C#使用Linq和Loop计算集合的平均值、方差【标准差】

方差【标准差】

标准差公式是一种数学公式。标准差也被称为标准偏差，或者实验标准差，公式如下所示：

样本标准差=方差的算术平方根=s=sqrt(((x1-x)^2 +(x2-x)^2 +......(xn-x)^2)/n)

总体标准差=σ=sqrt(((x1-x)^2 +(x2-x)^2 +......(xn-x)^2)/n )

注解：上述两个标准差公式里的x为一组数（n个数据）的算术平均值。当所有数（个数为n）概率性地出现时（对应的n个概率数值和为1），则x为该组数的数学期望。

公式意义

所有数（个数为n）记为一个数组[n]。将数组的所有数求和后除以n得到算术平均值。数组的所有数分别减去平均值，得到的n个差值分别取平方，再将得到的所有平方数求和，然后除以数的个数或个数减一若所求为总体标准差则除以n,若所求为样本标准差则除以(n-1)，最后把得到的商取算术平方根，就是取1/2次方，得到的结果就是这组数(n个数据)的标准差。

新建窗体应用程序AverageAndDeviationDemo，将默认的Form1重命名为FormAverageAndDeviation。

窗体FormAverageAndDeviation的视图编辑器源程序如下：

FormAverageAndDeviation.Designer.cs


namespace AverageAndDeviationDemo
{partial class FormAverageAndDeviation{/// <summary>/// 必需的设计器变量。/// </summary>private System.ComponentModel.IContainer components = null;/// <summary>/// 清理所有正在使用的资源。/// </summary>/// <param name="disposing">如果应释放托管资源，为 true；否则为 false。</param>protected override void Dispose(bool disposing){if (disposing && (components != null)){components.Dispose();}base.Dispose(disposing);}#region Windows 窗体设计器生成的代码/// <summary>/// 设计器支持所需的方法 - 不要修改/// 使用代码编辑器修改此方法的内容。/// </summary>private void InitializeComponent(){this.rtxtMessage = new System.Windows.Forms.RichTextBox();this.btnGenerate = new System.Windows.Forms.Button();this.label1 = new System.Windows.Forms.Label();this.SuspendLayout();// // rtxtMessage// this.rtxtMessage.Location = new System.Drawing.Point(217, 95);this.rtxtMessage.Name = "rtxtMessage";this.rtxtMessage.Size = new System.Drawing.Size(687, 550);this.rtxtMessage.TabIndex = 0;this.rtxtMessage.Text = "";// // btnGenerate// this.btnGenerate.Location = new System.Drawing.Point(38, 93);this.btnGenerate.Name = "btnGenerate";this.btnGenerate.Size = new System.Drawing.Size(149, 23);this.btnGenerate.TabIndex = 1;this.btnGenerate.Text = "生成随机集合后开始比较";this.btnGenerate.UseVisualStyleBackColor = true;this.btnGenerate.Click += new System.EventHandler(this.btnGenerate_Click);// // label1// this.label1.AutoSize = true;this.label1.Location = new System.Drawing.Point(215, 64);this.label1.Name = "label1";this.label1.Size = new System.Drawing.Size(143, 12);this.label1.TabIndex = 2;this.label1.Text = "迭代Loop与Linq性能比较:";// // FormAverageAndDeviation// this.AutoScaleDimensions = new System.Drawing.SizeF(6F, 12F);this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;this.ClientSize = new System.Drawing.Size(981, 714);this.Controls.Add(this.label1);this.Controls.Add(this.btnGenerate);this.Controls.Add(this.rtxtMessage);this.Name = "FormAverageAndDeviation";this.Text = "计算集合平均值和标准差【方差】的示例";this.Load += new System.EventHandler(this.FormAverageAndDeviation_Load);this.ResumeLayout(false);this.PerformLayout();}#endregionprivate System.Windows.Forms.RichTextBox rtxtMessage;private System.Windows.Forms.Button btnGenerate;private System.Windows.Forms.Label label1;}
}

窗体代码如下：

FormAverageAndDeviation.cs

using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Diagnostics;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows.Forms;namespace AverageAndDeviationDemo
{public partial class FormAverageAndDeviation : Form{public FormAverageAndDeviation(){InitializeComponent();rtxtMessage.ReadOnly = true;}/// <summary>/// 显示操作内容/// </summary>/// <param name="text"></param>private void DisplayMessage(string text) {this.BeginInvoke(new Action(() => {if (rtxtMessage.TextLength > 20480) {rtxtMessage.Clear();}rtxtMessage.AppendText($"{DateTime.Now.ToString("HH:mm:ss.fff")}->{text}\n");rtxtMessage.ScrollToCaret();}));}private void FormAverageAndDeviation_Load(object sender, EventArgs e){List<double> array = new List<double>() { 1, 2, 3, 4, 5, 6 };CalculateAverageAndDeviation(array);CalculateAverageAndDeviationUseLoop(array);}/// <summary>/// 计算 平均值和 标准差【方差】/// 使用Linq迭代查询/// </summary>/// <param name="array"></param>private void CalculateAverageAndDeviation(IList<double> array) {if (array == null || array.Count == 0) {throw new ArgumentException($"无法对空集合求取平均值");}Stopwatch stopwatch = new Stopwatch();stopwatch.Start();//获取 平均值double average = array.Average();//获取方差之和double sumDeviation = array.Select(x => Math.Pow(x - average, 2)).Sum();//目标 标准差double standardDeviation = Math.Sqrt(sumDeviation / array.Count);stopwatch.Stop();double elapsedTime = stopwatch.Elapsed.TotalMilliseconds;//耗时msDisplayMessage($"【Linq】average:{average}\nsumDeviation:{sumDeviation}\nstandardDeviation:{standardDeviation}\nElapsedTime:{elapsedTime}ms");}/// <summary>/// 计算 平均值和 标准差【方差】/// 使用循环迭代器/// </summary>/// <param name="array"></param>private void CalculateAverageAndDeviationUseLoop(IList<double> array){if (array == null || array.Count == 0){throw new ArgumentException($"无法对空集合求取平均值");}Stopwatch stopwatch = new Stopwatch();stopwatch.Start();double sum = 0;for (int i = 0; i < array.Count; i++){sum += array[i];}//获取 平均值double average = sum / array.Count;sum = 0;for (int i = 0; i < array.Count; i++){sum += Math.Pow(array[i] - average, 2);}//获取方差之和double sumDeviation = sum;//目标 标准差double standardDeviation = Math.Sqrt(sumDeviation / array.Count);stopwatch.Stop();double elapsedTime = stopwatch.Elapsed.TotalMilliseconds;//耗时msDisplayMessage($"【Loop】average:{average}\nsumDeviation:{sumDeviation}\nstandardDeviation:{standardDeviation}\nElapsedTime:{elapsedTime}ms");}/// <summary>/// 生成10.0~99.9之间的随机集合/// </summary>/// <param name="count"></param>/// <returns></returns>private double[] GenerateRandomArray(int count) {double[] array = new double[count];for (int i = 0; i < count; i++){array[i] = new Random(i + 1).Next(100, 1000) * 0.1;}return array;}private async void btnGenerate_Click(object sender, EventArgs e){double[] array = GenerateRandomArray(500);DisplayMessage($"打印源数组【{string.Join(",", array)}】");Task linqTask = Task.Run(() => CalculateAverageAndDeviation(array));Task loopTask = Task.Run(() => CalculateAverageAndDeviationUseLoop(array));Task.WaitAll(linqTask, loopTask);await loopTask;}}
}