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12 Jan 2022, 03:30
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A
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57% (00:53) correct
43%
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What is the Standard Deviation of a set of consecutive even integers ?
(1) There are 39 elements in the set.
(2) The mean of the set is 382.
(1) There are 39 elements in the set.
(2) The mean of the set is 382.
26 Jan 2022, 07:17
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Bunuel
SD= deviation from the mean
Consider two consecutive even integer sets both having same # of elements
\(x=\{2,4, 6\} \) Mean \(= 4\) SD \(= 2\)
\(y=\{6,8, 10\} \) Mean \(= 8\), SD \(=2 \)
SD is same hence we can conclude SD is NOT DEPENDENT on the mean for these kinds of set.
Now consider two consecutive even integer sets both having different # of elements
SD of \(\{2,4,6\} = 2\)
SD of \(\{2,4,6,8\}= \sqrt{5}\)
Here we see SD IS DEPENDENT on the number of elements for the given kind of sets.
(1) There are \(39 \) elements in the set.
As we have seen above SD IS DEPENDENT on the # of elements for the given kind of sets.
All sets of these kinds that have \(39\) elements will have the same SD doesn't matter what the elements are. As shown in the first example above by taking sets with \(3\) elements.
\(x=\{2,4, 6\} \) Mean \(= 4\) SD \(= 2\)
\(y=\{6,8, 10\} \) Mean \(= 8\), SD \(=2 \)
SUFF.
(2) The mean of the set is \(382.\)
As we have seen above SD is NOT DEPENDENT on the mean for the given kind of set.
Two sets of this kind that have the same mean will have different SD if # of elements are differnet.
\({2,4,6} \)-> Mean\(= 4\), SD \(= 2 \)
\({0,2,4,6,8} \)-> Mean \(= 4 \), SD \(= 2 \sqrt{2}\)
NOT SUFF.
Ans = A
Hope it's clear.
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