There is a LDS member's entry in the IGI for ELIZABETH BARRAN Christening: 26 FEB 1837 Kirk Michael, Father: JOHN BARRAN, Mother: ELIZTH. LACE, which is unreliable - but worth checking in the parish register, because members' entries often replace the original transcripts from the register.

Brian Lawson's census index has (1851):
Surname Forename Age Parish Piece Folio Schedule
BARRON Edward 1 Mic 2523 297 30
BARRON Elizabeth 39 Mic 2523 297 30
BARRON Elizabeth 14 Mic 2523 297 30
BARRON Eliza 9 Mic 2523 297 30
BARRON John 39 Mic 2523 297 30
BARRON John 12 Mic 2523 297 30
BARRON Thomas 5 Mic 2523 297 30
BARRON William 3 Mic 2523 297 30
www.iomfhs.im/lawsons/census/c51-b.html

I had a look at the census scan for Michael which has John Barron aged 39 ag lab, b.Michael, with wife Elizabeth, 39, and the 6 children, as above, all b.Michael.

Sue