# Is "The number of points scored during a basketball game." discrete or continuous?

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Discrete.

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A random variable is considered **discrete** if its possible values are countable. In a basketball game, for example, it is only possible for a team's score to be a whole number—no fractions or decimals are allowed, and so the score is discrete.

In statistics, it is possible for a discrete random variable to take on a specific, single value with non-zero probability. For example, if we let

On the other hand, a **continuous** random variable is one where the range of its possible values is uncountable. Good examples are time, length, mass, temperature, etc. It is not possible for an event to occur *exactly* at 4:27pm, or a person's height *exactly* 1.65 meters. There will always be some decimal places that we can't measure. In statistics, this is written as

For a continuous random variable, we must talk about the probability of it being *within a range* of values. We could find a value for

A good rule of thumb is this: if the variable you're measuring has to be rounded before it's written down, then it's continuous. If no rounding is necessary, as with anything that's countable, then it's discrete.

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