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# 按步骤计算标准偏差

## 如何计算标准差的概要

$\text{SD}=\sqrt{\frac{\sum _{}^{}|x-\mu {|}^{2}}{N}}$

## 注意

${\text{SD}}_{\text{样本}}=\sqrt{\frac{\sum _{}^{}|x-\overline{x}{|}^{2}}{n-1}}$

## 计算标准偏差的逐步的互动示例

$6,2,3,1$

### 步骤 1: 求出 $\sqrt{\frac{\sum _{}^{}|x-\mu {|}^{2}}{N}}$‍  里面的$\mu$‍

$\mu =$

### 步骤 2: 求出$\sqrt{\frac{\sum _{}^{}|x-\mu {|}^{2}}{N}}$‍ 里面的$|x-\mu {|}^{2}$‍

$6$$9$
$2$
$3$
$1$

### 步骤 3: 求出$\sqrt{\frac{\sum _{}^{}|x-\mu {|}^{2}}{N}}$‍ 里面的$\sum |x-\mu {|}^{2}$‍

$\sum |x-\mu {|}^{2}=$

### 步骤 4: 求出$\sqrt{\frac{\sum _{}^{}|x-\mu {|}^{2}}{N}}$‍ 里面的$\frac{\sum |x-\mu {|}^{2}}{N}$‍

$\frac{\sum |x-\mu {|}^{2}}{N}=$

### 步骤 5: 求出标准差 $\sqrt{\frac{\sum _{}^{}|x-\mu {|}^{2}}{N}}$‍

$\text{SD}=\sqrt{\frac{\sum _{}^{}|x-\mu {|}^{2}}{N}}\approx$

### 总结下我们所做的

$\mu =\frac{6+2+3+1}{4}=\frac{12}{4}=3$

$x$$|x-\mu {|}^{2}$
$6$$|6-3{|}^{2}={3}^{2}=9$
$2$$|2-3{|}^{2}={1}^{2}=1$
$3$$|3-3{|}^{2}={0}^{2}=0$
$1$$|1-3{|}^{2}={2}^{2}=4$
Steps 3, 4, and 5:

## 自己尝试

$\text{SD}=\sqrt{\frac{\sum _{}^{}|x-\mu {|}^{2}}{N}}$

$1,4,7,2,6$

$\text{SD}=$