as a previous poster said, the average resting heart rate for an adult is between 60-100. Every ten years after 20, the 'average' heart rate increases by about 10. So, in your 30's, 70-110 average, 40's 80-120 average, 50's 90-130 is 'average'.
This is the system medics have been using since around 1890, and it's only recently that medics have started expressing concerns around elevated heart rates within this narrower 60-100 bpm range, without factoring in age related changes, and that's probably 'big pharma' can start prescribing heart meds to people who clinically have no real need for them, and increasing profits for their companies...
If you're in your 40's/50's and you have a resting heart rate of 60, you're probably really healthy. (or you're taking beta-blockers).
My resting heart rate is also 60, and when I exercise hard I'm around 175. Walking, fast, I'm about 140. Totally normal. (for me). I do good cardio, and have a strong, healthy heart. If my resting heart rate was 135, I'd be concerned for myself, but, if I was 50 years old, and did no regular exercise, I wouldn't be too arsed.
certain medications, smoking, drinking, drug-taking, can all increase your resting heart rate. regular exercise and meditation have been proven to decrease it.
There's also a recognised phenomena called 'white coat syndrome'. Basically, people who are having bp/heart rate measurements often have higher than expected readings, thought to be triggered by the situation/fear/anticipation/nerves, etc. Even though you feel perfectly relaxed, the parasympathetic nervous system rushes adrenaline through you, elevating your bp and heart rate.
If you're concerned about your heart rate, you can buy a machine for around £30, on amazon, do your own readings at home, synch it to your phone, gives you a more accurate picture. You can take your stats to medical appointments, too. Nobody minds.