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The mean of n observations 1², 2², 3²,..., n² equals 46n/11. Find the value of n.

1. 6
2. 8
3. 10
4. 12

Correct answer: 8

Solution

The mean of 1², 2²,..., n² is [n(n+1)(2n+1)/6] / n = (n+1)(2n+1)/6. Setting this equal to 46n/11 and solving gives n = 8.

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