Here are a bunch of possible answers:
integers -15, -14, -13, -12, and -1 have sum -55 and therefore average -11.
integers -15, -14, -13, -11, and -2 have sum -55 and therefore average -11.
integers -15, -14, -13, -10, and -3 have sum -55 and therefore average -11.
integers -15, -14, -13, -9, and -4 have sum -55 and therefore average -11.
integers -15, -14, -13, -8, and -5 have sum -55 and therefore average -11.
integers -15, -14, -13, -7, and -6 have sum -55 and therefore average -11.
integers -15, -14, -12, -11, and -3 have sum -55 and therefore average -11.
integers -15, -14, -12, -10, and -4 have sum -55 and therefore average -11.
integers -15, -14, -12, -9, and -5 have sum -55 and therefore average -11.
integers -15, -14, -12, -8, and -6 have sum -55 and therefore average -11.
integers -15, -14, -11, -10, and -5 have sum -55 and therefore average -11.
integers -15, -14, -11, -9, and -6 have sum -55 and therefore average -11.
integers -15, -14, -11, -8, and -7 have sum -55 and therefore average -11.
integers -15, -14, -10, -9, and -7 have sum -55 and therefore average -11.
integers -15, -13, -12, -11, and -4 have sum -55 and therefore average -11.
integers -15, -13, -12, -10, and -5 have sum -55 and therefore average -11.
integers -15, -13, -12, -9, and -6 have sum -55 and therefore average -11.
integers -15, -13, -12, -8, and -7 have sum -55 and therefore average -11.
integers -15, -13, -11, -10, and -6 have sum -55 and therefore average -11.
integers -15, -13, -11, -9, and -7 have sum -55 and therefore average -11.
integers -15, -13, -10, -9, and -8 have sum -55 and therefore average -11.
integers -15, -12, -11, -10, and -7 have sum -55 and therefore average -11.
integers -15, -12, -11, -9, and -8 have sum -55 and therefore average -11.
integers -14, -13, -12, -11, and -5 have sum -55 and therefore average -11.
integers -14, -13, -12, -10, and -6 have sum -55 and therefore average -11.
integers -14, -13, -12, -9, and -7 have sum -55 and therefore average -11.
integers -14, -13, -11, -10, and -7 have sum -55 and therefore average -11.
integers -14, -13, -11, -9, and -8 have sum -55 and therefore average -11.
integers -14, -12, -11, -10, and -8 have sum -55 and therefore average -11.
integers -13, -12, -11, -10, and -9 have sum -55 and therefore average -11.
Edwin