Multiple choice

The mean of $9$ observations is $36$. If the mean of the first $5$ observations is $32$ and that of the last $5$ observations is $39$, then the fifth observation is __________.

  1. $28$
  2. $31$
  3. $43$
  4. $37$
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B Correct answer
Explanation

Total sum = 9 * 36 = 324. Sum of first 5 = 5 * 32 = 160. Sum of last 5 = 5 * 39 = 195. The fifth observation is (160 + 195) - 324 = 355 - 324 = 31.

AI explanation

The sum of all 9 observations is 9 multiplied by 36, which equals 324. The sum of the first 5 observations is 5 multiplied by 32, giving 160, and the sum of the last 5 observations is 5 multiplied by 39, giving 195. Adding these two sums gives 355, which counts the fifth observation twice, so the fifth observation is 355 minus 324, which is 31.

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