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.
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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.
It is a continuous variable.
No, it is a continuous variable.
Continuous variables have an unlimited number of possibilities between two points. In the scientific realm, age is a continuous variable.