Multiple choice

The mean of 25 observations is 36. If the mean of the first 13 observations is 32 and that of the last 13 observations is 39, then the 13th observation is:

  1. 16

  2. 23

  3. 21

  4. 18
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B Correct answer
Explanation

Sum of 25 = 25 * 36 = 900. Sum of first 13 = 13 * 32 = 416. Sum of last 13 = 13 * 39 = 507. 13th observation = (416 + 507) - 900 = 923 - 900 = 23.

AI explanation

The total sum of 25 observations is 25 * 36 = 900. The sum of the first 13 observations is 13 * 32 = 416, and the sum of the last 13 observations is 13 * 39 = 507. The 13th observation is included in both of these partial sums, so adding them gives 416 + 507 = 923. The value of the 13th observation is the excess of this combined sum over the total sum, which is 923 - 900 = 23.

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