{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from ipywidgets import *\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as stats\n",
    "from matplotlib.lines import Line2D\n",
    "plt.rcParams[\"figure.figsize\"] = (20,10)\n",
    "plt.rcParams.update({'font.size': 22})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def describe(data):\n",
    "    df = pd.DataFrame(data)\n",
    "    print(df.describe())\n",
    "\n",
    "def histogram(data, a=1, b=0):\n",
    "    data = data*a+b\n",
    "    plt.hist(x=data, bins='auto', color='#521422', alpha=0.7, rwidth=0.85)\n",
    "    plt.grid(axis='y', alpha=0.75)\n",
    "    plt.xlabel('X')\n",
    "    plt.ylabel('Liczność')\n",
    "    describe(data)\n",
    "    plt.xlim(xmin=-13,xmax=13)\n",
    "    \n",
    "def normal_dist():\n",
    "    x = np.linspace(-3, 3, 100)\n",
    "    plt.plot(x, stats.norm.pdf(x, 0, 1))\n",
    "    plt.grid()\n",
    "    \n",
    "def skewness(a=0):\n",
    "    data = (stats.skewnorm(a).rvs(1000)*10).astype(int)\n",
    "    \n",
    "    _, _, patches = plt.hist(x=data, bins='auto', color='#521422', alpha=0.7, rwidth=0.85)\n",
    "    plt.grid(axis='y', alpha=0.75)\n",
    "    plt.xlabel('X')\n",
    "    plt.ylabel('Liczność')\n",
    "    \n",
    "    stat = [np.mean(data), np.median(data), stats.mode(data)[0][0]]\n",
    "    cols = ['r', 'g', 'b']\n",
    "    lines = [Line2D([0], [0], color=c, lw=4) for c in cols]\n",
    "    \n",
    "    for col, st in zip(cols, stat):\n",
    "        for i, patch in enumerate(patches):\n",
    "            if st < patch.get_x():\n",
    "                patches[i-1].set_color(col)\n",
    "                break\n",
    "            if i == len(patches)-1:\n",
    "                patches[i].set_color(col)\n",
    "     \n",
    "    plt.suptitle(\"Skośność=\"+str(round(stats.skew(data),3)))\n",
    "    plt.legend(lines,[txt +'='+str(stat[i]) for i, txt in enumerate(['Średnia', 'Mediana', 'Dominanta'])]) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statystyka opisowa"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![histogramy](https://www.cs.put.poznan.pl/amensfelt/pub/pics/hists.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![weurl](https://assets.weforum.org/editor/F9EqAhZ_XqicwLxiJpPB4sLnnlbbAtrlnnnGWtARM1w.gif \"spread\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Źródło](https://www.weforum.org/agenda/2020/03/coronavirus-control-measures)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Przykład - wyniki maratonu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![histogramy](https://www.cs.put.poznan.pl/amensfelt/pub/pics/marathon_total.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Źródło](https://enduhub.com/pl/wyniki/2017/10/15/bieganie/18-pko-poznan-maraton,33686/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Przykład - wyniki maratonu 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![histogramy](https://www.cs.put.poznan.pl/amensfelt/pub/pics/marathon_km.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Miary rozkładu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{itemize}\n",
    "\t\\item Miary położenia\n",
    "\t\\item Miary rozproszenia\n",
    "\t\\item Miary asymetrii i koncentracji \n",
    "\\end{itemize}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dominanta"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dominantą nazywamy najczęściej występującą wartość w próbce."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mediana"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$n$ - liczba obserwacji\n",
    "\\vspace{0.5cm}\n",
    "\\begin{itemize}\n",
    "\t\\item $n$ nieparzyste\n",
    "\t$$\\textrm{Mediana} = x_{(n+1)/2}$$\n",
    "\t\\vspace{0.25cm}\n",
    "\t\\item $n$ parzyste\n",
    "\t$$\\textrm{Mediana} = \\frac{x_{n/2}+x_{n/2+1}}{2}$$\n",
    "\\end{itemize}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inne kwantyle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{itemize}\n",
    "\t\\item Percentyle\n",
    "\t\\item Decyle\n",
    "\t\\item Kwartyle\n",
    "\t\\item ...\n",
    "\\end{itemize}\n",
    "$$Poz_p = (n+1)p$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![siatka](http://bi.gazeta.pl/im/8/1326/m1326948.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Źródło](http://bi.gazeta.pl/im/8/1326/m1326948.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Średnia arytmetyczna"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{itemize}\n",
    "\t\\item w populacji:\n",
    "\t$$\\mu = \\frac{1}{n} \\sum_{i=1}^{n}x_i$$\n",
    "\n",
    "   \\item w próbce:\n",
    "\t$$\\bar{x} = \\frac{1}{n} \\sum_{i=1}^{n}x_i$$\n",
    "\\end{itemize}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![średnia](http://www.texample.net/media/tikz/examples/PNG/balance.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Źródło](http://www.texample.net/media/tikz/examples/PNG/balance.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inne średnie"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{itemize}\n",
    "\t\\item Średnia geometryczna\n",
    "\t\t$$\\bar{x}_g = {\\displaystyle \\left(\\prod _{i=1}^{n}x_{i}\\right)^{\\frac {1}{n}}={\\sqrt[{n}]{x_{1}x_{2}\\cdots x_{n}}}}$$\n",
    "        \n",
    "\\item Średnia harmoniczna\n",
    "\t\t\t$$\\bar{x}_h=\\frac{n}{\\sum\\limits_{i=1}^{n}\\frac{1}{x_i}} ~~~~~~~~~~~~~ \\bar{x}_{wh}=\\frac{\\sum\\limits_{i=1}^{n}w_i}{\\sum\\limits_{i=1}^{n}\\frac{w_i}{x_i}}$$\n",
    "            \n",
    "\\item Średnia ucinana\n",
    "\t\t\t$$\\bar{x}_{t} = \\frac{1}{n-2k}\\sum_{i=k+1}^{n-k}x_i$$\n",
    "\t\\end{itemize}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Przykład - wynagrodzenia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![wynagrodzenia](https://www.cs.put.poznan.pl/amensfelt/pub/pics/salary.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Źródło](https://stat.gov.pl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Skale pomiarowe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|\t\t            | Dominanta | Mediana | Średnia |\n",
    "|---|---|---|---|\n",
    "|Nominalne           |        |           |         |\n",
    "|Porządkowe           |       |           |         |\n",
    "|Interwałowe/Ilorazowe |      |           |         |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Miary rozproszenia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{itemize}\n",
    "\t\\item ? \n",
    "\t$$\\frac{1}{n}\\sum_{i=1}^{n}(x_i-\\bar{x})$$\n",
    "    \n",
    "\\item Odchylenie przeciętne\n",
    "\t$$D = \\frac{1}{n}\\sum_{i=1}^{n}|(x_i-\\bar{x})|$$\n",
    "\\end{itemize}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wariancja i odchylenie standardowe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{itemize}\n",
    "\t\\item Wariancja w populacji\n",
    "\t$$\\sigma^2=\\frac{1}{n}\\sum_{i=1}^{n}(x_i-\\bar{x})^2$$\n",
    "    \n",
    "\\item Wariancja w próbce\n",
    "\t$$s^2=\\frac{1}{\\boldsymbol{n}-\\boldsymbol{1}}\\sum_{i=1}^{n}(x_i-\\bar{x})^2$$\n",
    "    \n",
    "\\item Odchylenie standardowe\n",
    "\t$$s=\\sqrt{s^2}$$\n",
    "\\end{itemize}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Inne miary rozproszenia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{itemize}\n",
    "\t\t\\item Rozstęp \n",
    "\t\t\t$$R = x_{max}-x_{min}$$\n",
    "            \n",
    "\\item Rozstęp międzykwartylowy \n",
    "\t\t\t$$IQR = Q_3-Q_1$$\n",
    "            \n",
    "\\item Współczynnik zmienności \n",
    "\t\t\t$$V = \\frac{s}{\\bar{x}}$$\n",
    "\\end{itemize}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                 0\n",
      "count  1000.000000\n",
      "mean      1.033392\n",
      "std       0.998886\n",
      "min      -2.928110\n",
      "25%       0.358840\n",
      "50%       1.029475\n",
      "75%       1.699662\n",
      "max       3.705007\n"
     ]
    }
   ],
   "source": [
    "data = np.random.normal(loc=1, scale=1, size=1000)    \n",
    "describe(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "79b1e93c05604069901406c065528daf",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=1, description='a', max=3, min=-3), IntSlider(value=0, description='b', …"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.histogram(data, a=1, b=0)>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interact(histogram, data=fixed(data), a=(-3,3,1), b=(-10,10,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Wykres pudełkowy (boxplot)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![boxplot](https://www.cs.put.poznan.pl/amensfelt/pub/pics/boxplot2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Miary asymetrii i koncentracji"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Moment centralny rzędu \\textit{k}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$M_k = \\frac{1}{n}\\sum_{i=1}^{n}(x_i-\\bar{x})^k$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Współczynnik asymetrii (skośności)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$A = \\frac{M_3}{s^3}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Współczynnik wyostrzenia"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{itemize}\n",
    "\t\\item Współczynnik koncentracji (kurtoza)\n",
    "\t$$K=\\frac{M_4}{s^4}$$\n",
    "    \n",
    "\\item Współczynnik wyostrzenia\n",
    "\t$$E=K-3$$\n",
    "\\end{itemize}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "normal_dist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2434cdd48ee94b218f3aeb387523f9f7",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=0, description='a', max=20, min=-20, step=2), Output()), _dom_classes=('…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<function __main__.skewness(a=0)>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interact(skewness, a=(-20,20,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Miary rozkładu dla szeregu rozdzielczego"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Średnia i wariancja dla szeregu"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$n_i$ - liczność $i$-tego przedziału\n",
    "\n",
    "$\\dot{x_i}$ - środek $i$-tego przedziału\n",
    "\n",
    "\\begin{itemize}\n",
    "\t\t\\item Średnia:\n",
    "\t\t\t$$\\bar{x_S} \\approx \\frac{\\sum\\limits_{i=1}^kn_i*\\dot{x_i}}{n}$$\n",
    "            \n",
    "\\item Wariancja:\n",
    "\t\t\t$$s^2_S \\approx \\frac{\\sum\\limits_{i=1}^kn_i*(\\dot{x}-\\bar{x})^2}{n-1}$$\n",
    "\\end{itemize}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dominanta - szereg rozdzielczy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$x_{modS} \\approx x_0 + \\frac{n_0 - n_{-1}}{(n_0 - n_{-1})+(n_0 - n_{+1})}*h_0$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![dominanta](https://www.cs.put.poznan.pl/amensfelt/pub/pics/dominanta.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mediana - szereg rozdzielczy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$x_{medS} \\approx x_0 + \\frac{h_0}{n_0}*(\\frac{n}{2}-F_{-1})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![mediana](https://www.cs.put.poznan.pl/amensfelt/pub/pics/mediana.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Skośność"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$A=\\frac{\\bar{x}-D}{s}$$"
   ]
  }
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