1 text format
/// <summary>
/// Lesson 18 of "Xiaobai Programming": Random Number (Random) Fifth, the calculation method and code of variance and standard deviation (standard deviation)
/// Variance = SUM((Xi - X)^2 ) / n i=0...n-1 X = Average of X[i]
/// The variance is the sum of the squares (each value minus the average value), and then divided by the number.
/// The square of the variance = the standard deviation, otherwise, just take the square root.
/// This lesson is to verify the previous normal distribution function.
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
private void button18_Click(object sender, EventArgs e)
{ // Number of random numbers int m = 50000; // Range of random numbers (0---1023) int n = 1024; int[] num = new int[m]; int i = 0; while (i < m) { // Generate random numbers from a normal distribution // mean = 0.
int a = (int)(Rand(0.5, 0.1) * n);
if (a < 0) continue;
if (a >= n) continue;
num[i++] = a;
}
// Calculate the average
double sum = 0.0;
for (int j = 0; j < m; j++)
{ sum += num[j]; } double avg = sum / (double)m;
// Calculate the variance
double delta = 0.0;
for (int j = 0; j < m; j++)
{ // Original way of writing //delta = delta + (num[j] - avg) * (num[j] - avg) ; // Another way to write delta += Math.Pow((num[j] - avg), 2); } // Variance double variance_1 = delta / (double)m; // Standard deviation double standard_variance_1 = Math.Sqrt (delta / (double)(m)) / (double)n;
#region For more serious algorithms, the data should be normalized first,
// normalize the data to (0 --- 1.0) and then calculate the variance and so on.
double[] xnum = new double[m];
for (int j = 0; j < m; j++)
{ xnum[j] = num[j] / (double)n; } // mean also needs normalization avg /= n; // calculate variance delta = 0.0; for (int j = 0; j < m; j++) { delta += Math.Pow((xnum[j] - avg), 2.0); } double standard_variance_2 = Math.Sqrt (delta / (double)(m)); #endregion
StringBuilder sb = new StringBuilder();
sb.AppendLine("average=" + avg + "<br>");
sb.AppendLine("variance=" + variance_1 + "<br>");
sb.AppendLine(" Standard variance=" + standard_variance_1 + "<br>");
sb.AppendLine("Standard variance=" + standard_variance_2 + " (calculated after normalizing data)<br>");
webBrowser1.DocumentText = sb.ToString();
}
2 code format
/// <summary>
/// 《小白学程序》第十八课：随机数（Random）第五，方差及标准方差（标准差）的计算方法与代码
/// 方差 = SUM(（Xi - X)^2 ) / n i=0...n-1 X = Average of X[i]
/// 方差是 (各数值减去平均值)的平方 之和，再除以个数。
/// 方差的平方 = 标准差，反之，开平方即可。
/// 本课是为了验证前面的正态分布函数。
/// </summary>
/// <param name="sender"></param>
/// <param name="e"></param>
private void button18_Click(object sender, EventArgs e)
{
// 随机数个数
int m = 50000;
// 随机数的范围（0---1023）
int n = 1024;
int[] num = new int[m];
int i = 0;
while (i < m)
{
// 按正太分布生成随机数
// 平均值 = 0.5 * n
// 标准差 = 0.1 * n
int a = (int)(Rand(0.5, 0.1) * n);
if (a < 0) continue;
if (a >= n) continue;
num[i++] = a;
}
// 计算平均值
double sum = 0.0;
for (int j = 0; j < m; j++)
{
sum += num[j];
}
double avg = sum / (double)m;
// 计算方差
double delta = 0.0;
for (int j = 0; j < m; j++)
{
// 原始写法
//delta = delta + (num[j] - avg) * (num[j] - avg);
// 另一种写法
delta += Math.Pow((num[j] - avg), 2);
}
// 方差
double variance_1 = delta / (double)m;
// 标准差
double standard_variance_1 = Math.Sqrt(delta / (double)(m)) / (double)n;
#region 更严肃的算法，应该先进行数据规范化，
// 将数据规整到（0 --- 1.0）再计算方差等等。
double[] xnum = new double[m];
for (int j = 0; j < m; j++)
{
xnum[j] = num[j] / (double)n;
}
// 均值也需要规范化
avg /= n;
// 计算方差
delta = 0.0;
for (int j = 0; j < m; j++)
{
delta += Math.Pow((xnum[j] - avg), 2.0);
}
double standard_variance_2 = Math.Sqrt(delta / (double)(m));
#endregion
StringBuilder sb = new StringBuilder();
sb.AppendLine("平均值=" + avg + "<br>");
sb.AppendLine("方差= " + variance_1 + "<br>");
sb.AppendLine("标准方差=" + standard_variance_1 + "<br>");
sb.AppendLine("标准方差=" + standard_variance_2 + " （规范数据后计算）<br>");
webBrowser1.DocumentText = sb.ToString();
}
3 Calculation results
