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if the highest observation in the set S is 3 standard deviations above

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if the highest observation in the set S is 3 standard deviations above  [#permalink]

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New post 18 Mar 2018, 22:44
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if the highest observation in the set S is 3 standard deviations above the arithmetic mean and the lowest observation in the set is 5 standard deviations below the mean, what is the arithmetic mean of the set?
(1) The range of the set is 72
(2) The lowest term in the set is 40.
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if the highest observation in the set S is 3 standard deviations above  [#permalink]

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New post 19 Mar 2018, 11:23
rishabhmishra wrote:
if the highest observation in the set S is 3 standard deviations above the arithmetic mean and the lowest observation in the set is 5 standard deviations below the mean, what is the arithmetic mean of the set?
(1) The range of the set is 72
(2) The lowest term in the set is 40.


Let \(x\) be the mean, \(y\) be the highest term and \(z\) the lowest term

Given \(y=3S.D+x\) and \(z=x-5S.D\), we need to know the value of \(S.D\) and either \(y\) or \(z\) to know the mean

Statement 1: implies \(y-z=72\). so we have

\(3S.D+x-x+5S.D=72 => S.D=9\). but we cannot calculate the value of either \(y\) or \(z\) from this equation. Insufficient

Statement 2: implies \(z=40\). but nothing mentioned about \(S.D\). Insufficient

Combining 1 & 2: We know that \(S.D=9\) and \(z=40\), hence \(x=z+5S.D=40+5*9=85\). Sufficient

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if the highest observation in the set S is 3 standard deviations above &nbs [#permalink] 19 Mar 2018, 11:23
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