Is weight still a continuous variable if its measure is rounded to an integer? So it is obvious that weight is a continuous variable as it can be quantified with decimal precision;like 10.2 kg and 3.0122 kg.
If we were to round it to an integer like 10 kg and 3 kg. Would then this variable of weight be still considered a continuous numerical variable or discrete.
Asking because my stat text books says that only continuous numerical variables can be used with certain statistical analysis (Regression, ANCOVA .etc). And i wanted to make sure that I can still use certain "continuous variables" who's measurements have been rounded to integers.
 A: The normal distribution is a theoretical continuous function. 
In practice all data is, to some extent (if you look far enough behind the decimal point), discrete.
The normal distribution, in the end, is only used as a useful/easy/handy/simple/manageable approximation to the distribution of the data (this extends to variations from the theoretic distribution beyond the discreteness of data, e.g. different skew/kurtosis). Often unnoticed since the difference is so small, or in other words the approximation is so good (at least due to the aspect of discreteness).
Only in cases of few discrete levels do people consciously think about the deviation of the theoretic Gaussian distribution from the real distribution due to the discreteness of the data. For instance when using a continuity correction when applying a normal approximation to binomial or Poisson distributed data.
A: That assumption concerns more about the sample/population mean distribution, not how your data are recorded. In a way, 10 kg is also 0.01 metric ton, there is no magic introduced in rounding your readings to whole number here.
What you should be asking, however, is why the rounding to begin with. You lose some information that way so if that's not absolutely necessary, keep what they are, and perform necessary rounding only at the last stage when you present the results.
A: Yes, in that case you can still apply methods that work on continuous data. 
One piece of the puzzle is that the integers are a subset of the reals ($\mathbb{Z+} \in \mathbb{R}$). They also follow the same order.
A lazy intuitive argument for this would be to simply consider the input being continuous measurements that take integer values "by chance".
