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  "body": "\n## Definition\n\nLet $X$ be a real random variable with finite [[variance|007QED3E0Y]].\nThe standard deviation of $X$ is the [[square root|0VB8BFRABH]]\n$$\\sigma_X = \\sqrt{\\operatorname{Var}(X)} = \\sqrt{E\\left[(X - E[X])^2\\right]}.$$\n\n## Remarks\n\nThe standard deviation is in the same units as $X$, but the variance is in squared units.\nFor $a, b \\in \\mathbb{R}$, $\\sigma_{aX + b} = |a| \\, \\sigma_X$.\nFor the [[normal distribution|07RXBVTVZB]] $\\mathcal{N}(\\mu, \\sigma^2)$, the standard deviation is $\\sigma$. About $68\\%$ of the mass lies within one standard deviation of the mean.\n\n## Explanations\n\n### L1 human\n\nThe standard deviation is a typical size of the distance between a value and the mean.\nA small standard deviation means that the values stay close to the mean. A large one means that they spread out.\n",
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