As I was doing some family history, I came across two relatives that died at sea. One was the daughter of the other, she died about 4 days before the mother. My question is, on the passenger arrival list they were both listed the daughter as died at sea and the date, the mother was not. The mother's death date is listed (every where I have found it to be listed) as 26 July 1872, the ship made it's arrival on 27 July 1872. Can anyone explain this?
The passenger manifest is not an arrival record.
The manifest is the record created by the shipping company before departure. It is updated as needed during and after the journey.
Sometimes entries are crossed out in a manifest. This indicates people who bought tickets but did not actually board.
And sometimes people die aboard the boat. This will be noted in the manifest. It might be in the main section or it could be in a special section at the end for people who were detained after arrival (presumably the bodies would have been kept until someone could pick them up for burial, if not buried at sea; and their personal effects would also have been held). Many times unusual situations are recorded in both locations. Not all passages around 1872 had great records, so you might never get very much.
If people were sick when the boat arrived in port, they would be detained until they got better or were transferred somewhere else. It's entirely possible that the mother in your question was alive when the boat arrived at its destination but did not survive long enough to leave it.
Find the detention section of the manifest, if there is one. You may need to do some manual paging through the document online for this. It's not always at the end because Ancestry and other places often combine multiple manifests in the same set of scans. But it will be at the end of the individual manifest.
Your best bet is to find the death certificate. It would have been recorded in the city where the port is located.