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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.
(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.
12 Dec 2010, 05:46
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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.
Answer: A.
For more on this check Standard Deviation chapter of Math Book: math-standard-deviation-87905.html
Collection of PS questions on SD: ps-questions-about-standard-deviation-85897.html
Collection of PS questions on SD: ds-questions-about-standard-deviation-85896.html
Hope it's clear.
(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.
Answer: A.
For more on this check Standard Deviation chapter of Math Book: math-standard-deviation-87905.html
Collection of PS questions on SD: ps-questions-about-standard-deviation-85897.html
Collection of PS questions on SD: ds-questions-about-standard-deviation-85896.html
Hope it's clear.
vaivish1723
Hi,
I have attached few gmat prep DS Qs. Please respond with explanations. Apology if there is duplications.
I have attached few gmat prep DS Qs. Please respond with explanations. Apology if there is duplications.
Standard deviation measures dispersion around the mean i.e. how far apart the values are from mean. The actual calculation of the Standard Deviation is not asked in GMAT but you need to theoretically understand the concept.
e.g. If we are interested in SD of the following values:
2, 4, 5, 6, 8
Here, mean is 5.
I encourage you to visualize the numbers on a number line. The diagram below shows the 5 numbers with their mean 5. SD measures how far the numbers are from their mean.
Attachment:
Ques1.jpg [ 6.42 KiB | Viewed 89764 times ]
If we add 10 to each of the numbers, the numbers become:
12, 14, 15, 16, 18
New mean is 15 but relative to the new mean, the numbers are still dispersed in the say way around 15. So SD for these numbers is the same as SD above.
If we multiply/divide each number by some number, the SD changes. Look at the diagram below to understand why. If each number is multiplied by 3, the numbers are:
6, 12, 15, 18, 24
Attachment:
Ques2.jpg [ 6.51 KiB | Viewed 89286 times ]
On the number line, now they are much farther from their mean 15. Hence their SD is greater than before. It is actually 3 times the initial SD. (Check out the formula of SD to see why.)
In this question, initial SD was 10. When 30% of the water is removed from each tank, the leftover water is 70% i.e. 0.7*original volume of water. Since we are multiplying the original volume by 0.7, the SD will change. It will become 0.7*previous SD i.e. 0.7*10 = 7.
mehdiov: As we see from above, if we remove the same quantity, the SD will not change. Here we removed a fraction of the original quantity of each. e.g. if one tank had 50 gallons, we removed 30% i.e. 15 gallons. If another had 100 gallons, we removed 30 gallons.
