Discussion

If the mean of x, x+2, x+4, x+6, x+8 is 11, then the mean of the last three observations is:

Answer: C

Correct answer: 13

The five values are equally spaced, so their mean is the middle one:

\[x + 4 = 11 \quad\Longrightarrow\quad x = 7\]

The observations are therefore 7, 9, 11, 13, 15. The last three are 11, 13 and 15, again equally spaced, so their mean is their middle value:

\[\frac{11 + 13 + 15}{3} = \frac{39}{3} = 13\]

Answering 15 mistakes the largest observation for the mean of the last three.

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