Oh no they didn't. The 1881 was correct for Jane. Here they are in
1871:
4 Nelson Street, Inverness District 98 ED 18 Page 28
Jane McKenzie, hd, 36, sailor's wife, b. Lochbroom
John Mckenzie, 15, sailor abs able seaman), b. Inverness
Alexina McKenzie, 10, scholar, b. Inverness
Catherine McKenzie, 8, scholar, b. Inverness
I presume John,snr, was at sea both 1871 and 1881. I'll have a look.
Gadget