Multiple choice

The mean of 9 observations is 20. If the mean of the first 5 observations is 18 and the mean of the last 5 observations is 22, the middle observation is:

  1. 20

  2. 18

  3. 22

  4. 24
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A Correct answer
Explanation

Total sum = 9 * 20 = 180. Sum of first 5 = 5 * 18 = 90. Sum of last 5 = 5 * 22 = 110. Sum of first 5 + last 5 = 200. The middle observation (5th) is counted twice. Middle = 200 - 180 = 20.

AI explanation

The total sum of all 9 observations is 9 times 20, which equals 180. The sum of the first 5 observations is 5 times 18, giving 90, and the sum of the last 5 observations is 5 times 22, giving 110. Adding these two sums gives 200, which counts the middle observation twice. Subtracting the overall sum of 180 from 200 leaves the middle observation as 20.

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