Q: IF SET A AND B HAVE 50 INTEGERS IN EACH SET. IS THE STANDARD DEVIATION OF SET A GREATER THAN THAT OF SET B?
A: RANGE OF SET A IS GREATER THAN THAT OF B
B: AVG. OF SET A IS GREATER THAN THAT OF B
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DS: S . D
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[email protected]
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sl750
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I took a small set of numbers
A-{1,3,3,7} Range=6
B-{1,3,3,5} Range=4
Avg of A = 3.5; Avg of B = 3. Just by eyeballing the respective averages and the elements of their respective sets, we can see that A has a higher SD
Take another case
A-{1,1,1,7} Range=6
B-{1,4,4,5} Range=4
Avg of A = 2.5; Avg of B = 3.5. I took a case with set B having a higher average. In this case too, we see that set A has a higher SD. So sufficient
Statement 2 is not sufficient. As we can see in statement 1, the second example shows that in-spite of set A having a lower average, the SD was larger. So basically, it depends on how far from the mean
the elements of the set are. The farther apart the elements are from the mean, the greater is the SD
A-{1,3,3,7} Range=6
B-{1,3,3,5} Range=4
Avg of A = 3.5; Avg of B = 3. Just by eyeballing the respective averages and the elements of their respective sets, we can see that A has a higher SD
Take another case
A-{1,1,1,7} Range=6
B-{1,4,4,5} Range=4
Avg of A = 2.5; Avg of B = 3.5. I took a case with set B having a higher average. In this case too, we see that set A has a higher SD. So sufficient
Statement 2 is not sufficient. As we can see in statement 1, the second example shows that in-spite of set A having a lower average, the SD was larger. So basically, it depends on how far from the mean
the elements of the set are. The farther apart the elements are from the mean, the greater is the SD
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prateek_guy2004
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What do we need to find standard deviation?
Mean and Range
Statement 1 suff
statement 2 insuff
IMOA
Mean and Range
Statement 1 suff
statement 2 insuff
IMOA
Don't look for the incorrect things that you have done rather look for remedies....
https://www.beatthegmat.com/motivation-t90253.html
https://www.beatthegmat.com/motivation-t90253.html
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Ian Stewart
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We want to know which set has the greater standard deviation - that is, we want to know in which set the elements tend to be further from the mean. We don't care at all how big the mean is; we only care how far away elements are from the mean. So Statement 2 here is completely useless.
Statement 1 is also not sufficient. The range of a set only takes into account two elements: the largest and the smallest. The standard deviation, on the other hand, is based on the distances from *every* element to the mean. If you take the two sets below:
A = {0, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 100}
and
B = {1, 1, 1, 1, 1, 1, 50, 99, 99, 99, 99, 99, 99}
the first set has a greater range than the second set. But because most of the elements in set A are clustered around the mean, while most of the elements in set B are far from the mean, set A will have a much smaller standard deviation than set B.
The answer is E.
Statement 1 is also not sufficient. The range of a set only takes into account two elements: the largest and the smallest. The standard deviation, on the other hand, is based on the distances from *every* element to the mean. If you take the two sets below:
A = {0, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 100}
and
B = {1, 1, 1, 1, 1, 1, 50, 99, 99, 99, 99, 99, 99}
the first set has a greater range than the second set. But because most of the elements in set A are clustered around the mean, while most of the elements in set B are far from the mean, set A will have a much smaller standard deviation than set B.
The answer is E.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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[email protected]
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SIR, I IS IT TRUE THAT S.D IS < OR EQUAL TO RANGE/2 ( HALF OF RANGE) ?Ian Stewart wrote:We want to know which set has the greater standard deviation - that is, we want to know in which set the elements tend to be further from the mean. We don't care at all how big the mean is; we only care how far away elements are from the mean. So Statement 2 here is completely useless.
Statement 1 is also not sufficient. The range of a set only takes into account two elements: the largest and the smallest. The standard deviation, on the other hand, is based on the distances from *every* element to the mean. If you take the two sets below:
A = {0, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 100}
and
B = {1, 1, 1, 1, 1, 1, 50, 99, 99, 99, 99, 99, 99}
the first set has a greater range than the second set. But because most of the elements in set A are clustered around the mean, while most of the elements in set B are far from the mean, set A will have a much smaller standard deviation than set B.
The answer is E.
IF THIS IS TRUE THAN WHY WE CAN'T ANSWER THIS BY USING STATEMENT A
PLEASE HELP , HELP
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Yes, that is true. It is not something you will *ever* need to use on the GMAT (if you think that fact is needed on a GMAT question, you've misunderstood something). That relationship is also irrelevant for the question above - I don't see why you think it makes statement 1 sufficient, so I can't help more than that.[email protected] wrote:
SIR, I IS IT TRUE THAT S.D IS < OR EQUAL TO RANGE/2 ( HALF OF RANGE) ?
IF THIS IS TRUE THAN WHY WE CAN'T ANSWER THIS BY USING STATEMENT A
PLEASE HELP , HELP
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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