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A store sells coats at different prices. Is the deviation of

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getzgetzu
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A store sells coats at different prices. Is the deviation of [#permalink] New post   22 Jul 2006, 06:31
A store sells coats at different prices. Is the deviation of the price less than $120?

1) The median of the price is $90
2) The range of the price is $ 100



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Re: A store sells coats at different prices. Is the deviation of [#permalink] New post   22 Jul 2006, 13:20
I will go with B
1) Median 90 means (80,90, 100) or (80, 90, 600) deviation can be anything.
2) Range means difference betwen first and last element if it si 100 then devaition can not be more than 100 So ans is B.

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Re: A store sells coats at different prices. Is the deviation of [#permalink] New post   22 Jul 2006, 16:05
getzgetzu wrote:
A store sells coats at different prices. Is the deviation of the price less than $120?

1) The median of the price is $90
2) The range of the price is $ 100


What is meant by "deviation" here? Is it the same as standard deviation?
If it is then I don't think we can solve this (E).
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Re: A store sells coats at different prices. Is the deviation of [#permalink] New post   23 Jul 2006, 14:16
Futuristic wrote:
getzgetzu wrote:
A store sells coats at different prices. Is the deviation of the price less than $120?

1) The median of the price is $90
2) The range of the price is $ 100


What is meant by "deviation" here? Is it the same as standard deviation?
If it is then I don't think we can solve this (E).


we do not need to solve this one for SD

I think B too

oa please
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Re: A store sells coats at different prices. Is the deviation of [#permalink] New post   26 Jul 2006, 02:32
E . If we care looking for Standard deviation.
B If we are looking only for the deviation
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Re: A store sells coats at different prices. Is the deviation of [#permalink] New post   26 Jul 2006, 02:53
jaynayak wrote:
E . If we care looking for Standard deviation.
B If we are looking only for the deviation


Even in terms of STDEV ...

Consider Example JUST 3 PRICES ARE USED: 0$ 90$ 100$

RANGE: 100
MEDIAN: 90
STDEV: 55

SO NIETHER STATEMENT IS SUFFICIENT, whether Its asked STDEV or Just Deviation.... MEANABSDEV ... etc... :))
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Re: A store sells coats at different prices. Is the deviation of [#permalink] New post   26 Jul 2006, 20:42
yes the range is max - min and standard deviation will not be > range...i thought...isnt it ? Please correct me...it is not true
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Re: A store sells coats at different prices. Is the deviation of [#permalink] New post   26 Jul 2006, 22:34
B

Even if SD is asked then also answer should be B. SD is ralative to mean. It doesn't matter values in the set are high or low. SD is the measure of dispersion of values of a set measured from mean.

Correct me if I am wrong.
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Re: A store sells coats at different prices. Is the deviation of [#permalink] New post   26 Jul 2006, 22:53
ps_dahiya wrote:
B

Even if SD is asked then also answer should be B. SD is ralative to mean. It doesn't matter values in the set are high or low. SD is the measure of dispersion of values of a set measured from mean.

Correct me if I am wrong.


Thanks ps_dahiya, I was also thinking the same...
Ans should be B.
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Re: A store sells coats at different prices. Is the deviation of [#permalink] New post   26 Jul 2006, 23:29
Here's my 2cents about deviation, variance, and standard deviation.

Let, set X = {X1,X2,....,Xn} (asscending order)
no matter what the value of a term is sum of each term's deviation is "0"
deaviation of 1st term = X1-mean
deaviation of 2nd term = X2-mean
....
deaviation of nth term = Xn-mean
Sum of deviations = X1+X2+....+Xn - (mean*n) = Total - Total = 0
Range = Xn-X1
Max. deviation = Xn - mean
Min. deviation = X1 - mean
Range > Max. devation > Min. deviation ('cuz mean 0

Standard devation
= sqrt(variance )

Range > Standard deviation
(Except, when range = 0, Range = varicance = standard deviation = 0)
Range = Xn-X1
Variance = (X1^2+X2^2...+Xn^2)/n - mean^2
Standard deviation = sqrt((X1^2+X2^2...+Xn^2)/n - mean^2)
Range - standard deviation
= Xn-X1 - sqrt((X1^2+X2^2...+Xn^2)/n - mean^2)
Square both side.
(Range - standard deviation)^2
= (Xn-X1 - sqrt((X1^2+X2^2...+Xn^2)/n - mean^2))^2
(Range - standard deviation)^2
= (Xn-X1)^2 - 2(Xn-X1)sqrt((X1^2+X2^2...+Xn^2)/n - mean^2))^2
Stuck here.. will try tomorrow. :oops:



Logical proof:
Purpose of those measures - deviation and standard deviation - is to see how far each term is from the mean.
Range is max. distance in a set.
Thus, Range is greater than or equal to those measures.

getzgetzu wrote:
A store sells coats at different prices. Is the deviation of the price less than $120?

1) The median of the price is $90
2) The range of the price is $ 100



1.
the deviation means each deviation.
S1. median of the price is $90. insuff.
S2. range of the price is $100.
tells that Max. deviation is less than $100 suff.
Hence, B.

2.
if question is asking about sum of each deviation.
Then, this question turns to be trivial. Doesn't need to consider S1 and S2.
0 is less than 120.
Hence, D.

3.
if question is asking about standard deviation.
1) The median of the price is $90 insuff.
2) The range of the price is $ 100 suff.
Range is always greater than standard deviation.(Except when range = 0)
Hence, B.



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Re: A store sells coats at different prices. Is the deviation of [#permalink]
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