akhil911 wrote:
The Department of Environmental Protection measured the volume of water in 10 similarly sized reservoirs in State X and found that the standard deviation of their volumes at the start of the year was 4 million cubic gallons. Was the standard deviation of those 10 volume measurements lower at the end of the year?
(1) At the end of the year, the average volume of the water in the 10 reservoirs had decreased by 20%.
(2) The percent decrease in the volume of the water in each reservoir during the year was the same.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient to answer the question asked
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
I have issues solving such problems.
Can someone please let me know how do we solve such problems.
Here is quick summary for SD:
TIPS:
1. |Median-Mean| <= SD.
2. Variance is the square of the standard deviation.
3. If Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.
4. SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).
5. Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.
6. 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.
7. If we increase or decrease each term in a set by the same percent:
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.8. Changing the signs of the element of a set (multiplying by -1) has no effect on SD.
9. The SD of any list is not dependent on the average, but on the deviation of the numbers from the average. So just by knowing that two lists having different averages doesn't say anything about their standard deviation - different averages can have the same SD.
The above is from Math Expert Bunuel. It's very handy.
For more on this topic refer to
math-standard-deviation-87905.htmland
ps-questions-about-standard-deviation-85897.htmlComing back to the question
We need to find whether SD lower than what it was in the beginning of the year
St 1 says average vol of water had decreased by 20%. So if Total volume of water for 10 resevoirs was 100lts then at the end of the year Volume of 10 resevoirs was 80 lts.
Case 1 :Now Imagine if 9 resevoirs see an increase of 2 lts each and 1 resevoirs sees a decrease of 38 Lts then volume of water is still 80 lts (Average vol of water is 8 lts) but SD will be different (lower or more is not important)
Case 2:Also another case where each resevoir has volume of 10 lts each and each sees uniform decrease of 20% ie. at the end of the year each resevoir has 8 lts and Total volume is 80 lts and average volume is 8 ltr--------> In this case we can safely say SD is lower but not in Case 1
So ST 1 is not sufficient
Consider St 2 points out that each resevoir saw percent decrease and is pointing to Case 2 of St 1 and hence it is sufficient. It is in line with Pt 7
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”