Discrete Random Process Can instance average be greater than global average?

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Assume that I am observing samples of a random variable I am interested in on a daily basis. For now, assume that number of samples I observe daily is fixed to some $K$. After a period of N days, I take the samples across all days estimate the mean. Also, I calculate a daily average. Is it possible that daily average is higher than the mean for most of the days? PS: This question is not clearly thought out. Please feel free to point out the issues.