set is 3SD above the Mean. The lowest term is 4S

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Sangeeta2018
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The highest term in a set is 3SD above the Mean. The lowest term is 4S [#permalink] New post   15 Nov 2017, 22:06
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The highest term in a set is 3SD above the Mean. The lowest term is 4SD below the mean. If the highest term is 200 and Range is 140, find the Standard Deviation.

A. 20
B. 60
C. 140
D. 200
E. 300

Source: Experts' Global
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A
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Bunuel
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Re: The highest term in a set is 3SD above the Mean. The lowest term is 4S [#permalink] New post   15 Nov 2017, 23:03
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Sangeeta2018 wrote:
The highest term in a set is 3SD above the Mean. The lowest term is 4SD below the mean. If the highest term is 200 and Range is 140, find the Standard Deviation.

A. 20
B. 60
C. 140
D. 200
E. 300

Source: Experts' Global


The highest term in a set is 3SD above the Mean: Highest term = Mean +3SD ;

The lowest term is 4SD below the mean: Lowest term = Mean - 4SD;

Subtract 2 from 1:

Highest term - Lowest term = (Mean +3SD) - (Mean - 4SD);

Range = 7SD;

140 = 7SD;

SD = 20.

Answer: A.
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gmathighh
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Re: The highest term in a set is 3SD above the Mean. The lowest term is 4S [#permalink] New post   15 Nov 2017, 23:09
Sangeeta2018 wrote:
The highest term in a set is 3SD above the Mean. The lowest term is 4SD below the mean. If the highest term is 200 and Range is 140, find the Standard Deviation.

A. 20
B. 60
C. 140
D. 200
E. 300

Source: Experts' Global


Let mean be denoted as M
Highest term = M + 4SD
Lowest term = M - 3SD

Range = 140, i.e.
M + 4sd - M + 3sd = 140
7sd = 140
sd = 20;

or

M+4sd = 200 .. eq 1
Range = 140 --> 200 - Least number = 140 ==> least number = 60
M - 3sd = 60 .. eq 2

Solve for sd from eq 1 and 2; you will get 7sd = 140 and sd = 20;

Now my doubt is - where is 20 in the answer choices ??? or did I make a mistake :cool: :cool:
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Bunuel
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Re: The highest term in a set is 3SD above the Mean. The lowest term is 4S [#permalink] New post   15 Nov 2017, 23:11
Expert Reply
gmathighh wrote:
Sangeeta2018 wrote:
The highest term in a set is 3SD above the Mean. The lowest term is 4SD below the mean. If the highest term is 200 and Range is 140, find the Standard Deviation.

A. 20
B. 60
C. 140
D. 200
E. 300

Source: Experts' Global


Let mean be denoted as M
Highest term = M + 4SD
Lowest term = M - 3SD

Range = 140, i.e.
M + 4sd - M + 3sd = 140
7sd = 140
sd = 20;

or

M+4sd = 200 .. eq 1
Range = 140 --> 200 - Least number = 140 ==> least number = 60
M - 3sd = 60 .. eq 2

Solve for sd from eq 1 and 2; you will get 7sd = 140 and sd = 20;

Now my doubt is - where is 20 in the answer choices ??? or did I make a mistake :cool: :cool:


The correct answer is A. Check here: https://gmatclub.com/forum/the-highest- ... l#p1962998

P.S. Edited the options in the original post.
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gmathighh
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Re: The highest term in a set is 3SD above the Mean. The lowest term is 4S [#permalink] New post   15 Nov 2017, 23:18
Bunuel wrote:
gmathighh wrote:
Sangeeta2018 wrote:
The highest term in a set is 3SD above the Mean. The lowest term is 4SD below the mean. If the highest term is 200 and Range is 140, find the Standard Deviation.

A. 20
B. 60
C. 140
D. 200
E. 300

Source: Experts' Global


Let mean be denoted as M
Highest term = M + 4SD
Lowest term = M - 3SD

Range = 140, i.e.
M + 4sd - M + 3sd = 140
7sd = 140
sd = 20;

or

M+4sd = 200 .. eq 1
Range = 140 --> 200 - Least number = 140 ==> least number = 60
M - 3sd = 60 .. eq 2

Solve for sd from eq 1 and 2; you will get 7sd = 140 and sd = 20;

Now my doubt is - where is 20 in the answer choices ??? or did I make a mistake :cool: :cool:


The correct answer is A.
P.S. Edited the options in the original post.


I have checked the link, Bunuel.
Thank you for ackowledging.
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gps5441
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Re: The highest term in a set is 3SD above the Mean. The lowest term is 4S [#permalink] New post   22 Nov 2017, 06:38
Range=Max value-min value
Range=140
Max value=200
200=140-min or Min Value=60
we are given
Mean+3SD=200
Mean-4SD=60
subtract the above 2 equations
7SD=140 or SD=140/7=20
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Re: The highest term in a set is 3SD above the Mean. The lowest term is 4S [#permalink]
22 Nov 2017, 06:38
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