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# You make a new sequence by removing 2 elements from the

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Director
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You make a new sequence by removing 2 elements from the [#permalink]  24 Nov 2005, 04:38
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You make a new sequence by removing 2 elements from the sequence {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}. What is the standard deviation of the new sequence?

(1) The median of the new sequence is 10.
(2) The new sequence has the same average as the original sequence.
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Re: DS - Standard deviation [#permalink]  24 Nov 2005, 07:22
E.

from i, sequuences {1, 3, 5, 7, 13, 15, 17, 19} and {3, 5, 7, 9, 11, 13, 15, 17}, both, have median 10 but they have different SDs.

from ii, sequuences {1, 3, 5, 7, 13, 15, 17, 19} and {3, 5, 7, 9, 11, 13, 15, 17}, both, have the same mean 10 as the original has but their SDs are different.

from i and ii also the have different SDs with same mean and median.
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Re: DS - Standard deviation [#permalink]  24 Nov 2005, 23:42
HIMALAYA wrote:
E.

from i, sequuences {1, 3, 5, 7, 13, 15, 17, 19} and {3, 5, 7, 9, 11, 13, 15, 17}, both, have median 10 but they have different SDs.

from ii, sequuences {1, 3, 5, 7, 13, 15, 17, 19} and {3, 5, 7, 9, 11, 13, 15, 17}, both, have the same mean 10 as the original has but their SDs are different.

from i and ii also the have different SDs with same mean and median.

HIMALAYA...
can you pls explain ..how you concluded that these different sets will have different SD.. .....any trick or just observation ...
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Re: DS - Standard deviation [#permalink]  10 Jun 2006, 19:35
gamjatang wrote:
You make a new sequence by removing 2 elements from the sequence {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}. What is the standard deviation of the new sequence?

(1) The median of the new sequence is 10.
(2) The new sequence has the same average as the original sequence.

Pick E in this one.
(1) in order to maintain the median of 10, we have several cases:
Keep (9,11) , we can remove any number of the rest : one number in the left side of (9,11) and another in the right side of (9,11).
For example: remove 1 and 19 ...then compare with removal of (3,19). The two standard deviations are different ---> that means we can't have exactly the same SD for all removals ---> can't find such SD --> insuff

(2) this statement means: the two removed numbers have a sum which is equal to mean*2 . The mean here is 10 . Thus, the pairs of removal can be either ( 1,19) , (3,17) , (5,15) , (3,13) , (9,11) . Since the mean is unchanged, the removal of (1,19) yields a smaller SD than that of (3,13) because (1,19) has wider distances to the mean than (3,13) does. --> no common SD for all removal --> insuff
Re: DS - Standard deviation   [#permalink] 10 Jun 2006, 19:35
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