# Uncertainty Principle - Accuracy or Precision? [closed]

While discussing about the Uncertainty Principle, some books use the word 'accuracy' and some other books use the word 'precision'. Some even use them both interchangeably.
For instance, in Griffiths' text, he says that

the more precisely determined a particle's position is, the less precisely is its momentum.

In Feynman lectures,

If you make the measurement on any object, and you can determine the $$x$$-component of its momentum with an uncertainty $$Δp$$, you cannot, at the same time, know its $$x$$-position more accurately than $$\Delta x≥ℏ/2\Delta p$$.

In Quantum Physics by Eisberg and Resnick,

Our precision of measurement is inherently limited by the measurement process itself such that $$\Delta x\Delta p_{x}≥ℏ/2$$ ....
the more we modify an experiment to improve our measure of $$p_{x}$$, the more we give up ability to determine $$x$$ accurately.

Which is the right word to use - accuracy or precision?
What does the term 'uncertainty of a single variable' in quantum mechanics mean? Can it be explained without going into the uncertainty principle?

The word that is most correct is variance. One should not forget that each single measurement of $$x$$ or $$p$$ will yield a (more or less) concrete value. The $$\Delta x$$ however stands for the variance that you get when making repeated measurement at identical quantum systems.
Therefore, the sentence "you cannot know its x-position more accurately than..." is meant in the following sense: Repeated measurements of $$x$$ will give you a variance greater than $$\hbar/2 \Delta p$$, so you cannot get a "sharper" set of measurements and there is always a lower bound on variance. Variance is a measure for the "accuracy" of your measurement in a sense known to all experimentalists, because it determines how large the "possible error" is that has to be given with each measurement result.