No, they do not. They are pure numbers.
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It's obviously part of the lethogram which is used to measure ciramic units.
They are effectively the same but the standard deviation is more popular because the units of measurement are the same as those for the variable.
The same units as the mean itself. If the units of the mean, are, for example miles; then the error units are miles.
No. The units of the two variables in a correlation will not change the value of the correlation coefficient.
Discrete means tangible units (In statistics it is individual units in a data). Continuous is a linear/series in ascending/descending form/order of individual units. (In statistics it is the continuous series of unit data)