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This problem trains for: SAT-I, GMAT, AMC-10, AMC-8.

The average of five odd consecutive integers is:

Denote the smallest number with 2m+1. Then the five consecutive odd integers can be written as:

Their average is:

which is pretty obvious since the average of an odd number of consecutive terms of an arithmetic sequence is equal to the middle number (median). This is an arithmetic sequence with common difference 2.

This number is an odd integer. Any integer number is also a real number.

The sign of the average depends on the choice of numbers.