The Prophet ﷺ said that "wasat" means just, referring to the verse "Thus We have made you a justly balanced nation" [Baqarah 2:143].
حدثنا وكيع حدثنا الأعمش عن أبي صالح
عن النبي ﷺ الوسط العدل {جعلناكم أمة وسطا}
Its isnad is sahih. The hadith is found in Bukhari 6/371, no. 3339, Fath, Prophets, "Indeed We sent Nuh," and Tirmidhi 5/207, no. 2961, who said, hasan sahih.