Each of those is better in some situations. Also, you often have no choice. Some
quantities, like speed and temperature, are inherently continuous, whereas some
quantities, like the number of girls, cars, or beans, are inherently discrete.
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Date is a discrete variable whereas date/time would be continuous.
Hair color is considered a discrete variable because it falls into distinct categories such as blonde, brown, black, red, etc. Each category is separate and distinct from the others, with no intermediate shades. In contrast, a continuous variable would have an infinite number of possible values within a range, which is not the case with hair color.
No, this is a discrete variable since it can assume only whole number values: 0, 1, 2, 3, ... . A continuous variable would be one such as volume of water in a swimming pool which could be measured in real number units of volume.
If there is one independent variable, and one or more dependent variables, then they would be plotted on the y-axis. If there are a mix of discrete and continuous variables, then the continuous variables should be plotted on the y-axis. In general, though, any variable can be plotted on the y-axis.
No, it is a discrete variable. Since there are no fractional people, a count of people can only be a positive integer. For a variable to be continuous, it must be able to take on *any* real value in a domain. So, if populations could take on any real value, including rational and irrational ones, between 1 and say 10^12, including ones like 6.1385391..., then population would be a continuous variable.