方差的化简：
∑ ( a i − a v e ) 2 n \frac{\sum (a_i-ave)^2}{n} n∑(ai−ave)2
= ∑ a i 2 + a v e 2 − 2 a i a v e n =\frac{\sum a_i^2+ave^2-2a_iave}{n} =n∑ai2+ave2−2aiave
= ∑ a i 2 n + ∑ a v e 2 n − 2 a v e ∑ a i n =\frac{\sum a_i^2}{n}+\frac{\sum ave^2}{n}-\frac{2ave\sum a_i}{n} =n∑ai2+n∑ave2−n2ave∑ai
= ∑ a i 2 n + a v e 2 − 2 a v e ∑ a i n =\frac{\sum a_i^2}{n}+ave^2-\frac{2ave\sum a_i}{n} =n∑ai2+ave2−n2ave∑ai
= ∑ a i 2 n + a v e 2 − 2 a v e 2 =\frac{\sum a_i^2}{n}+ave^2-2ave^2 =n∑ai2+ave2−2ave2
= ∑ a i 2 n − a v e 2 =\frac{\sum a_i^2}{n}-ave^2 =n∑ai2−ave2
方差的化简
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转载自blog.csdn.net/zhy_Learn/article/details/118819398
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