origin求解方差方法

### 如何在编程中计算方差 #### Java 中计算方差 Java 实现方差计算的核心在于先求得各个数值与均值之差的平方和，再除以数据长度来获得方差。 ```java public class VarianceCalculator { public static void main(String[] args) { double[] data = {1.0, 2.0, 3.0, 4.0}; // 计算平均数 double mean = calculateMean(data); // 计算方差 double variance = calculateVariance(data, mean); System.out.println("The calculated variance is " + variance); } private static double calculateMean(double[] data){ double sum = 0; for (double num : data) { sum += num; } return sum / data.length; } private static double calculateVariance(double[] data, double mean){ double sumOfSquaredDifferences = 0; for (double num : data) { sumOfSquaredDifferences += Math.pow(num - mean, 2); } return sumOfSquaredDifferences / data.length; // 计算方差[^1] } } ``` #### C/C++ 中计算方差 对于C/C++而言，同样遵循上述逻辑流程，即先求取样本均值随后基于此计算各观测值减去该均值得到的结果的平方总和并最终得到方差。 ```cpp #include <iostream> #include <vector> #include <cmath> using namespace std; int main(){ vector<double> numbers{1.0, 2.0, 3.0, 4.0}; double avg = accumulate(numbers.begin(),numbers.end(),0.0)/numbers.size(); double var=0.0; for(auto &num:numbers) var+=pow((num-avg),2); cout << "Calculated variance is:"<<var/numbers.size()<<endl;// 计算方差[^2] return 0; } ``` #### Python 中定义函数计算方差 Python 提供了一种简洁的方式来创建用于执行特定任务的功能模块——函数。下面展示了一个简单的例子，其中定义了一个名为`calculate_variance()` 的函数来进行方差运算。 ```python def calculate_mean(values): """Calculate the arithmetic mean of a list of numbers.""" n = len(values) total_sum = sum(values) if n == 0: raise ValueError('Cannot compute the mean of an empty list.') average_value = float(total_sum/n) return average_value def calculate_variance(values): """Compute sample variance via a function""" n = len(values) if n == 0: raise ValueError('Cannot compute variance from no data.') mu = calculate_mean(values) squared_diffs = [(x-mu)**2 for x in values] variance = sum(squared_diffs)/(n-1) # 使用无偏估计量[n-1]而非[n][^4] return variance data_points=[1.,2.,3.,4.] print(f'The computed variance value is {calculate_variance(data_points)}') ```