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I am wondering how to compare the volatility of two sets of samples.

Can I consider the ratio $\mathrm{Var}(x)/E(x)$ as a normalized variance?

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Yes. The quantity $\sigma^2/\mu$ is called the index of dispersion. You can read about its properties and interpretation on the Wikipedia page, including its use to compare dispersion in different samples. There are some other measures of normalized dispersion as well; see, for example, here. The coefficient of variation $\sigma/\mu$, which is dimensionless (unlike the index of dispersion) is probably the best-known of these other measures.

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