In the standard way of definining it, probability values are unitless. Say you had 2 green apples and 1 red apple. The probability of you picking a red apple is (1 apple)/(3 apples)=1/3. Essentially, the units of "apple" cancel, leaving only a number.
However, the mean, mode, median, variance, and standard deviation all have units. The first three are essentially ways of averaging, and so must have units of apples. The variance has units of apples^2, and the standard deviation has units of apples.
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