I often hum to myself in public places but am less inclined to sing properly, except at home where anything goes. My daughters were used to me singing around the house, but once when one of them was having a friend come round after school, she said to me, "Mum, I don't think other people's Mums .. you know... sing around the house like you do..."
In other words "Be quiet and don't embarrass me!"

As for the workmen who sing - we used to have a builder who did odd jobs for us, accompanied by his portable radio. He used to have it playing quite softly but from time to time he would suddenly start bellowing a sort of tuneless backing vocal; "Oh Baby! Ooooh, ahhhh, doop-do-doop!" and so on, which caused us some amusement. We also had a window cleaner who listened to music on headphones and emitted similar sounds as he worked, although we couldn't hear the track he was listening to, and could rarely guess what on earth it was.

Marje