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The mean of a series x1, x2,..., xn is x_bar. If each term xi is replaced by xi + 2i (for i = 1, 2,..., n), what will be the new mean?

1. x_bar + n
2. x_bar + n + 1
3. x_bar + 2
4. x_bar + 2*n

Correct answer: x_bar + n + 1

Solution

The new series is xi + 2i, so the new mean is x_bar + (1/n)*sum(2i) = x_bar + (2/n)*(n(n+1)/2) = x_bar + (n+1).

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