Multiple choice

The mean of $11$ observations is $50$. If the mean of first six observations is $49$ and that of last six observations is $52$, which option is the sixth observation?

  1. $55$
  2. $56$
  3. $57$
  4. $58$
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B Correct answer
Explanation

The sum of 11 observations is 11 * 50 = 550. The sum of the first 6 is 6 * 49 = 294, and the sum of the last 6 is 6 * 52 = 312. The sixth observation is (294 + 312) - 550 = 606 - 550 = 56.

AI explanation

The sum of all 11 observations is 11 times 50 equal to 550. The sum of the first six observations is 6 times 49 equal to 294, and the sum of the last six observations is 6 times 52 equal to 312. The sixth observation is counted twice when adding the sum of the first six and the last six observations. Using the method of overlapping sums, the sixth observation is 294 plus 312 minus 550, resulting in 56.

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