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1 solution
Define the variance as:
V(x) = SUM{1 <= i <=7: p i * (x i - mean)^2} (i)
where x i is our discrete random variable. The numbers 1, 2, ..., 7 are each equally likely (hence p i = 1/7, and their mean equals 4. Plugging away these values into (i) above yields 4 for the result.