Let \(X\) be the random variable denoting the number of heads out of 100 independent, fair coin tosses. What is the variance of \(X\)?

**Details and assumptions**

The **variance** of a random variable measures the extent to which values are spread out. It can be calculated as \( \mbox{Var}(X) = \sum (X- \bar{X})^2 f(x) \).

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