[siddharthaduggirala]

Originally Posted by bhavin422

Why do u say so buddy ?
from the question we have original SD of 10 ..

St 1: My point was (somebody correct if its wrong) 30 % reduction of each value ,reduces new mean by 30 % and hence also the SD is reduced by 30 % ...So new SD = 7 ...Sufficeint ...Ans A

P.S : i am loving the cross correction, it only helps to get better !! ..Pls correct me again dude ..

Cheers

P.S :This post also makes me hardcore Pagal !!

I also like this kind of discussion.

U got this right man:

If you multiply all terms by x then SD =x times old SD and mean = x times old mean

[nuttyvarun]

this is something that tricks everyone I guess, including me... SD as a concept is very delicate, and change in single entity can change the whole value of SD.. and for the candidate to find the value he should have the individual water amounts, range etc..

1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
- the 30% decrease might mean diff values for diff initial tank values. NOT SUFF

2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
- Since we dont know the inidividual values of tank waters, we cant solve using this either. NOT SUFF

Try both together.. still doesnt help.. since you dont get any value as such

I would have marked option E






PS: If the question would have been something like, DOES THE SD CHANGE AT ALL, then the options would have helped to conlude something substantial I guess.

Originally Posted by Arijit sen

During an experiment, some water was removed from each of 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?

1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.

2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

I found this is one of the earlier threads but the soln wasn't there. Please provide the explaantory soln.

Thanks.

[Arijit sen]

Originally Posted by nuttyvarun

this is something that tricks everyone I guess, including me... SD as a concept is very delicate, and change in single entity can change the whole value of SD.. and for the candidate to find the value he should have the individual water amounts, range etc..

1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
- the 30% decrease might mean diff values for diff initial tank values. NOT SUFF

2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
- Since we dont know the inidividual values of tank waters, we cant solve using this either. NOT SUFF

Try both together.. still doesnt help.. since you dont get any value as such

I would have marked option E






PS: If the question would have been something like, DOES THE SD CHANGE AT ALL, then the options would have helped to conlude something substantial I guess.

HI Puys,
Thanks for the explanations. But I do not have the OA wid me, so can't tell which option A/E is correct. If some one knows the source of this problem, please post the OA here for our reference.
Thanks a lot!

[nuttyvarun]

Tumhi ki bolchi dada.. no OA!!

Originally Posted by Arijit sen

HI Puys,
Thanks for the explanations. But I do not have the OA wid me, so can't tell which option A/E is correct. If some one knows the source of this problem, please post the OA here for our reference.
Thanks a lot!

[bhavin422]

Originally Posted by nuttyvarun

this is something that tricks everyone I guess, including me... SD as a concept is very delicate, and change in single entity can change the whole value of SD.. and for the candidate to find the value he should have the individual water amounts, range etc..

1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
- the 30% decrease might mean diff values for diff initial tank values. NOT SUFF

2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.
- Since we dont know the inidividual values of tank waters, we cant solve using this either. NOT SUFF

Try both together.. still doesnt help.. since you dont get any value as such

I would have marked option E

PS: If the question would have been something like, DOES THE SD CHANGE AT ALL, then the options would have helped to conlude something substantial I guess.

Hey Varun ,
On a GMAT SD is very rarely asked and is often a topic left out for discussion ..And we are not expected to calculate SD in GMAT, and it is tricky for sure ...

However ,
When every qty changes by same %, Irresepective of initial values, New SD also changes by same % ...THERE is no doubt regarding this concept ..

For Fun and learning try it out on excel ...take 6 random values and calculate SD by stdev function on excel ..Change the initial values to 70 % and calculate the SD again ....You would notice that new SD is 70% of original ..IF there is still a niggling doubt, change original values again, yet New SD changes by same % of Original ...

Given an original SD and an equal change of each values, we can calculate the new SD irrespective of original values

If there is still an doubt lets understand the reason behind it :

P.S : we are not expected to know or calculate SD for exam .This is for concept building only.

Let X1, X2 ,....X6 be the 6 original values .
Mean = X bar = (X1+X2+...+X6)/6
SD = sq root ( (X1-Xbar)^2 + (X2-X bar)^2 +......+(X6-Xbar)^2)/6)

Now new values are 0.7X1, 0.7X2 .......0.7X6
New mean = new X bar = 0.7(X1+X2+...+X6)/6 = 0.7 original X bar

New SD = sq root ((0.7^2(X1-Xbar)^2 +0.7^2(X2-X bar)^2 +........+0.7^2(X6-Xbar)^2)/6)

=0.7 original SD

Hence, irrespective of original values, for same % change, relation between original and new SD remains the same ..

Hence Ans A

Hey Arijit, does not matter if u do not know OA, we can discuss it to length to make sure there is no error..

[siddharthaduggirala]

HI Puys,
SD is a freq topic.And rule of thumb is

If you multiply all terms by x then SD =x times old SD and mean = x times old mean

This might help to get to the answer quickly.

Siddhartha

[siddharthaduggirala]

HI puys,
I got an idea yesterday.Shall we start a thread where we can discuss all the DS OG questions at length? this is just a proposal we can do the same in this thread also.

Siddhartha

PS: I'm an expert pagal now.

[nuttyvarun]

I tried the entire calculation thing.. and got the facts straightened.. thanks man!!

Originally Posted by bhavin422

Hey Varun ,
On a GMAT SD is very rarely asked and is often a topic left out for discussion ..And we are not expected to calculate SD in GMAT, and it is tricky for sure ...

However ,
When every qty changes by same %, Irresepective of initial values, New SD also changes by same % ...THERE is no doubt regarding this concept ..

For Fun and learning try it out on excel ...take 6 random values and calculate SD by stdev function on excel ..Change the initial values to 70 % and calculate the SD again ....You would notice that new SD is 70% of original ..IF there is still a niggling doubt, change original values again, yet New SD changes by same % of Original ...

Given an original SD and an equal change of each values, we can calculate the new SD irrespective of original values

If there is still an doubt lets understand the reason behind it :

P.S : we are not expected to know or calculate SD for exam .This is for concept building only.

Let X1, X2 ,....X6 be the 6 original values .
Mean = X bar = (X1+X2+...+X6)/6
SD = sq root ( (X1-Xbar)^2 + (X2-X bar)^2 +......+(X6-Xbar)^2)/6)

Now new values are 0.7X1, 0.7X2 .......0.7X6
New mean = new X bar = 0.7(X1+X2+...+X6)/6 = 0.7 original X bar

New SD = sq root ((0.7^2(X1-Xbar)^2 +0.7^2(X2-X bar)^2 +........+0.7^2(X6-Xbar)^2)/6)

=0.7 original SD

Hence, irrespective of original values, for same % change, relation between original and new SD remains the same ..

Hence Ans A

Hey Arijit, does not matter if u do not know OA, we can discuss it to length to make sure there is no error..

[bhavin422]

well ... i havent seen many questions on SD being posted ...n by the flow of last question many concepts of SD are yet unexplored ..

So, here is 1 question from me ..its a good one ...give it a try ...will post the approach and answer after few replies .

A school surveyed 100 students to determine the average number of minutes studied per night. If 84 percent of the students studied for at least 114 minutes per night and the students’ responses had a normal distribution, what is the average number of minutes studied per night?

(1) The new average would be 10 percent greater, If 20 more students averaging 192 minutes per night were added to the sample,
(2) Only 2 students studied at least 132 minutes per night.

Cheers !!

[nuttyvarun]

@Bhavin..
I have no clue what this question is about.. but if I have to guess in the exam, I would mark option C

Could you please explain the question.. and also share the means to solve this..