![\"Open](\"https://colab.research.google.com/assets/colab-badge.svg\"){kind=icon}
"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "_k5tMB9V9yTc"
},
"source": [
"# $x_i$ 의 평균, 분산, 표준편차(Mean, Variance, Standard Deviation of $x_i$)[Sage Math이용]"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "RN20_e8N93t2"
},
"source": [
"### [참고]\n",
"\n",
"[Geogebra와 수학의 시각화](https://www.geogebra.org/m/gsARCQs5)"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "eF0DuRj6r6PN"
},
"source": [
""
]
},
{
"cell_type": "markdown",
"source": [
""
],
"metadata": {
"id": "2p9Zx6NVL12n"
}
},
{
"cell_type": "markdown",
"source": [
"아래는 Sage Math의 Text 파일이다. 위의 Nims 서버와 같은 내용인데, 혹시나 Nims 서버가 없어지는 경우를 대비하여 Text 형식을 아래에 붙여 놓았다.\n",
"\n",
"~~~\n",
"$\\begin{array}{rcl}\n",
"\\displaystyle \\text{Mean : } m &=&\\displaystyle\\frac{x_1+x_2+x_3+\\cdots+x_n}{n} \\\\\n",
"&=&\\displaystyle \\frac{1}{n}\\sum_{i=1}^n x_i \\\\\n",
"\\end{array}$\n",
"\n", "$\\begin{array}{rcl}\n", "\\displaystyle \\displaystyle \\text{Variance : }\n", "\\sigma^2& =&\\displaystyle\\frac{(x_1-m)^2+(x_2-m)^2+\\cdots+(x_n-m)^2}{n} \\\\\n", "&=&\\displaystyle \\frac{1}{n}\\sum_{i=1}^n(x_i-m)^2\n", "=\\displaystyle \\frac{1}{n}\\sum_{i=1}^n(x_i^2-2mx_i+m^2) \\\\\n", "&=&\\displaystyle \\frac{1}{n}\\sum_{i=1}^n x_i^2\n", "- 2m \\times \\frac{1}{n}\\sum_{i=1}^n x_i\n", "+m^2 \\times \\frac{1}{n}\\sum_{i=1}^n 1 \\\\\n", "&=&\\displaystyle \\frac{1}{n}\\sum_{i=1}^n x_i^2\n", "- 2m \\times m\n", "+m^2 \\times \\frac{1}{n} \\times n \\\\\n", "&=&\\displaystyle \\frac{1}{n}\\sum_{i=1}^n x_i^2 - 2m^2 + m^2\n", "=\\displaystyle \\frac{1}{n}\\sum_{i=1}^n x_i^2 -m^2\\\\\n", "\\end{array}$\n", "
\n", "$\\text{Standard Deviation } : \\sigma=\\sqrt{\\sigma^2}$\n", "sage: variate_list=[1,2,3,4,5]\n", "sage: %latex\n", "sage: Variate list: $\\displaystyle=\\sage{latex(variate_list)}$\n", "sage: mean_of_variate_list=mean(variate_list)\n", "sage: %latex\n", "sage: $m=\\displaystyle\\sage{latex(mean_of_variate_list)}$\n", "sage: variance_of_variate_list=variance(variate_list, bias=True)\n", "sage: %latex\n", "sage: $\\sigma^2\\displaystyle=\\sage{latex(variance_of_variate_list)}$\n", "sage: standard_deviation_of_variate_list=std(variate_list, bias=True)\n", "sage: %latex\n", "sage: $\\sigma\\displaystyle=\\sage{latex(standard_deviation_of_variate_list.simplify())}$\n", "sage: squar_of_variate_list=[]\n", "sage: for i in range(len(variate_list)):\n", "... squar_of_variate_list.insert(i,variate_list[i]^2)\n", "sage: %latex\n", "sage: squar of variate list : $\\displaystyle=\\sage{latex(squar_of_variate_list)}$\n", "sage: mean(squar_of_variate_list)-mean(variate_list)^2\n", "2\n", "~~~" ], "metadata": { "id": "axKWI8U7L-X7" } } ] }