Measure equals Estimate

The distinction between a Measurement and an Estimate is artificial and not useful.

We have got into a lazy habit of thinking that a measurement is perfect and an estimate nearly worthless. Both parts of that are just wrong.

Any real measurement has uncertainty in it. If we measure a distance with a tape measure, we may see uncertainty when the tape measure sags a bit between the two points, but we might not be thinking about whether it has stretched over time, or whether the air temperature now has caused it to be longer or shorter than it was when it left the factory.

So a measurement we write down represents in fact a range of possible values. We may not think about those things because, for the purpose of the measurement, they are probably too small to matter. If we had a sense that they might matter, we could write down an estimate of the minimum and maximum real values the measurement might represent. So then our measurement is clearly in fact, an estimate.

If our measurement uses a well used cloth surveyor's tape measure it might well have stretched with age but is unlikely to have got shorter. So the central value of our tape measurement will be close to the maximum value (the reading from a stretched tape), but perhaps further from the minimum value (the reading from a tape that has never stretched at all).

So too with an estimate. A useful estimate also has at least three values: a minimum likely value, a maximum likely value and a central value (probably not half way between minimum and maximum, if we think about it with a little care). Unfortunately often, we only get to see the central value and perhaps no evidence that the author has even thought about the minimum and maximum values.