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I've run into this multiple times on my maternal side. Example: my gg-uncle (Inus)'s children were listed as "Mulatto," as well as he and his wife. I just surmised that the whole family was of lighter complexion, which prompted the census taker to record "Mu." However, Inus's mother was listed "Black" and "Mu" alternatively and his paternal heritage is unknown. It's possible he could have been mulatto. His wife's father was listed as "Mu," but I don't know her mother's heritage. For her, I believe she was likely just light-skinned and her father may have been truly "Mu."
1 year, 10 months ago on The Mulatto Factor in Black Family Genealogy