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15 Oct 2009, 12:32
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Please help to understand...
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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
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15 Oct 2009, 13:51
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kt00381n
we know that SD = 10 gallons. Average volume of 6tanks be V and individual be V1,V2,V3,V4,V5,V6.
1. if 30% water is removed from each tank we know that individual volume and average/mean volme will decrease by 30% and hence calculate SD. Suff
2. It says about avg at end as 63 gallons which is not sufficient info to calculate new SD
hence A
15 Oct 2009, 14:30
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This is good question to understand the concept of SD.
Let's consider set (2,4,12)
Mean=6
Sd=(((6-2)^2+(6-4)^2+(6-12)^2)/3)^1/2=(56/3)^1/2=2*(14/3)^1/2
Let's add a constant of 3 to each term of the set= (5,7,15)
Mean=9 (Increased by the same constant)
SD=(((9-5)^2+(9-7)^2+(9-15)^2)/3)^1/2=(56/3)^1/2=2*(14/3)^1/2
SD=2*(14/3)^1/2, didn't change!
Let's increase each term of a set by the same (50%) percent=(3,6,18)
Mean=9 (Increased by the same percent)
SD=(((9-3)^2+(9-6)^2+(9-18)^2)/3)^1/2=(126/3)^1/2=3(14/3)^1/2
SD=3(14/3)^1/2, increased by the same percent
So, here is the TIP:
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:
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent
Basically from the above it's obvious that if we were only told that mean decreased, increased or remained the same we won't be able to determine new SD.
So, in our question:
(1) As each term decreased by the same percent SD will decrease by the same percent --> 10*0.7=7=New SD. Sufficient.
(2) The average decreased by 37 percent, says nothing about the SD. Not sufficient
Answer A.
Let's consider set (2,4,12)
Mean=6
Sd=(((6-2)^2+(6-4)^2+(6-12)^2)/3)^1/2=(56/3)^1/2=2*(14/3)^1/2
Let's add a constant of 3 to each term of the set= (5,7,15)
Mean=9 (Increased by the same constant)
SD=(((9-5)^2+(9-7)^2+(9-15)^2)/3)^1/2=(56/3)^1/2=2*(14/3)^1/2
SD=2*(14/3)^1/2, didn't change!
Let's increase each term of a set by the same (50%) percent=(3,6,18)
Mean=9 (Increased by the same percent)
SD=(((9-3)^2+(9-6)^2+(9-18)^2)/3)^1/2=(126/3)^1/2=3(14/3)^1/2
SD=3(14/3)^1/2, increased by the same percent
So, here is the TIP:
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:
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent
Basically from the above it's obvious that if we were only told that mean decreased, increased or remained the same we won't be able to determine new SD.
So, in our question:
(1) As each term decreased by the same percent SD will decrease by the same percent --> 10*0.7=7=New SD. Sufficient.
(2) The average decreased by 37 percent, says nothing about the SD. Not sufficient
Answer A.
