Neither. It is a discrete variable.
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On the contrary, the number of children in a given family is a discontinuous variable. If you were talking about averagenumbers of children, that would be a continuous variable because the average could be any number, 2.3987, or 3.07428, and so forth. But in a given family, the number of children is always an integer. You can have none, or one, or two, or three, etc., but you cannot have two and a quarter children. So the variable is not continuous.
Continuous variables have an unlimited number of possibilities between two points. In the scientific realm, age is a continuous variable.
Basically categorical variable yield data in the categories e.g sex (male, female), modes of transport (Bus, railway, etc) and numerical variables yield data in numerical form e.g. age (0-100), number of accident on a certain highway (0,1,2,..).
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.
No, the number of employees can only take discrete integer values. For a variable to be continuous, it has to be able to take any/every point of a particular range. e.g. any point between 0 and 1.