public static void Example_2_3()
{
Basics_of_Statistical_Data_Analysis.Quote();
Console.WriteLine("例題2.3を解きます。");
Console.WriteLine("引用(は例題に関係するNo.1から16のみ記載)\n");
Console.Write("表2.2のうち,No.1から16のデータについて,メジアン,第1四分位数点,第3四分位数点を求めなさい.");
Console.Write("\n\n");
double[,] design_Matrix = new double[16, 1];
design_Matrix[0, 0] = 565; design_Matrix[1, 0] = 685; design_Matrix[2, 0] = 714;
design_Matrix[3, 0] = 743; design_Matrix[4, 0] = 779; design_Matrix[5, 0] = 823;
design_Matrix[6, 0] = 824; design_Matrix[7, 0] = 945; design_Matrix[8, 0] = 967;
design_Matrix[9, 0] = 996; design_Matrix[10, 0] = 1056; design_Matrix[11, 0] = 1089;
design_Matrix[12, 0] = 1102; design_Matrix[13, 0] = 1147; design_Matrix[14, 0] = 1152;
design_Matrix[15, 0] = 1255;
for (int j = 0; j < design_Matrix.GetLength(0); j++)
{
for (int k = 0; k < design_Matrix.GetLength(1); k++)
{
Console.Write(design_Matrix[j, k] + "\t");
}
Console.WriteLine("");
}
Console.WriteLine("\n\n引用終わり\n");
double[,] summary = Statistics.Summary(design_Matrix);
Console.Write("[1,*] 第一四分位数\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[1, k] + "\t");
}
Console.WriteLine("");
Console.Write("[2,*] 中央値\t\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[2, k] + "\t");
}
Console.WriteLine("");
Console.Write("[4,*] 第三四分位数\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[4, k] + "\t");
}
Console.WriteLine("");
}
public static void Example_2_1()
{
Basics_of_Statistical_Data_Analysis.Quote();
Console.WriteLine("例題2.1を解きます。");
Console.WriteLine("引用(数式は改変)\n");
Console.Write("下記は,2015年度の都道府県別栽培きのこ類生産量(単位千円)である。");
Console.Write("このデータについて、平均x_average,メジアンx_medianを計算しなさい。\n");
string[,] Label = new string[7, 1];
Label[0, 0] = "大阪\t";
Label[1, 0] = "佐賀\t";
Label[2, 0] = "山口\t";
Label[3, 0] = "東京\t";
Label[4, 0] = "山梨\t";
Label[5, 0] = "神奈川\t";
Label[6, 0] = "長野\t";
for (int j = 0; j < Label.GetLength(0); j++)
{
Console.Write(Label[j, 0] + "\t");
}
Console.Write("\n");
double[,] design_Matrix = new double[7, 1];
design_Matrix[0, 0] = 14;
design_Matrix[1, 0] = 21;
design_Matrix[2, 0] = 22;
design_Matrix[3, 0] = 23;
design_Matrix[4, 0] = 25;
design_Matrix[5, 0] = 39;
design_Matrix[6, 0] = 4955;
for (int j = 0; j < design_Matrix.GetLength(0); j++)
{
Console.Write(design_Matrix[j, 0] + "\t\t");
}
Console.Write("\n");
Console.WriteLine("\n引用終わり(数式は改変)\n");
double[,] summary = Statistics.Summary(design_Matrix);
Console.WriteLine("[0,*] 最小値\t\t" + summary[0, 0]);
Console.WriteLine("[1,*] 第一四分位数\t" + summary[1, 0]);
Console.WriteLine("[2,*] 中央値\t\t" + summary[2, 0]);
Console.WriteLine("[3,*] 平均値\t\t" + summary[3, 0]);
Console.WriteLine("[4,*] 第三四分位数\t" + summary[4, 0]);
Console.WriteLine("[5,*] 最大値\t\t" + summary[5, 0]);
}
public static void Example_2_2()
{
Basics_of_Statistical_Data_Analysis.Quote();
Console.WriteLine("例題2.2を解きます。");
Console.WriteLine("引用(数式は改変)\n");
Console.Write("次のデータ(a)について,平均x_average,メジアンx_median,偏差平方和S,分散s^2,標準偏差sを計算しなさい。");
Console.Write("次にデータ(b)から(d)のそれぞれについて,x_average,x_median,S,s^2,sを求めなさい。");
Console.Write("その際、(b)のデータは(a)のデータに100を加えている。");
Console.Write("(c)のデータは平均からの偏差が倍であるなどの特徴に着目して計算しなさい。\n\n");
double[,] design_Matrix = new double[9, 4];
design_Matrix[0, 0] = 53; design_Matrix[1, 0] = 55; design_Matrix[2, 0] = 52;
design_Matrix[3, 0] = 57; design_Matrix[4, 0] = 51; design_Matrix[5, 0] = 56;
design_Matrix[6, 0] = 58; design_Matrix[7, 0] = 59; design_Matrix[8, 0] = 54;
design_Matrix[0, 1] = 153; design_Matrix[1, 1] = 155; design_Matrix[2, 1] = 152;
design_Matrix[3, 1] = 157; design_Matrix[4, 1] = 151; design_Matrix[5, 1] = 156;
design_Matrix[6, 1] = 158; design_Matrix[7, 1] = 159; design_Matrix[8, 1] = 154;
design_Matrix[0, 2] = 51; design_Matrix[1, 2] = 55; design_Matrix[2, 2] = 49;
design_Matrix[3, 2] = 59; design_Matrix[4, 2] = 47; design_Matrix[5, 2] = 57;
design_Matrix[6, 2] = 61; design_Matrix[7, 2] = 63; design_Matrix[8, 2] = 53;
design_Matrix[0, 3] = 53; design_Matrix[1, 3] = 55; design_Matrix[2, 3] = 52;
design_Matrix[3, 3] = 57; design_Matrix[4, 3] = 51; design_Matrix[5, 3] = 56;
design_Matrix[6, 3] = 58; design_Matrix[7, 3] = 149; design_Matrix[8, 3] = 54;
Console.WriteLine("(a)\t(b)\t(c)\t(d)");
for (int j = 0; j < design_Matrix.GetLength(0); j++)
{
for (int k = 0; k < design_Matrix.GetLength(1); k++)
{
Console.Write(design_Matrix[j, k] + "\t");
}
Console.WriteLine("");
}
Console.WriteLine("\n\n引用終わり(数式は改変)\n");
double[,] summary = Statistics.Summary(design_Matrix);
Console.Write("[0,*] 最小値\t\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[0, k] + "\t");
}
Console.WriteLine("");
Console.Write("[1,*] 第一四分位数\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[1, k] + "\t");
}
Console.WriteLine("");
Console.Write("[2,*] 中央値\t\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[2, k] + "\t");
}
Console.WriteLine("");
Console.Write("[3,*] 平均値\t\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[3, k] + "\t");
}
Console.WriteLine("");
Console.Write("[4,*] 第三四分位数\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[4, k] + "\t");
}
Console.WriteLine("");
Console.Write("[5,*] 最大値\t\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[5, k] + "\t");
}
Console.WriteLine("");
Console.Write("[6,*] 偏差平方和\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[6, k] + "\t");
}
Console.WriteLine("");
Console.Write("[7,*] 標本分散\t\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[7, k] + "\t");
}
Console.WriteLine("");
Console.Write("[8,*] 標本標準偏差\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[8, k].ToString("G3") + "\t");
}
Console.WriteLine("");
}
public static void Exercise_2_1()
{
Basics_of_Statistical_Data_Analysis.Quote();
Console.Write("第2章 単一変数データの記述統計量と視覚的表現");
Console.WriteLine("演習問題1を解きます。");
Console.WriteLine("引用(数式は改変)\n");
Console.Write("本問は,データ変換後に統計量を計算すると,計算が容易になる例を示している.");
Console.Write("5人の高校生の50m走のタイムx1 , ・・・ , x5 (秒) を6.7 , 6.1 , 7.5 , 7.1 , 6.3 とする.\n\n");
double[,] design_Matrix_x = new double[5, 1];
design_Matrix_x[0, 0] = 6.7; design_Matrix_x[1, 0] = 6.1; design_Matrix_x[2, 0] = 7.5;
design_Matrix_x[3, 0] = 7.1; design_Matrix_x[4, 0] = 6.3;
Console.WriteLine("(a) 5人の高タイムから6を引いて10倍した数値y1 , ・・・ , y5を求めなさい。");
double[,] design_Matrix_y = new double[5, 1];
for (int j = 0; j < design_Matrix_x.GetLength(0); j++)
{
design_Matrix_y[j, 0] = Math.Round(10 * (design_Matrix_x[j, 0] - 6));
Console.WriteLine("y" + (j + 1) + "\t" + design_Matrix_y[j, 0]);
}
Console.WriteLine("");
Console.WriteLine("(b) 上記の5つの数値について,平均,平方和,分散,標準偏差を求めなさい.");
double[,] summary = Statistics.Summary(design_Matrix_y);
Console.Write("[3,*] 平均値\t\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[3, k] + "\t");
}
Console.WriteLine("");
Console.Write("[6,*] 偏差平方和\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[6, k].ToString("G3") + "\t");
}
Console.WriteLine("");
Console.Write("[7,*] 標本分散\t\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[7, k].ToString("G3") + "\t");
}
Console.WriteLine("");
Console.Write("[8,*] 標本標準偏差\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[8, k].ToString("G3") + "\t");
}
Console.WriteLine("");
Console.WriteLine("");
Console.WriteLine("(c) 上記の結果を利用して,この5人の50m走のタイムの平均,平方和,分散,標準偏差を求めなさい.");
Console.WriteLine("y = 10 ( x - 6 )=10x -60");
Console.WriteLine("x = y/10 + 6");
Console.WriteLine("");
Console.WriteLine("したがって、 E[x] = E[y/10 + 6] = E[y]/10 + 6");
Console.Write("[3,*] 平均値\t\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write(summary[3, k] / 10 + 6 + "\t");
}
Console.WriteLine("");
Console.WriteLine("");
Console.WriteLine("同様に、 S[x] = S[y/10 + 6] = S[y/10] = S[y]/10^2");
Console.Write("[6,*] 偏差平方和\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write((summary[6, k] / 100).ToString("G3") + "\t");
}
Console.WriteLine("");
Console.WriteLine("");
Console.WriteLine("s2[x] = s2[y/10 + 6] = s2[y/10] = s2[y]/10^2");
Console.Write("[7,*] 標本分散\t\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write((summary[7, k] / 100).ToString("G3") + "\t");
}
Console.WriteLine("");
Console.WriteLine("");
Console.WriteLine("s[x] = s[y/10 + 6] = s[y/10] = s[y]/10");
Console.Write("[8,*] 標本標準偏差\t");
for (int k = 0; k < summary.GetLength(1); k++)
{
Console.Write((summary[8, k] / 10).ToString("G3") + "\t");
}
Console.WriteLine("");
}
