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**undefined** I think you should be thinking mean = expected value for this one. Usually the data is given as exact probabilities, so my terminology may be slightly off since this is just a random sample, but the calculations should be valid.

We take X as the streak length, a discrete random variable, and we assume that the sample distribution reflects the population distribution, so for all intensive purposes the probability of getting a streak of length 0 is

P(0) = 40/78

The expected value is

0*P(0) + 1*P(1) + 2*P(2) + ...

an infinite probability-weighted sum. In this case you should get 58/78 $\displaystyle \approx$ 0.7435897.

That is, we expect over a long period of time that the average streak length will be 58/78.

Increasing sample size should get you closer and closer to the true expected value.