I assume the date of birth of 1875 on the profile of George's wife Jane is actually a typo - the 1871 census on Frederick's profile shows Jane as being born in 1838. There is also a baptism record on Ancestry showing Frederick's mother was called Jane - see free-to-view image at https://www.ancestry.co.uk/sharing/20041204?h=322820.
On the 1871 census Frederick is shown with Clare, Ellen and George. Their birth records all show their mother's maiden name as BUDWORTH, so I think the maiden name shown on Frederick's birth record that Ros found is also a typo. That means Clare, Ellen and George are all full siblings of Frederick.
George MORGAN married Jane BUDWORTH in 1862 - "England and Wales Marriage Registration Index, 1837-2005," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:2DV7-BQC : 13 December 2014), Jane Budworth, 1862; from "England & Wales Marriages, 1837-2005," database, findmypast (http://www.findmypast.com : 2012); citing 1862, quarter 4, vol. 7B, p. 373, Nottingham, Nottinghamshire, England, General Register Office, Southport, England.
The 1871 census shows Jane being born in Leicester in about 1838. There is a birth registration for Jane BUDWORTH in Leicester in the Oct-Dec quarter of 1837 - "England and Wales Birth Registration Index, 1837-2008," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:2NHK-4W9 : 1 October 2014), Jane Budworth, 1837; from "England & Wales Births, 1837-2006," database, findmypast (http://www.findmypast.com : 2012); citing Birth Registration, Leicester, Leicestershire, England, citing General Register Office, Southport, England.