This is known locally as The Stone Man and sits in front of Laigh Markethill cottage. Market Hill Road continues up thee hill towards Glasgow from here and was originally the site of the market during the time when the plague was present in Glasgow. This meant that traders from Glasgow would be kept out of East Kilbride on market days.
The following exert is from East Kilbride, the History of Parish and Village by Thomas Eric Niven, published originally in 1965
"Many stories have been woven around its origin but none more fanciful as this. At one time Laigh Markethill was occupied by Davie Robertson, a local stone mason and master builder, who was responsible for many houses and farm buildings in this district. As a youthful apprentice, the story goes, Dauvit was fired with the idea of becoming a famous sculptor. He procured a block of freestone from a neighbouring field, hid it in a shed, and worked upon it secretly at night. When the task was completed, he invited his neighbours to view the work and state the name of the famous man represented. Many guesses were hazarded, all wide of the mark and Robertson, bitterly disappointed, dug a hole in the garden and buried the statue. There it lay until it was ressurected after his death.
The truth of the matter is that Robertson, though a skilful tradesman, never found time for sculpting, but procured the figure from William Arneil, an Eaglesham mason, who had actually carried out the carving. The Stone Man - a figure of Sir Walter Scott, of course - was the scene of the local celebrations in honour of the great novelist's centenary in 1871.
William Gememell, an Eaglesham master joiner, made a considerable number of stone figures which can still be seen at Pillar House, Eaglesham. Gemmell was credited with the East Kilbride figure, but he denied this, allowing, that the East Kilbride figure had actually encouraged him to do something better"
As a child I remember when this had no head, but I'm unsure if that was the case or when it would have been repaired. If you do know, please let me know if your log.
The coordinates have been recorded using an iphone and as such can be inaccurate. It is a magnetic nano and I have given you a good hint...good luck!