In this talk, we give an informal discussion about how varieties that appear in Bhargava's arithemtic statistics setting also coincidentally arise in orbital integrals and characters of reductive p-adic groups. More precisely, orbital integrals and characters happen to count points on these varieties over the residue field. We will mostly concentrate on examples regarding hyperelliptic curves. If time permits, we shall demonstrate one endoscopic identity, which orbital integrals and characters must satisfy, that follows from basic geometric properties of hyperelliptic curves.