This record seems to contain some incorrect information in listing Joseph and Sarah's children as the offspring of William - William would have had his first child at the age of 14. However, it makes sense if the children (with the exception of Mary) listed are considered the offspring of Joseph and Sarah. The birth order of children matches the order shown in Joseph’s citizenship application. Perhaps Mary was the daughter of William and Mary.
The 1881 Census for England and Wales lists:
Joseph Phibbs
Age (Original): 30
Gender: Male
Birth Year: 1851
Birthplace: Dudley, Worcestershire, England
Relationship to Head of Household: Cousin
Address: 6 Boscobel St
Event Place: Tipton, Staffordshire, England
Record Type: Household
Affiliate Publication Number: RG11
Piece/Folio: 2863 / 145
Page Number: 19
William Phibbs Head M 23 Dudley, Worcestershire, England
Mary A Phibbs Wife F 23 Dudley, Worcestershire, England
John Phibbs Son M 9 Dudley, Worcestershire, England
William Phibbs Son M 7 Dudley, Worcestershire, England
Joseph Phibbs Son M 4 Dudley, Worcestershire, England
Mary A Phibbs Daughter F 2 Dudley, Worcestershire, England
Sarah A Phibbs Daughter F 0 Tipton, Staffordshire, England
Joseph Phibbs Cousin M 30 Dudley, Worcestershire, England
Sarah Phibbs Cousin F 29 Dudley, Worcestershire, England
"England and Wales Census, 1881," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/X3VF-YMH : accessed 28 Nov 2014), Joseph Phibbs in household of William Phibbs, Tipton, Staffordshire, England; from "1881 England, Scotland and Wales census," index and images, findmypast (www.findmypast.co.uk : DC Thomson, n.d.); PRO RG 11/, p. , The National Archives, Kew, Surrey; FHL microfilm .