# Random note

## 平均值與標準差

原始數據 $S = \{2, 4, 6, 8, x\}$
數據共有 $n = 5$ 筆
平均值 $\mu = \dfrac{\displaystyle \sum^n_{i=1} S_i}{n} = \dfrac{20+x}{5}$
變異數 $\sigma^2$ = 標準差($\sigma$)的平方 = $\dfrac{\displaystyle \sum^n_{i=1} (S_i - \mu)^2}{n}$
變異數 $\sigma^2$ 也可寫成 $\displaystyle \sum^n_{i=1} S_i^2 - n\mu^2$

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$(2^2+4^2+6^2+8^2+x^2)-5*(\dfrac{20+x}{5})^2=2^2$
$\dfrac{4}{5}x^2+8x+36=0$
$D=b^2-4ac=-51.2<0$
$\therefore \text{實數域無解}$

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