[Answer] What is the square of the standard deviation?

Answer: is step #4 page 41 ??variance

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What is the square of the standard deviation? Sum of the Squares SS - Changing Minds Standard Deviation vs Variance - Difference and Comparison ... Statistics: How to calculate combined mean and SD from 2 ... Statistics Formula: Mean Median Mode & Standard Deviation The square of the standard deviation is called the variance . That is because the standard deviation is defined as the squareroot of the variance . Let X be a random variable with mean value μ: ${\displaystyle \operatorname {E} [X]=\mu .\ \!}$ Here the operator E denotes the average or expected value of X. Then the standard deviation of X is the quantity ${\displaystyle {\begin{aligned}\sigma &={\sqrt {\operatorname {E} \left[(X-\mu )^{2}\right]}}\\&={\sqrt {\operatorname {E} \left[X^{2}\right]+\operatorname {E} [-2\mu X]+\operatorname {E} \left[\mu ^… Let X be a random variable with mean value μ: ${\displaystyle \operatorname {E} [X]=\mu .\ \!}$ Here the operator E denotes the average or expected value of X. Then the standard deviation of X is the quantity ${\displaystyle {\begin{aligned}\sigma &={\sqrt {\operatorname {E} \left[(X-\mu )^{2}\right]}}\\&={\sqrt {\operatorname {E} \left[X^{2}\right]+\operatorname {E} [-2\mu X]+\operatorname {E} \left[\mu ^{2}\right]}}\\&={\sqrt {\operatorname {E} \left[X^{2}\right]-2\mu \operatorname {E} [X]+\mu ^{2}}}\\&={\sqrt {\operatorname {E} \left[X^{2}\right]-2\mu ^{2}+\mu ^{2}}}\\&={\sqrt {\operatorname {E} \left[X^{2}\right]-\mu ^{2}}}\\&={\sqrt {\operatorname {E} \left[X^{2}\right]-(\operatorname {E} [X])^{2}}}\end{aligned}}}$ (derived using the properties of expected value). In other words the standard deviation σ (sigma) is the square root of the variance of X; i.e. it is the square root of the average value of (X − μ) . The standard deviation of a (univariate) probability distribution is the same as that of a random variable having that distribution. Not all random variables have a standard deviation since these expected values need not exist. For example the standard deviation of a random variable that follows a Cauchy distribution is undefined because its expected valu...

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