A successful grouping will split dogs such that (a) each group has a low variance of dog weights (meaning the group is relatively homogeneous) and (b) the mean of each group is distinct (if two groups have the same mean, then it isn't reasonable to conclude that the groups are, in fact, separate in any meaningful way).
ɐ səksˈɛsfəl ɡɹˈuːpɪŋ wɪl splˈɪt dˈɑːɡz sˈʌtʃ ðæt ɐ ˈiːtʃ ɡɹˈuːp hɐz ɐ lˈoʊ vˈɛɹiəns ʌv dˈɑːɡ wˈeɪts mˈiːnɪŋ ðə ɡɹˈuːp ɪz ɹˈɛlətˌɪvli həmˈoʊdʒniəs ænd bˈiː ðə mˈiːn ʌv ˈiːtʃ ɡɹˈuːp ɪz dɪstˈɪŋkt ɪf tˈuː ɡɹˈuːps hæv ðə sˈeɪm mˈiːn, ðˈɛn ɪɾ ˌɪzənt ɹˈiːzənəbəl tə kəŋklˈuːd ðætðə ɡɹˈuːps ɑːɹ, ɪn fˈækt, sˈɛpɹət ɪn ˌɛni mˈiːnɪŋfəl wˈeɪ.