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Let $S=\{6, 10, 7, 13, 5, 12, 8, 11, 9\}$ and $a=\underset{x \in S}{\Sigma} (x-9)^2$ & $b = \underset{x \in S}{\Sigma} (x-10)^2$. Then

  1. $a <b$
  2. $a>b$
  3. $a=b$
  4. None of these
in Verbal Ability by Boss (16.8k points)
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1 Answer

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S = {5,6,7,8,9,10,11,12,13}. a = $4^2+3^2+2^2+1^2+0^2+1^2+2^2+3^2+4^2$ and b = $5^2+4^2+3^2+2^2+1^2+0^2+1^2+2^2+3^2$ and it is obvious that b > a (OPTION A). In general the sum of square of differences from the median is minimum when all the numbers are positive.
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