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The arithmetic mean of 11 observations is 11. The arithmetic mean of the first 6 observations is 10.5 and the arithmetic mean of the last 6 observations is 11.5. What is the sixth observation?

The arithmetic mean of 11 observations is 11. The arithmetic mean of the first 6 observations is 10.5 and the arithmetic mean of the last 6 observations is 11.5. What is the sixth observation? Correct Answer 11.0

Sum of numbers = Average of the numbers × Number of observations

Sum of 11 observations = Sum of first 6 numbers + Sum of last 6 number - 6th number

11 × 11 = 10.5 × 6 + 11.5 × 6 - 6th number

121 = 63 + 69 - 6th number

∴ 6th number = 132 - 121 = 11

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