More generally, because the arithmetic mean is a convex combination (meaning its coefficients sum to ), it can be defined on a convex space, not only a vector space.
mˈoːɹ dʒˈɛnɚɹəli, bɪkˈʌz ðɪ ɚɹˈɪθmətˌɪk mˈiːn ɪz ɐ kɑːnvˈɛks kˌɑːmbᵻnˈeɪʃən mˈiːnɪŋ ɪts kˌoʊɪfˈɪʃənts sˈʌm tʊ, ɪt kæn biː dᵻfˈaɪnd ˌɔn ɐ kɑːnvˈɛks spˈeɪs, nˌɑːt ˈoʊnli ɐ vˈɛktɚ spˈeɪs.