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Data Sufficiency Problem-STDEV/AVGS

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Data Sufficiency Problem-STDEV/AVGS

by jd6199 » Sat Jan 20, 2007 10:48 am
SOURCE: PEARSON PRACTICE TEST 1

I need help understanding the reasoning on this problem.

DURING AN EXPERIMENT WATER WAS REMOVED FROM EACH OF 6 WATER TANKS. IF THE STANDARD DEV OF THE VOLUMES OF WATER IN THE TANKS AT THE BEGINNING OF THE EXPERIMENT WAS 10 GALLONS, WHAT WAS THE STDEV AT THE END OF THE EXPERIMENT?

1. FOR EACH OF THE TANKS 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 (MEAN) VOLUME OF WATER IN THE TANKS AT THE END OF THE EXPERIMENT WAS 63 GALLONS.

Please explain why the answer is A
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SOURCE: PEARSON PRACTICE TEST 1

by gviren » Sat May 19, 2007 10:05 am
[color=red]SOURCE: PEARSON PRACTICE TEST 1

I need help understanding the reasoning on this problem.

DURING AN EXPERIMENT WATER WAS REMOVED FROM EACH OF 6 WATER TANKS. IF THE STANDARD DEV OF THE VOLUMES OF WATER IN THE TANKS AT THE BEGINNING OF THE EXPERIMENT WAS 10 GALLONS, WHAT WAS THE STDEV AT THE END OF THE EXPERIMENT?

1. FOR EACH OF THE TANKS 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 (MEAN) VOLUME OF WATER IN THE TANKS AT THE END OF THE EXPERIMENT WAS 63 GALLONS.

Please explain why the answer is A[/color]

The answer is A as to calculate SD, we have to follow the following steps

1) For each value xi calculate the difference between xi and the average value .
2) Calculate the squares of these differences.
3) Find the average of the squared differences. This quantity is the variance σ2.
4) Take the square root of the variance.

So the final SD will be 7 i.e. 10 X 70%= 7
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