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# 总体与样本标准差回顾

## 总体和样本标准差

• 如果数据本身被视为一个总体, 我们将除以数据点的数量, N.
• 如果数据是来自更大数据集的样本, 我们将除以比样本中的数据点少一个的数, n, minus, 1.

sigma, equals, square root of, start fraction, sum, left parenthesis, x, start subscript, i, end subscript, minus, mu, right parenthesis, squared, divided by, N, end fraction, end square root

s, start subscript, x, end subscript, equals, square root of, start fraction, sum, left parenthesis, x, start subscript, i, end subscript, minus, x, with, \bar, on top, right parenthesis, squared, divided by, n, minus, 1, end fraction, end square root

### 总体标准差

sigma, equals, square root of, start fraction, sum, left parenthesis, x, start subscript, i, end subscript, minus, mu, right parenthesis, squared, divided by, N, end fraction, end square root

### 例子：总体标准差

6, 2, 3, 1

mu, equals, start fraction, 6, plus, 2, plus, 3, plus, 1, divided by, 4, end fraction, equals, start fraction, 12, divided by, 4, end fraction, equals, 3

66, minus, 3, equals, 3
22, minus, 3, equals, minus, 1
33, minus, 3, equals, 0
11, minus, 3, equals, minus, 2

66, minus, 3, equals, 3left parenthesis, 3, right parenthesis, squared, equals, 9
22, minus, 3, equals, minus, 1left parenthesis, minus, 1, right parenthesis, squared, equals, 1
33, minus, 3, equals, 0left parenthesis, 0, right parenthesis, squared, equals, 0
11, minus, 3, equals, minus, 2left parenthesis, minus, 2, right parenthesis, squared, equals, 4

9, plus, 1, plus, 0, plus, 4, equals, 14

start fraction, 14, divided by, 4, end fraction, equals, 3, point, 5

square root of, 3, point, 5, end square root, approximately equals, 1, point, 87

### 样本标准偏差

s, start subscript, x, end subscript, equals, square root of, start fraction, sum, left parenthesis, x, start subscript, i, end subscript, minus, x, with, \bar, on top, right parenthesis, squared, divided by, n, minus, 1, end fraction, end square root

### 例子：样本标准差

2, 2, 5, 7

x, with, \bar, on top, equals, start fraction, 2, plus, 2, plus, 5, plus, 7, divided by, 4, end fraction, equals, start fraction, 16, divided by, 4, end fraction, equals, 4

22, minus, 4, equals, minus, 2
22, minus, 4, equals, minus, 2
55, minus, 4, equals, 1
77, minus, 4, equals, 3

22, minus, 4, equals, minus, 2left parenthesis, minus, 2, right parenthesis, squared, equals, 4
22, minus, 4, equals, minus, 2left parenthesis, minus, 2, right parenthesis, squared, equals, 4
55, minus, 4, equals, 1left parenthesis, 1, right parenthesis, squared, equals, 1
77, minus, 4, equals, 3left parenthesis, 3, right parenthesis, squared, equals, 9

4, plus, 4, plus, 1, plus, 9, equals, 18

start fraction, 18, divided by, 4, minus, 1, end fraction, equals, start fraction, 18, divided by, 3, end fraction, equals, 6

square root of, 6, end square root, approximately equals, 2, point, 45