[bhritchie]

The first paragraph reminds me of the great example by which J.L. Austin distinguished precision from exactness: a stick could be exactly, but not precisely, six bananas long.

In the present case we could say that six random bananas could accurately but not precisely represent the length of a stick.

[bitofhope]

My go-to example of explaining accuracy vs. precision is the distance from Earth to its moon. 400 000 km or 250 000 miles is a fairly accurate, but imprecise figure. 31 415 926 nanometers is a ludicrously precise, and incredibly inaccurate one.

Also, accuracy is dependent on appropriate precision. Rounded up to nearest billion kilometers the moon is zero terameters away from the Earth, which is only accurate if you're comparing it on a scale where the Moon is insignificant. Conversely, reporting the exact distance to the nearest meter will imply variations insignificant on one-meter scale, which is obviously wrong, making a less precise figure more accurate for use over an arbitrary period of time.