Ononot — Given a dataset X with mean \mu and variance \sigma^2, we de

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Descriptive Statisticshard

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Given a dataset $X$ with mean $\mu$ and variance $\sigma^2$ , we define a new variable $Y = aX + b$ where $a < 0$ . What is the relationship between the standard deviation of $Y$ ( $\sigma_Y$ ) and the standard deviation of $X$ ( $\sigma_X$ )?