That's interesting since I've checked Robert Preece's official history of the school just to confirm that the coat of arms, which is shown in the centre of the medal, was created for the school's centenary in 1892. On the other hand there's not a huge gulf between "circa 1880" and 1892 and this may even be a later version of the medal.
I can find no trace of the award in the index of Robert Preece's book but I would be interested to find out more about this medal.
Googling it reveals similar information to IHE's plus the name of the winner, a "Lissie Wedderspoon" or on another site "Lizzie Wetherspoon".
I am sufficiently interested to do some checks over the next week or two since I still have access to the school archive which includes enrolment lists.
If it helps, there was only one Wedderspoon listed in 1900 in Inverness at Gowanlea Ballifeary Road. He is listed as John Wedderspoon Sanitary Inspector for the County of Inverness so presumably his daughter