Hi. - Donna posted a burial for James Hogg age 25 Braddan 3 Jun 1847, which makes him b.c. 1822, so your b.1823 looks right. What is confusing?

As it looks as though Jane Kelly was only 20 at their marriage, he must have been around the same age. It would be worth looking at the marriage record (on LDS film if not in the Manx Museum) to see what was written about permission to marry, because of being underage.

You can look at the IGI for yourself (on FamilySearch.org), to see the baptism you have been given:
JAMES HOGG Christening: 03 APR 1823 Saint George, Douglas, Isle Of Man Father: ALEXANDER HOGG, Mother: CATHERINE.

Other children at that time with father Alex. Hogg and mother Catherine:
MARGARET HOGG Christening: 07 AUG 1825 Saint George, Douglas. Death: 26 SEP 1825. Father: ALEXANDER HOGG, Mother: CATHERINE PRECIE
THOMAS HOGG Christening: 04 MAR 1827 Saint Mathews, Douglas, Father: ALEXANDER HOGG, Mother: CATHRINE PRESTON
ALEXANDER HOGG Christening: 02 SEP 1830 Saint Mathews, Douglas, Father: ALEXANDER HOGG, Mother: CATHERINE
JOHN HOGG Christening: 16 JAN 1833 Saint Mathews, Douglas, Father: ALEXANDER HOGG, Mother: CATHERINE PLASSER
JOSEPH HOGG Christening: 01 OCT 1840 Saint Barnabas, Douglas, Father: ALEXANDER HOGG, CATHN ROBINSON. [all IGI]

I couldn't see a marriage for Alexander Hogg & Catherine in the IoM.

In the 1841 census the House of Industry in Onchan has:
Catharine Hogg 45 born "F" (Foreign parts) i.e. not IoM, Eng., Ire., Scot.
Joseph Hogg 7 Pauper Inmate "Y" (IoM)
Alexander Hogg, 12 " " "Y"
[not listed together].

What happened to Mary Jane HOGG bapt 1 Feb 1846? Where was she in 1861?

Sue