母體標準差的計算
Author: 藍邦偉老師

$%v筆資料$

$ 母體標準差的計算 $

$μ\;為整數：\; σ^2=\frac{1}{n}\sum_{i=1}^{n}{ (x_i-μ)²}$

$ μ\;不為整數：\;σ²=\frac{1}{n}\sum_{i=1}^{n}{x_i^2 }-μ²$

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$第%v步$

s = 0.2 (slider from 0 to 1, step 0.1)
k = 4 (slider from 4 to 8, step 1)
List = Sequence(Random[1, 10] + 0 * s, t, 1, k)
Sum = Sum(List)
μ: Sum / k
a = Element(List, 1)
a_1 = Element(List, 1)
a_2 = Element(List, 2)
a_3 = Element(List, 3)
a_4 = Element(List, 4)
a_5 = Element(List, 5)
a_6 = Element(List, 6)
a_7 = Element(List, 7)
a_8 = Element(List, 8)
σ_{xx} = SXX(List)
t_{13}: "$ =" + (LaTeX[σ_{xx} / k]) + " $"
b = false
c = false
t_{21}: "$σ²=\frac{1}{" + (LaTeX[k]) + "}[" + (LaTeX[a_1]) + "^2+" + (LaTeX[a_2]) + "^2+" + (LaTeX[a_3]) + "^2+" + (LaTeX[a_4]) + "^2" + (LaTeX[If[k ≥ 5, "+"]]) + "" + (LaTeX[a_5]) + "" + (LaTeX[If[k ≥ 5, "^2"]]) + "" + (LaTeX[If[k ≥ 6, "+"]]) + "" + (LaTeX[a_6]) + "" + (LaTeX[If[k ≥ 6, "^2"]]) + "" + (LaTeX[If[k ≥ 7, "+"]]) + "" + (LaTeX[a_7]) + "" + (LaTeX[If[k ≥ 7, "^2"]]) + "" + (LaTeX[If[k ≟ 8, "+"]]) + "" + (LaTeX[a_8]) + "" + (LaTeX[If[k ≟ 8, "^2"]]) + "] -" + (LaTeX[μ]) + "^2 $"
t_{11}: "$σ² =\frac{1}{" + (LaTeX[k]) + "} [(" + (LaTeX[a_1]) + "-" + (LaTeX[μ]) + ")²+(" + (LaTeX[a_2]) + "-" + (LaTeX[μ]) + ")²+(" + (LaTeX[a_3]) + "-" + (LaTeX[μ]) + ")^2+(" + (LaTeX[a_4]) + "-" + (LaTeX[μ]) + ")²" + (LaTeX[If[k ≥ 5, "+("]]) + "" + (LaTeX[a_5]) + "" + (LaTeX[If[k ≥ 5, "-" * μ * ")^2"]]) + "" + (LaTeX[If[k ≥ 6, "+("]]) + "" + (LaTeX[a_6]) + "" + (LaTeX[If[k ≥ 6, "-" * μ * ")^2"]]) + "" + (LaTeX[If[k ≥ 7, "+("]]) + "" + (LaTeX[a_7]) + "" + (LaTeX[If[k ≥ 7, "-" * μ * ")^2"]]) + "" + (LaTeX[If[k ≟ 8, "+("]]) + "" + (LaTeX[a_8]) + "" + (LaTeX[If[k ≟ 8, "-" * μ * ")^2"]]) + "]$"
t_μ: "$\sum_{i=1}^{" + (LaTeX[k]) + "}{x_i }=" + (LaTeX[Element[List, 1]]) + "+" + (LaTeX[Element[List, 2]]) + "+" + (LaTeX[Element[List, 3]]) + "+" + (LaTeX[Element[List, 4]]) + "" + (LaTeX[If[k ≥ 5, "+"]]) + "" + (LaTeX[Element[List, 5]]) + "" + (LaTeX[If[k ≥ 6, "+"]]) + "" + (LaTeX[Element[List, 6]]) + "" + (LaTeX[If[k ≥ 7, "+"]]) + "" + (LaTeX[Element[List, 7]]) + "" + (LaTeX[If[k ≟ 8, "+"]]) + "" + (LaTeX[Element[List, 8]]) + "= " + (LaTeX[Sum]) + " ⇒μ＝\frac{1}{n}\sum_{i=1}^{" + (LaTeX[k]) + "}{ x_i}＝\frac{" + (LaTeX[Sum]) + "}{" + (LaTeX[k]) + "}＝" + (LaTeX[μ]) + "$"
n = 0 (slider from 0 to 6, step 1)
S1 = SigmaXX(List)
t_{12}: "$ =\frac{1}{" + (LaTeX[k]) + "} × " + (LaTeX[σ_{xx}]) + "$"
t_{14}: "$ σ=\sqrt{" + (LaTeX[σ_{xx} / k]) + "}=" + (LaTeX[sqrt(σ_{xx} / k)]) + " $"
t_{22}: "$ =\frac{" + (LaTeX[S1]) + "}{" + (LaTeX[k]) + "}-" + (LaTeX[μ^(2)]) + "$"
t_{23}: "$ =" + (LaTeX[S1 / k - μ^(2)]) + " $"
t_{24}: "$ σ=\sqrt{" + (LaTeX[S1 / k - μ^(2)]) + "}=" + (LaTeX[sqrt(S1 / k - μ^(2))]) + " $"
t_{Seq}: "${a_n}= " + (LaTeX[List]) + " $"