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During an experiment, some water was removed from each of 6 [#permalink]

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07 Jul 2007, 17:27

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During an experiment, some water was removed from each of the 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% 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.

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.

OA later

A. since .3 is being removed from each tank won't SD remain the same?

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.

OA later

A. since .3 is being removed from each tank won't SD remain the same?

no, the concept that i missed here was that the standard deviation would decrease by .3 since the distances between the values were all decreased by 30%.

My computer doesnot support the supericacl, I must write it in a very detail, i explain A only

A. Beginning: 6 water tanks: t1, t2, t3, t4....t6 mean t =(t1+t2+t3+...+t6)/6 SD =10 = √∑(ti - t)^2 (i = 1...6)

After removing each tanhk 30% water:

6 water tanks: 0.7*t1,.....0.7*t6 new mean =(0.7*t1 + 0.7*t2 +....+0.7*t6)/6 = 0.7* t new SD = √∑(0.7*ti - 0.7*t)^2 (i = 1...6) new SD = 0.7*10 =7 _________________

Two important properties of std dev: 1. Adding a constant to each term does not alter the std dev 2. Multiplying each term by a constant leads to the new std dev = constant * old std dev

Re: During an experiment, some water was removed from each of 6 [#permalink]

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11 May 2014, 05:19

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Re: During an experiment, some water was removed from each of 6 [#permalink]

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11 May 2014, 06:22

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During an experiment, some water was removed from each of the 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% 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.

You should know that: 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 (multiply all terms by the constant): Mean will increase or decrease by the same percent. SD will increase or decrease by the same percent.

You can check it yourself: SD of a set: {1,1,4} will be the same as that of {5,5,8} as second set is obtained by adding 4 to each term of the first set.

That's because Standard Deviation shows how much variation there is from the mean. And when adding or subtracting a constant to each term we are shifting the mean of the set by this constant (mean will increase or decrease by the same constant) but the variation from the mean remains the same as all terms are also shifted by the same constant.

So according to this rules statement (1) is sufficient to get new SD, it'll be 30% less than the old SD so 7. As for statement (2) it's clearly insufficient as knowing mean gives us no help in getting new SD.

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