Standard Deviation: During an experiment, some water...

[jurikondratev]

During an experiement, some water was removed from each of teh 6 tanks. If standard deviation of the 6 tanks at the beginning of the experiement was 10 gallons, what was it at the end of the experient?
(1) 30% of water was removed from each tank
(2) Average/mean at the end of experiement was 63 gallons


Answer: A

Why? How can we calculate the new stand. dev. with % change?

[adiagr]

During an experiement, some water was removed from each of teh 6 tanks. If standard deviation of the 6 tanks at the beginning of the experiement was 10 gallons, what was it at the end of the experient?
(1) 30% of water was removed from each tank
(2) Average/mean at the end of experiement was 63 gallons


Answer: A

Why? How can we calculate the new stand. dev. with % change?

Say tanks have volumes (v1, v2, v3...,v6)

After removal Tank1 will have volume as 0.7v1, Tank 2 as 0.7v2 ....and so on.

That is we are multiplying each member of a set by a constant 0.7.

Remember:
When we multiply / divide each observation of a data by a constant k. Then the Std Dev. also gets mult./ divided by the same constant.

Initial value of SD is given so we can find the new value.

So (1) is sufficient.

(2) gives the mean at the end of the experiments, but does not give any info abt individual tanks. Nothing can be said about new SD.

Not Sufficient.


Answer will be (A)


Aditya

[jurikondratev]

So statement (1) does not mean that the SD is 70% of previous SD, just that we can calculate?

[adiagr]

So statement (1) does not mean that the SD is 70% of previous SD, just that we can calculate?

Can you pls elaborate?

If I understand correctly, Statement 1 does indicate that New SD will be 70 % of the previous one.

As such statement (1) is sufficient.

Aditya

[mschwrtz]

jurikondratev, correct me if I'm wrong, but I think that you missed an important time- and effort-saving move adiagr made. He did not mean to imply that the new SD could be anything other than 7. Rather, he didn't bother calculating the new SD once he had determined that the new SD was possible to determine.

He was correctly focused on the minimum information needed to answer the question, rather than on the value itself.