You age, your height, your mass, the speed at which you run, the energy you burn in doing so. They may be measured as discrete quantities but the underlying variables are all continuous.
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It is not continuous.
Yes, if you have two limiting variables with other possibles variables between them, the variables between the limiting variables would be continuous.
Not continuous => Discrete variable. Continuous => Continuous variable.
the value of variables is determined by the equation, discrete variables have absolute single value while the continuos have a range value
If the variables are something continuous, then you should connect the points. For example, if it is your height and weight then since those variables are continuous it is necessary to connect the points plotted on the coordinate graph.