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E
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Difficulty:
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Is the standard deviation of set A is greater than standard deviation of set B ?
(1) Set A consists of consecutive multiples of 10
(2) Set B consists of consecutive multiples of 2
(1) Set A consists of consecutive multiples of 10
(2) Set B consists of consecutive multiples of 2
Is the standard deviation of set A is greater than standard deviation of set B ?
Thinking this way, it becomes easy to answer this questions.
As questions asks to find which SD is greater then first thing that must pop is that there must be relationship between the two sets - A and B.
So...
(1) Set A consists of consecutive multiples of 10
Clearly, not sufficient.
(2) Set B consists of consecutive multiples of 2
Clearly, not sufficient.
Hence answer must be either C or E. Here, it looks like details of two sets are available and we might be tempted to pick C which is a trap. Here's why
Together 1 and 2.
\(SD(σ) = \sqrt{variance} = \sqrt{\frac{∑(x_i - x_{avg})^2}{n}}\)
As you can see SD depends on three parameters. So, \(SD_A < SD_B\) or \(SD_A > SD_B\) because it depends on 'n - number of elements in the set'. For example
Let Set A = {10, 20, 30}, \(SD_A = \frac{2*10^2}{3}\)
Set B = {2, 4, 6}, \(SD_B = \frac{2*2^2}{3}\)
Then \(SD_A > SD_B\)
But if
Set A = {10, 20, 30}, \(SD_A = \frac{2*10^2}{3}\)
Set B = {2, 4, 6, 8, .... , 98}, \(SD_B = \frac{2(48^2 + 46^2 + ... + 2)}{49}\)
Then \(SD_A < SD_B\)
Answer E.
Thinking this way, it becomes easy to answer this questions.
As questions asks to find which SD is greater then first thing that must pop is that there must be relationship between the two sets - A and B.
So...
(1) Set A consists of consecutive multiples of 10
Clearly, not sufficient.
(2) Set B consists of consecutive multiples of 2
Clearly, not sufficient.
Hence answer must be either C or E. Here, it looks like details of two sets are available and we might be tempted to pick C which is a trap. Here's why
Together 1 and 2.
\(SD(σ) = \sqrt{variance} = \sqrt{\frac{∑(x_i - x_{avg})^2}{n}}\)
As you can see SD depends on three parameters. So, \(SD_A < SD_B\) or \(SD_A > SD_B\) because it depends on 'n - number of elements in the set'. For example
Let Set A = {10, 20, 30}, \(SD_A = \frac{2*10^2}{3}\)
Set B = {2, 4, 6}, \(SD_B = \frac{2*2^2}{3}\)
Then \(SD_A > SD_B\)
But if
Set A = {10, 20, 30}, \(SD_A = \frac{2*10^2}{3}\)
Set B = {2, 4, 6, 8, .... , 98}, \(SD_B = \frac{2(48^2 + 46^2 + ... + 2)}{49}\)
Then \(SD_A < SD_B\)
Answer E.
07 Jul 2020, 05:41
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In theory, the standard deviation of either set could be zero if one of the sets contains only one element. If we allow that possibility, the answer is immediately E.
If we disallow that possibility, then if the set of consecutive multiples of 10 is {10, 20}, its standard deviation is 5 (every element in the set is 5 away from the mean, so that is automatically the standard deviation). If you take a very large set of consecutive multiples of 2, say all the multiples of 2 between 0 and 1000, almost every value in this set will be more than 5 away from the mean, and the standard deviation will be much larger than 5. So the answer is still E.
If we knew the sets were the same size, then both statements would be sufficient together, since then the elements of A would be a greater distance apart than the elements of B (in fact, the standard deviation of A would be precisely five times as big as that of B, because the distances within A would be five times as big).
If we disallow that possibility, then if the set of consecutive multiples of 10 is {10, 20}, its standard deviation is 5 (every element in the set is 5 away from the mean, so that is automatically the standard deviation). If you take a very large set of consecutive multiples of 2, say all the multiples of 2 between 0 and 1000, almost every value in this set will be more than 5 away from the mean, and the standard deviation will be much larger than 5. So the answer is still E.
If we knew the sets were the same size, then both statements would be sufficient together, since then the elements of A would be a greater distance apart than the elements of B (in fact, the standard deviation of A would be precisely five times as big as that of B, because the distances within A would be five times as big).
