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Q: What is a line graph in the coordinate plane that has no breaks in it a qualitative graph a continuous graph a discrete graph a cosmograph?

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Discrete.

It is discrete even though time itself is continuous.

Neither, since it is "qualitative data", not "quantitative". Only quantitative data can be discrete or continuous. (Unless your assigning a numerical "value" to each nationality type, in which case it would be quantitative discrete). Answer 2: If considering the percentage, eg 100% Irish, 50% Irish, etc., then it is theoretically a continuous variable, assuming an infinite number of generations. However, in terms of currently existing and past living people, for any nationality, it is a discrete variable.

discrete

Discrete random variable

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It is a discrete variable.

It is discrete even though time itself is continuous.

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