{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ciência de Dados <br>Análise Exploratória de Dados"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Francisco Aparecido Rodrigues, francisco@icmc.usp.br.<br>\n",
    "Universidade de São Paulo, São Carlos, Brasil.<br>\n",
    "https://sites.icmc.usp.br/francisco <br>\n",
    "Copyright: Creative Commons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nesta aula, vamos mostrar como descrevemos os dados em termos de medidas de estatística. Medidas de posição, dispersão e correlação serão descritas, com aplicações em diferentes conjuntos de dados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Visualização"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uma das maneiras mais simples de visualizar a distribuição dos dados é através de gráficos de frequência e histogramas."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Um exemplo de um gráfico de frequência:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.mlab as mlab\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = [21,22,23,4,5,6,77,8,9,10,31,32,33,34,35,36,37,18,49,50,100]\n",
    "\n",
    "fig= plt.figure(figsize=(6,4))\n",
    "\n",
    "num_bins = 10\n",
    "n, bins, patches = plt.hist(x, num_bins, facecolor='blue', alpha=0.5, density=False, edgecolor='black', linewidth=1.2)\n",
    "plt.xlabel(\"X\", Fontsize = 15)\n",
    "plt.ylabel(\"Frequencia\", Fontsize = 15)\n",
    "plt.xticks(fontsize=10)\n",
    "plt.yticks(fontsize=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No caso do histograma, a área sob a curva deve ser igual a 1 (notem a diferença na escala do eixo das ordenadas (y))."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.mlab as mlab\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = [21,22,23,4,5,6,77,8,9,10,31,32,33,34,35,36,37,18,49,50,100]\n",
    "\n",
    "fig= plt.figure(figsize=(6,4))\n",
    "\n",
    "num_bins = 10\n",
    "n, bins, patches = plt.hist(x, num_bins, facecolor='blue', alpha=0.5, density=True, edgecolor='black', linewidth=1.2)\n",
    "plt.xlabel(\"x\", Fontsize = 15)\n",
    "plt.ylabel(\"f(x)\", Fontsize = 15)\n",
    "plt.xticks(fontsize=10)\n",
    "plt.yticks(fontsize=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No caso de variáveis nominais, podemos usar gráficos de barra ou gráficos de setores. Notem que o valor no eixo das abscissas (x) é arbitrário e não deve ser levando em conta."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Y: ['Bom', 'Ruim', 'Ótimo', 'Regular', 'Regular', 'Ótimo', 'Ótimo', 'Bom', 'Ótimo', 'Bom', 'Ótimo']\n",
      "Valores possíveis: ['Bom' 'Regular' 'Ruim' 'Ótimo']\n",
      "Frequencia dos valores: [3. 2. 1. 5.]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Y = [\"Bom\", \"Ruim\", \"Ótimo\", \"Regular\", \"Regular\", \"Ótimo\", \"Ótimo\",\"Bom\", \"Ótimo\", \"Bom\", \"Ótimo\"]\n",
    "import matplotlib.pyplot as plt #biblioteca gráfica para mostrar os gráficos\n",
    "values = np.sort(np.unique(Y)) #usamos a funções sort e unique do Numpy para encontrar os valores possíveis.\n",
    "# vamos calcular a frequência de cada valor presente na lista\n",
    "freq = np.zeros(len(values)) # armazena as frequencias\n",
    "ind = 0 # indice do vetor de frequências\n",
    "for i in values: # para os valores diferentes\n",
    "    counter = 0 # conta as ocorrências\n",
    "    for j in range(0,len(Y)):\n",
    "        if(Y[j] == i):\n",
    "            counter = counter + 1\n",
    "    freq[ind] = counter\n",
    "    ind = ind + 1\n",
    "\n",
    "print('Y:',Y)\n",
    "print('Valores possíveis:', values)\n",
    "print('Frequencia dos valores:', freq)\n",
    "\n",
    "fig= plt.figure(figsize=(6,4))\n",
    "\n",
    "y_pos = np.arange(len(values))\n",
    "plt.xticks(y_pos, values)\n",
    "plt.bar(y_pos, freq)\n",
    "plt.xticks(fontsize=10)\n",
    "plt.yticks(fontsize=10)\n",
    "plt.xlabel(\"Valores\",fontsize = 15) \n",
    "plt.ylabel(\"Frequência\", fontsize = 15) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gráfico de setores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "labels = values\n",
    "sizes = freq\n",
    "explode = (0.1, 0, 0, 0)\n",
    "\n",
    "fig1, ax1 = plt.subplots(figsize=(10,6))\n",
    "ax1.pie(sizes, explode=explode, labels=labels, autopct='%1.1f%%', shadow=True, startangle=90)\n",
    "ax1.axis('equal')  # Equal aspect ratio ensures that pie is drawn as a circle.\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Outro gráfico importante é o scatterplot, usado quando queremos verificar a relação entre duas variáveis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "N = 100\n",
    "X = np.linspace(-1,1, N) # gera N valores em [-1,1]\n",
    "erro = np.random.uniform(-1,1,N) # ruído a ser incluído na relação linear.\n",
    "sigma= 0.5\n",
    "Y = 0.8*X + erro*sigma\n",
    "\n",
    "fig= plt.figure(figsize=(6,4))\n",
    "\n",
    "plt.scatter(X, Y, marker='o', color = 'black');\n",
    "plt.xticks(fontsize=10)\n",
    "plt.yticks(fontsize=10)\n",
    "plt.xlabel(\"X\",fontsize = 15) \n",
    "plt.ylabel(\"Y\", fontsize = 15) \n",
    "plt.show(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quando temos três variáveis, uma maneira de visualizarmos os dados é considerar um gráfico de calor, sendo que a escala de cores define a terceira variável."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np; np.random.seed(0)\n",
    "import seaborn as sns; sns.set()\n",
    "uniform_data = np.random.rand(10, 12)\n",
    "\n",
    "plt.figure(figsize=(12,6))\n",
    "\n",
    "flights = sns.load_dataset(\"flights\")\n",
    "flights = flights.pivot(\"month\", \"year\", \"passengers\")\n",
    "# mostra o gráfico\n",
    "ax = sns.heatmap(flights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Medidas de posição"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Moda"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uma medida importante de tendência central é a moda, que retorna o elemento mais comum em um conjunto de dados. Geralmente, essa medida é usada para atributos nominais."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para calcularmos a moda, usamos o pacote Statistics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A moda de X: 1\n"
     ]
    }
   ],
   "source": [
    "from statistics import mode\n",
    "X = [1,2,3,1,2,3,4,1,3,6,4,1]\n",
    "m = mode(X)\n",
    "print('A moda de X:', m)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notem que essa biblioteca retorna um erro se houver mais de uma moda. Nesse caso, temos que implementar uma função para retornar todas a modas possíveis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "ename": "StatisticsError",
     "evalue": "no unique mode; found 2 equally common values",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mStatisticsError\u001b[0m                           Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-15-01bf3126b5e2>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mm\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'A moda de X:'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/Anaconda3/anaconda3/lib/python3.7/statistics.py\u001b[0m in \u001b[0;36mmode\u001b[0;34m(data)\u001b[0m\n\u001b[1;32m    504\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0mtable\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    505\u001b[0m         raise StatisticsError(\n\u001b[0;32m--> 506\u001b[0;31m                 \u001b[0;34m'no unique mode; found %d equally common values'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtable\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    507\u001b[0m                 )\n\u001b[1;32m    508\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mStatisticsError\u001b[0m: no unique mode; found 2 equally common values"
     ]
    }
   ],
   "source": [
    "X = [1,1,2,2,3]\n",
    "m = mode(X)\n",
    "print('A moda de X:', m)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Moda: [1, 2]\n"
     ]
    }
   ],
   "source": [
    "def new_mode(X):\n",
    "    values = np.sort(np.unique(X)) \n",
    "    # vamos calcular a frequência de cada valor presente na lista\n",
    "    freq = np.zeros(len(values)) # armazena as frequencias\n",
    "    ind = 0 # indice do vetor de frequências\n",
    "    for i in values: # para os valores diferentes\n",
    "        counter = 0 # conta as ocorrências\n",
    "        for j in range(0,len(X)):\n",
    "            if(X[j] == i):\n",
    "                counter = counter + 1\n",
    "        freq[ind] = counter\n",
    "        ind = ind + 1\n",
    "    mx = max(freq)\n",
    "    md = []\n",
    "    for i in range(0,len(freq)):\n",
    "        if(freq[i] == mx):\n",
    "            md.append(values[i])\n",
    "    return md\n",
    "moda = new_mode(X)\n",
    "print('Moda:', moda)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos também identificar a moda visualmente em um gráfico de barras, que representa o valor mais frequente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: [1, 1, 2, 2, 3]\n",
      "Valores possíveis: [1 2 3]\n",
      "Frequencia dos valores: [2. 2. 1.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt #biblioteca gráfica para mostrar os gráficos\n",
    "\n",
    "# Usamos a funções sort e unique do Numpy para encontrar \n",
    "# os valores possíveis em ordem crescente.\n",
    "# esses valores serão mostrados na abscissa do gráfico.\n",
    "values = np.sort(np.unique(X)) \n",
    "# vamos calcular a frequência de cada valor presente na lista\n",
    "freq = np.zeros(len(values)) # armazena as frequencias\n",
    "ind = 0 # indice do vetor de frequências\n",
    "for i in values: # para os valores diferentes\n",
    "    counter = 0 # conta as ocorrências\n",
    "    for j in range(0,len(X)):\n",
    "        if(X[j] == i):\n",
    "            counter = counter + 1\n",
    "    freq[ind] = counter\n",
    "    ind = ind + 1\n",
    "\n",
    "print('X:',X)\n",
    "print('Valores possíveis:', values)\n",
    "print('Frequencia dos valores:', freq)\n",
    "\n",
    "y_pos = np.arange(len(values))\n",
    "plt.xticks(y_pos, values)\n",
    "plt.bar(y_pos, freq)\n",
    "plt.xlabel(\"Valores\",fontsize = 20) \n",
    "plt.ylabel(\"Frequência\", fontsize = 20) \n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos aplicar a função em dados nominais:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A moda de Y: red\n"
     ]
    }
   ],
   "source": [
    "Y = [\"red\", \"blue\", \"blue\", \"red\", \"green\", \"red\", \"red\"]\n",
    "print('A moda de Y:', mode(Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O gráfico de barras mostrando a frequêbncia:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Y: ['red', 'blue', 'blue', 'red', 'green', 'red', 'red']\n",
      "Valores possíveis: ['blue' 'green' 'red']\n",
      "Frequencia dos valores: [2. 1. 4.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt #biblioteca gráfica para mostrar os gráficos\n",
    "values = np.sort(np.unique(Y)) #usamos a funções sort e unique do Numpy para encontrar os valores possíveis.\n",
    "# vamos calcular a frequência de cada valor presente na lista\n",
    "freq = np.zeros(len(values)) # armazena as frequencias\n",
    "ind = 0 # indice do vetor de frequências\n",
    "for i in values: # para os valores diferentes\n",
    "    counter = 0 # conta as ocorrências\n",
    "    for j in range(0,len(Y)):\n",
    "        if(Y[j] == i):\n",
    "            counter = counter + 1\n",
    "    freq[ind] = counter\n",
    "    ind = ind + 1\n",
    "\n",
    "print('Y:',Y)\n",
    "print('Valores possíveis:', values)\n",
    "print('Frequencia dos valores:', freq)\n",
    "\n",
    "y_pos = np.arange(len(values))\n",
    "plt.xticks(y_pos, values)\n",
    "plt.bar(y_pos, freq)\n",
    "plt.xticks(fontsize=18)\n",
    "plt.yticks(fontsize=18)\n",
    "plt.xlabel(\"Valores\",fontsize = 20) \n",
    "plt.ylabel(\"Frequência\", fontsize = 20) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ou ainda em um gráfico de setores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cJhTWULjIcPd66RYqO2p03pbEDBUeMVQ0GuXV199m9a0386e3TlLd2G10JBEZAFGi/HDXLwlGVHgkNqjwiKGOnygFIGxy8vrOcoPTiMhAavd18tvD6/AFdcioGE+FRwzT3tHJq6+/zR2rbuHH644S1ckRInFna/luarsbiUR0qVqMpcIjhohGo7z48uvcvuoWNu6ppKpBl7JE4tVP9vxGl7bEcCo8YohjhSWEQ1Hy8/N5/q2TRscRkUFU393IhtJ3dKq6GEqFR4acx9PLX17bxKfvW8OzLx4nENJQt0i8+3PRm/T4PUbHkBFMhUeG3BtvbeP6ZYspPN3O0bJmo+OIyBAIRUI8u/c3OmtLDKPCI0OqvKKak6fKWbhgDr987YTRcURkCBU3n2J/7VGCYR0bI0NPhUeGTDAY4rmX1rN2zSrWvVNGZ4/+0hMZaf7ryEtEtCRTDKDCI0Nm+469JCUmkDkqiw07K4yOIyIG6PR1saH0HV3akiGnwiNDorWtgzfe2srdn7qd37xerOMjREawV4o3EYzospYMLRUeGRJvvr2N+XNm0RswseNIndFxRMRA/nCAPx59WTswy5BS4ZFBV11bz+EjJ1h920386rUio+OISAzYUr6LLn+P0TFkBFHhkUEVjUZ5dcPbrLhhKSerOykqbzM6kojEgGg0yq8OPq/NCGXIqPDIoCo5eYaqmlquX76E/1xfbHQcEYkhRxpOUNVRSySqOX0y+FR4ZNCEQiH+/OqbrLzpevYWNlDXol1WReTj/uvISwS0L48MARUeGTQHDh+no7OLxQvnsW7zKaPjiEgMKmstp6az3ugYMgKo8Mig8Pn9vPr6O6xcsZyjZc0a3RGR8/rTsVe0YksGnQqPDIpDhwsJ+AMsXjSf59/R6I6InF9hUylNnlajY0icU+GRARcIBHnjrW3cdMNSSis7qKjvMjqSiMS4Px17Ba9GeWQQqfDIgDt6vBhPby9LFi/kubfLjI4jIsPAofpCOn3dRseQOKbCIwMqFAqxYeMWrlu2iOpGD2XVHUZHEpFhQqM8MphUeGRAHS86SXtHJ0sWLeSFLZq7IyL9t7f2sDYilEFjNTqAxI9wOMwbm7Zw9aypRKIWjpW1GB1pQHTVHKLt9HZMJjBZ7GTNWIMztYCW0rfoqT8GJhPOlNFkzbobs8X2icd31x+n7dQWopEQNlcaOXPux2JPwNteRcORFwAYNf0OErOnAdB68h2szmRSxlwzpD+niNGi0SjrS9/h/pl34rDajY4jcUYjPDJgSk6eprGxhSXXLGD9zgqj4wyIQE8TzcWvM3rR44y97q9In7iCugO/p7flNN11Rxmz/OuMve6bhIM+Oip2fuLxvo5qmgpfIW/+w4y7/q+xJWTSUrIRgPbT28iZ82kKlnyZ1pNvARD0ttPbcorkgoVD+nOKxIqt5bswmYxOIfFIhUcGRDQa5a3N75GTk8X4sQVsOVBtdKQBYTJbyb76XqzOZACcqQWE/N1EI6Gz/wkHIRomGglhMn9ydKer9jApBQuxudMByJh8C2kTbnj/uS1EQn4iIS8m89nB1uaiDWROW41Jv/FlhPIEetlfc4xwRMdNyMDSJS0ZEPUNTZRX1nDvp1ax42gtvb6Q0ZEGhM2d3ldWotEozUXrScyeTkLWFNyZkziz+XuYzBbsCaNIHbvoE48P9DTjSM6ldv9vCfa240jOYdT0OwFIn3QzjcdeIhoJkzVjDZ7mMsxWJ660MUP6M4rEmvWlbzM/fxYWs8PoKBJHNMIjA2L3vkPY7TaunjWDDXFyOeujIqEA9Yf+QNDTSvbse+ms2k/I28aEW/4XV938bWzudJqLNnzygdEInsZismfdw9jrvo7VkUTjsT8D4EjKZsy1X2Xs8q/hTC2gtXQTmVNX0Vm1j5q9v6bh6EtEwvFRHEUuxZn2Klp7242OIXFGhUeuWK/Xx649h1h8zVya2ryU18XXRoNBbztVO/8Dk8nM6CVfwmJz0dNwnKT8uZitTswWKyljFtHbevoTj7U6k0nImozVmYTJZCa5YAG+9spP3K+9/D2S8udgtthoP/Me+dc8is2dRnftoaH4EUVizivFm7REXQaUCo9csWPHiwiFw8y5ehbrd37yw3w4i4R81Oz+OUm5M8md91DfKixHSj499YVEI2Gi0Sg9DYU4Uz95KSoxdxY9jcWEA2fPEuupL8SZOvpj9wn5uuhpOEHquKVEo1EgCpgAExGdIi0j1K7qg0ZHkDijOTxyRSKRCG9v3cno/Bxyc7LYdeyw0ZEGVEfFLoK97fQ0FNLTUNh3e97Cx2g7tYWK7c9gMltxJOeSNfNTZx9TuRtfRw05s+8jMXs6IW8n1bt/BtEoVlcaObPv/dhrNBe/TuaU2zCZzFhsThJzZlCx9ftYnSnkLfj8kP68IrEiGA6yq+ogN4xfgsWsv83lypmiZ/+kFLksp8sr+clP/4s1d9yMOSGfHz53xOhIEuMeunUKM6828U/bf2R0FIlxkzOu4lvX/w9cNqfRUSQOqDbLFdmx6wA2u5Upkyax9VCt0XFEJI6cbD1DUJd1ZYCo8Mhl8/R6OXq8mIkTxpKcnMTRONlZWURix/aKPYQiWq0oV06FRy7bybIzhCMRZkydzHtHaolEdHVURAbWtoo9hCJho2NIHFDhkcu2a98h3G4XUyZPYtthXc4SkYFX3VlHt7/H6BgSB1R45LJ0dnVzsqycyRPHYbJYKanQJmEiMjg2n9lJIBwwOoYMcyo8clmKSsoAmDplEtsP1RmcRkTi2XuV+4yOIHFAhUcuy669h0hKSmD82LHsLmwwOo6IxLFmTysd3vjawV2GngqPXLLmljaqqmvJz8shIcHFqWpdzhKRwbW35ghhTV6WK6DCI5esqKQMEyYmjBvD4dImtDhLRAbbgbqj+DWPR66ACo9csoOHC0lKSmDMmDHsK2oyOo6IjAAnW85gMVmMjiHDmAqPXJKeHg+V1bWkpCQxbkwuh0pVeERk8IWjEYqaTxodQ4YxFR65JOWVNZiAMQX5VDV00d2rbd9FZGjsrj6EN+gzOoYMUyo8ckmOnSjBZrcxTpezRGSIHak/gdWsy1pyeVR4pN/C4TDHCktITUlm3NgCDpSo8IjI0OnwddHaq1WhcnlUeKTf6hqa8Pn8pKYmk5Dgpry20+hIIjLCHK4/QSQSMTqGDEMqPNJvZacqMAGj83I4Wdmq5egiMuQKm0rxhfxGx5BhSIVH+u3Q0UKSkhPJy83h2Ok2o+OIyAhU0nwKm8VmdAwZhlR4pF+8Ph/VNfUkJrjJzc3lxBkVHhEZet0BD13+bqNjyDCkwiP9UlffiNlkwm63MSojlVM1HUZHEpERqqi5zOgIMgyp8Ei/VFTWEo1CdlYmNY2dBEOaNCgixjjRdBJfUPN45NKo8Ei/FJWUkZjoJjc7m+IKLQsVEeOUtZYTRasm5NKo8MhFhUIhKqpqSEx0k52TTUmlLmeJiHFquuqxaANCuUQqPHJRzS1tRMIRLBYLWZkZnNb+OyJioGg0SkO3Nj6VS6PCIxdV39BEJBrFarWQnOSmvsVjdCQRGeHOtFcZHUGGGRUeuaiyMxXYbFbS01JpbO0hrB0HRcRgZ9qrCIQCRseQYUSFRy6qorKGxAQ3ozLSqWzQ/hciYrzqzjqCkZDRMWQYUeGRCwqHwzQ2tuByOUlPT6O8ToVHRIxX3VmvHZflkqjwyAW1tXcSiUYxm82kpadT1ajCIyLG6/J3E46EjY4hw4gKj1xQa1s7JtPZ/61LWiISSxp6tFJL+k+FRy6oqbmVSCSKzWYlMcFJY6tWaIlIbDjdppVa0n8qPHJBldW1OJ12UlOSaWrzoAVaIhIrqjvrCIS1Ukv6R4VHLqi6ph63y0VSYgItHV6j44iI9GnpbSMU1jwe6R8VHjmvUChEU3MrTqeDpKREmttVeEQkdrT26lw/6T8VHjmvru4eAMxmM4mJiTR1+AxOJCLyoVZvB1aLztSS/lHhkfPq7vZgen+JVmJCIs0qPCISQ7p83VhMKjzSPyo8cl7dPR6i0bOzlBMTEzWHR0RiSpQoPYFeo2PIMKHCI+fV2dVNNBIBIClJk5ZFJPa0+zqNjiDDhAqPnFdraztWmxWAlCQ3LZ0qPCISW5o9rUZHkGFChUfOq7mlFbvdjsNhJxyJ4g9o+aeIxJamnhajI8gwocIj59XS1o7DbsNht9Pr1eZeIhJ7ugMeItGI0TFkGFDhkfNqa+/E7jg7wuP1BY2OIyLyCd6gj5AOEZV+UOGRcwoGQ/h8fqwWC3a7jV5/yOhIIiKf0Bv06tR06RcVHjmnQCCAyQQmk+nsJS2fCo+IxJ7eoLdv+wyRC1HhkXPyBwLA2U0H7XY7Hl3SEpEY5A36iKLCIxenwiPnFAgEeX+T5fcnLWuER0RiT29Q22VI/6jwyDn5AwE+aDwOh50eXdISkRjkDfowm/RRJhend4mcUyAQhPevi9tsNnr9mhQoIrHHG1Lhkf7Ru0TOye8P8NHL4pGIrpGLSOyJaMKy9JMKj5xTIBDQygcREYkbKjxyToFgUH85iYhI3LAaHUBik0Z3ZCBZzbBwRi7XXp3H/MlplPdUGx1JREYYFR4RGXBpSQ5uXFDA/CmZjB/lICExgVBvF76qIsy2NHZU7TM6ooiMMCo8InLFpo1L47p5o7l6XArZqXZsDif+lhp85bvxHC6mtfYkkd4uEmevwDFxDu9WqvCIyNBS4RGRS+KwmVk2ZzSLZmQzJddFSrILImG8NaX4it6lpaYEf0M5RD65d5P7uvt54cTrOvtIRIacCo/0i8noAGKYvMwEbpg/mrmTMhiTYceVkECwswVvZSH+nSeorS4h1Nl00edJmLoEk9PNlvJdQ5BaRgoT+v0k/aPCIxcVDoex27SgbyQwmWDelCyWzc5jxpgkMlMcWKw2fA3l+Cq20rm7mMbaMqKBS9/OP2HFZ3m5aCPBsM5lk4Fjt9iI6Cwt6QcVHrmoQCBAglNvlXiU5LZx/dzRLJyexYQsJ0lJbiL+XrzVJfgOb6KxpoRAczVEI1f0Oq6r5mJJTGXT6XcHKLnIWS6bi8gVvj9lZNCnmJzXB8PE/kCAxCS9VeLBVXkp3DB/NLOvSiUv3Y7D5cbfWoev4iC+wiI6aksJ97QP+Osm3fIIG0rfwR/yD/hzy8jmsjm1jYb0iz7F5JysFium9w8PDQSCjNIIz7BjtZpZMjOXJbNymZrvIi3ZhdkE3tpT+E7toa2mBH/9aaKhwKDmcIyeijV1FG+8u3VQX0dGJrfNZXQEGSb0KSbn5HDY+4Z4/IEACS6bsYHkojJSnKxYUMC8yZmMG+XAneAm5OnAW1mEf89x6mtKCbbVDXmulNue4K2y7XiCvUP+2hL/3DYnZpOmLcvFqfDIOdntNj5oPH5/ALdDb5VYM2tCBsvnjGbWuCSyUh1Y7Q78TVX4ynfQfbCYlpqTRHw9hma0Z4/DlpHHa7t/amgOiV8um1OnpUu/6FNMzslht/PBH02BQBCXUyM8RnLarVw/L49rpucwKcdJcpKbaCiAt6YUf+EWmmtK8DdWQIztb5Oy+ktsK99Nl7/b6CgSp9w2FxazPsrk4vQukXOy2+2Y+GAOTwCXQ4VnKBVkJ3Lj/AJmT0inIMOO0+0i0NGMt+I4/ndPUFNTQrirxeiYF2RNy8WRNY6X3/iN0VEkjiXYXFjNFqNjyDCgwiPnZLfbiL6/t4XX58ftsmE2QUSLIQac2QwLp+Vw7dV5TCtIIDPZgdlqxVd/Bl/5O7TvLMFfW0Y06DM66iVJu/1JdlUdpM3bYXQUiWPprjSjI8gwocIj5+R02PlgL69IJEKvN0BqkpO2ruH1oRuLUhLs3LiggAVTRjE+y0FikpuwtwdvVTH+g8eprykh2FwDw3gzNXNSBvb8Sfx543eNjiJxLjsx0+gIMkyo8Mg52e12Ih/Z26Kr20NmqkuF5zJMHpPK9fNGc/X4VHLT7NidrrMHa1bso/dYEe21pYQ9nUbHHFAZtz/JobrjNHpi+7KbDH/p7lSjI8gwocIj52S327BYzEQiEcxmM93dPWSmOjlZZXSy2Ga3mrl2dh6LZuYyNddJarILiOKtOYm/dCct1SUEGs4QjePjFVhbtNkAACAASURBVMzuZOxjp7Pu7X8xOsqwVLexjI4TTVje3wrCkenGlmCnp/LDS4PBLj+2JDtTvrronM8R9gY59Z+HKPjUNNz5yQB0lrRQt7EMs9VMwdoPb69+pZjUWdkkTUgf5J9scKQ4koyOIMOECo+ck8lkIi01BX8ggMvppMfTw6hUbfD132WnubhxQQFzJ2cyNtOOy+0m1N2Ot6oQ/+5CamtKCbU3GB1zSKWv+hInGk9S2zWyfu6B4qnqZOx9M0kYk3LO7wfavZz69SHG3D39nN/vOtlC3ZunCHR8/Lyzxq1nmPj4PAIdPpreq2TcA7Poreki7A8P27LjsNixaoWW9JPeKXJe6Wmp1Dc04XI68fT0MCpV18rnTB7F8jn5zByTSGbK2b1vfI0V+Mq307W3mObak0T8I3iDPbsT+4S5vLD1h0YnGZYioQjehh6adlQSaPPiyHSTd9sk7KnOvvtUv1rCqKUFuHLPPbLRsqeGMfdOp+KFwo/dbrKYiQTChH0hTBYz0WiUurdOnbc4DQcZ7jQC4SAurdKSflDhkfPKzEyjoqoGgO4eD9n5ow1ONLQSnFaunzeahdOymPj+3jeRgB9vTQn+Y2/TVFNCoLHyig/WjCeZt32R020VlLfr2uflCHb7SRyfRs5NV+HMSqB5ZxXlfzrG5CcXYjKZ6DrZSrDTT+bigvM+x1Wfm3PO23NXTqRy3QlMNjMFd02l7WAdSVelfaxMDTcZ7jQdHCr9psIj55WVmUEgeHauSXd3D1OH8S/G/hiXm8QN8wqYMzGN/DQ7DrebQFsD3soj+LcVUV1TQri7zeiYsctiwzblGp5/79+NTjJsOdJcXPXw7L6vR107hsbtFQQ6fDjSXDTvriLrurGYzJd+lELiuFQmP7kQgJA3SNvBeiY8NpfG7RV4qjpxZieQt3LigP0sQyHDnaZdlqXfVHjkvFJSkvtWRnd295CVlmBsoAFkNcM1M3JZenUe00a7SU92Yjab8dadxnf6rfcP1jxFNKjTvfsrc+Vj1HY3UNpyxugow5a3oQdvQzfpc3I/vDEKJrOJkCdAb00X4z5z9RW/TsPmM2RdP5Zgp5+eM+1MeHQu1a8U0326bVjN58lOyMRhtRsdQ4YJFR45r+SkRCzms3899fR4cNgtJLps9HiH3wqjtCTH+3vfnD1YMyExgXBvF96qIvz7j1NfXUKwtY7hvPeNscxYZyzjud2/NDrI8GaCujfKSBibiiPNRev+WpzZidhTnHQWN+POT8Ziv7L5Kt6GboIdPlKmjsLb2AMfjBaZTESCw+vy0MSMcRrhkX5T4ZHzSkpMIPqRvXiaWjoYk5NEUXnsX9aZPj6d6+aOZta4ZHJSHVgdDvzN1fgqduM5XExrTSkRr853GijpN32WFm87xxtLjI4yrLmyE8m/fTIVfzxGNBLFluxg7H0zAPC39p5zvk3L/lq8tV0UfGpav16jbuMpRt8xpe/1bIl2in+0G2dWAsmThs/oDsDo5NyL30nkfSo8cl7JyYlEolGi0Sgmk4nWtnbG5CTHXOFx2s0smz2aRTOymZznIiXJBZEw3ppSfEXbzx6s2VAOkZDRUeOWfc5NPLf/90bHiAtps3NIm53ziduzlo095/0zF+bDwvxP3D79m0vPef8Jj8z92Ndj7hmeq7SsZiupzmSjY8gwosIj5+VyOklKSiAQCOJw2Glvb2N8bpbRscgblcCN80Yzd1IGBRl2XAkJBDtb8FYW4n/v/b1vOpuMjjlipC77NF3BXg7VHTc6iowgeUnZ+MMB3GbtDyb9o8IjFzQ6L5eqmlocDjstrW3MnD1hSF/fbIZ5U7JYNjuP6WOSyEx2YLHa8DWU46vYSufuYhpry4gGvBd/MhkUjoW38V9HXuw7bFZkKBSk5GHi0lerycilwiMXNHZMPiVlp0lLTaGltZ2C7MEdQk5y27hh3mgWTMtmYraDxEQ3EX8v3uoSfIc20VhTQqC5WnvfxIjka+7AFw2zp+aQ0VFkhBmbmo/DohVa0n8qPHJBeTlZ8P7EZY+nF7PZREqinc6ewIA8/4T8FG6YP5rZV6WSm+bA4XLhb63DV3EAb2ER7bUlhHs6Lv5EYgjnkk/xuxPrPza5XWQoTEofh9msFVrSfyo8ckEZGWmYTB8OGze1tDM2N5ljZZd+CrbVambpzFwWz8plWr6L1GQXZsBbdwpf2Z739745TTQ0MGVKBlfi7BWErRbeq9hrdBQZgUanaIWWXBoVHrmgzIw0IpEPV2o1NzUxuSC1X4UnM8XJigVjmDc5g7GjHLgT3IQ8HXgrT+DfU0h9TSnBtroh+ClkMLivu58XTrxOWJcXZYgl2RNw29xGx5BhRoVHLsjpcJCakow/EMDpcFDf0Mj0cedexnr1hEyWzc1n1tgkslLPHqzpb6rCV76D7oPFtNScJOLrGeKfQAZDwtQl4HSx5cwuo6PICDQxYzyBcACbRR9h0n96t8hFjRmdy6nyyvcLTxM3XLcMl8PKdXPzuWZ6NpNynaQkuomEA3irS/EXbnn/YM0KiISNji+DwL3is7xStImg9jYSA0zNnIDT6jA6hgwzKjxyUZMmjuf4iVJIO3tqup0QL3z3VgIdTXgrjuPffuLswZpdlz6vR4Yf14S5WBNT2HT6XaOjyAg1K3sqFvOVHbFxqR5++GGeeuopFi1aNKSvKwNHhUcuKj8v+2MTlxsaG0ks2UT30S0GphKjJN38KOtL38Ef0sGqMvTMJjNjUj+5s7TIxajwyEXl5mQTiUYJ+AO0tzSxZ99BVk6ZDCo8I45j9FSsqZm8+e42o6PICDU+rYBQJITdYrvs59i7dy8/+MEPiEQi5Ofn43a7KSsrIxwO88QTT3DHHXcQCAT41re+RWFhIfn5+bS3tw/gTyFGUOGRi3K7nDhCnRzevI2kxARqXEGctzxFp9HBZMil3PYEm8q24wn2Gh1FRqhpmROxmq/8o6uiooKtW7fy85//nKysLL7//e/T09PDAw88wOzZs3nrrbcAePPNN6moqGDNmjVX/JpiLBUe6Zebli9ilDtKVk4eJpMJe1I6Zncykd4uo6PJELFnj8OWkcdru//D6Cgygs3Nm3lFozsfGD9+PElJSezatQufz8ef//xnAHp7eykrK2Pfvn3cf//9AIwbN465c+de6OlkGFDhkX4ZP3kqR/fvBiAajdJYU4n7qjn0FGri6kiRsvrLbD2zi26/thYQY1jMFqZkXDUgz+V0OgGIRCL84Ac/YMaMGQC0tLSQkpLCunXrPraDuNWqj8vhTvtyS79k543+2NdVVZU4Ji4wKI0MNWtaLo6ssbxSssnoKDKCTcm4itAAb3WxePFinnvuOQCamppYs2YN9fX1LFmyhPXr1xOJRKitreXQIZ0XN9yp8Ei/JKemkZCYRMDvA6C2shz3+Nlg0ltoJEi74yvsrDpAm1fnmolxFubPHvD9d5566il8Ph933HEHn//853n66acZM2YMDz74IImJiaxatYpvf/vbTJ48eUBfV4aeKapT/6Sf3n7tJY4d2ENmVg4An7r/IXpe/wn+2pMGJ5PBZEnOJOfJZ/nrjd+lyaO9lsQ4/3HH/2FUQrrRMWSY0p/n0m8Tps4gHPpwOLm6sgLnxPkGJpKhkL76SQ7VHVfZEUNluNNIcSYaHUOGMRUe6be8grGYTGcn+QHUVFXi1DyeuGZ2J2MfO411JzYYHUVGuLm5M4jogoRcARUe6Teny03B+Il4us8uRW9qqMOemoUlMdXgZDJY0ld9mcLGk9R2NRgdRUa4pQULdH6WXBEVHrkkU2bNoddzdllyNBKhvqoC94R5BqeSwWCyu7BPmMMLha8ZHUVGOJvZyuTMgVmOLiOXCo9ckjHjJ8JHRpXLz5zGOX25cYFk0KTf9gSnWiuo6KgxOoqMcHNzZxIKh4yOIcOcCo9ckvRRWSQkJeP3eQGorjiNM28SloQUg5PJgLLacUy5huc1uiMx4OYJy3DbXUbHkGFOhUcuiclkYtrseXR3nj1JKxwKUVtxCve0pQYnk4GUecujVHc1cLL1jNFRZIRz2ZxMz9IeOHLlVHjkkk2aPotw6MPh5VNlZbhmXG9gIhlQJgvWGcs0uiMx4Zr8OYQHeHdlGZlUeOSS5Y0ZhyshoW/X5brqCuzpuVhTsgxOJgMhfcVDtHjbON5YYnQUEW6ZsByXzWl0DIkDKjxyySwWC7MXLqGjrQ04u1qr4tRJEmYsMziZDAT7nJt47rhGd8R4KY4kxqUVGB1D4oQKj1yWKTPnfOwk4TOnTuKacZ2BiQZXNBrl/9tRw0snPrnb8He3VfHTvXXnfFwwHOEnu2v54qtlfPHVMn55oJ5w5Oy/257qLh5/+SRffq2Mky3evsf8aFcth+uMOZE8dfmn6Qr2crDuuCGvL/JRSwrmE41GjI4hcUKFRy5LVl4+ySmpeHt7AWisq8HkTMKeNdbgZAOvqsPH379dwY6qzk9878XCZgobPed97PrSNjr9YX62ZiL/986JFDX18l7l2ef5w9EmfnDreL6+JJ91hc0AlLb00hsMMzfPmC30HQtW8dzxVw15bZH/buXE63Bos0EZICo8cllMJhNzFl1Ld+eHp2eXFhWSOP82A1MNjg2lbdw6MY3lYz++9P5YQw8H63q4ffL5DzO8e3omf39dAWaTiS5/GE8wQpLdAoDNbMIbitAbCGMzm4hGo/z6YANfmJ8zqD/P+SRfcyfeaIg9NYcNeX2RjxqfVkCmDgqVAaTCI5dt0vRZRCORvktbJ4uPkzB9GaY42y/jK4vyuPGqjx+f0dob5Gf7G/ify0ZjNl348Vazif882MBjL58k1WlhRnYCAI/Pz+Ff3q3mT8eaeXB2FhvL2pmTm0hWon2wfpQLci65ixcK13/sUqWIUW6ffDM2s9XoGBJHVHjksqWPymJUbi69PWfnm3g9HuqrK0icFd9L1EORKP/yXjVfXJBDutvWr8c8Nj+HFx+YRnainX/fc3a+z8zsBJ69YyLPrLqKVKeVTafauXdGJs8fb+Lbmyv49cGhO78qafZNhK0WdlTuG7LXFDkft83F4tFzsJgtRkeROKLCI5fNZDKxcNkKurs+nNtSVHicxAWrDUw1+MpavTR0B/jlgQa+uv4Ub5xsZ3tFJz/aVfuJ+55o8lDT5QfOjvTcMiGV023eT9zvd0caeWDWKJo8QY7Ue/juTePo9oc5XD80k5dd132aFwtfJ6wJohIDbhy/hAgaaZSBpfFCuSKTps/EZrMRDAax2Ww01lYTMtlwjpmOr6rI6HiDYtooN7+/d2rf13840kiXP8xXFuV94r5HGzyUNPfyjzeOxWSCrWc6mZ3z8QnJZ9q8NHmCLC5Iprzdh8V09hqZyQT+0OAXkIRpS8HhYmv5rkF/LZH+uHPKLToZXQacRnjkijicLuYuWkZH64fLtYsKj5EwP75HeS7k9dK2vtGe+2ZkkpVg5yvrT/HV9acwm008Mi/7Y/f/5YEGnlhwdqLy+DQnaS4rj718kg5viAX5SYOe173is7xcvJFgRIczivFmZk3RRoMyKExRzVCUK9TS1MCv/+2fyc4bjclkwma3c9/Dj1P3868R9nRc/AnEMK4J80i955t88bW/xx/yGx1HhH+47ilm50zHZLrIagCRS6QRHrlimVk5FIyf2LdEPRgIUF5WSlKcz+WJB4m3PML6kndUdiQmZCdkMj1rksqODAoVHhkQ1yy/kV7PhxvwHT9ykKR5t2J2uA1MJRfiGD0NW0omb5RtNTqKCAD3zrwds0krs2RwqPDIgBg3cQruhAT8vrMHivZ0dVJTWU7SglUGJ5PzSV71BTaVbac3+MlVYyJDLcOVxpKCeVi1FF0GiQqPDAirzcY1y1fQ0dbad9vRQ/tJWngHJptWW8Qae/Z47Ol5vFb6ttFRRABYO/02TOhSlgweFR4ZMLMWLMJitRIMBADobG+jsb6WxLkrDU4m/13q6i+z9cwuuv3GHFIq8lHJjiSuH7cYm6V/G3mKXA4VHhkw7oRErll+I20fWaJ+5MB+UhZ/CpN+kcUMa3oe9qwxvFyy0egoIgDcNXUlmqcsg02FRwbU3EXXYjaZCIWCALS1NNHS0kzi7BsNTiYfSLv9SXZWHqDd+8nT30WGWoLNzcqJy7FbjDlDTkYOFR4ZUInJKcxfch3tzc19tx05uI+kJfeARRt7G82anIk9byIvFb9hdBQRAO6YchNo7o4MARUeGXDzli4nGo0SDp/dube5oZ629naS5t1mcDJJu/1JDtYeo9nTevE7iwyyFGcyd0y5GYdVozsy+FR4ZMClpKVz9TVLaPvIKM/+3TtIufZezM4EA5ONbGZ3MvYx03nxxOtGRxEB4MFZn8KsyTsyRFR4ZFAsXHYj4XCYcDgMQEdbK1Xlp0heeq/ByUau9NVfprCxhNruBqOjiJCfnMPSMfO1MkuGjAqPDIr0zFHMWbSUtqbGvtsO7dtD0pybsKaMMjDZyGS2u7FfNYcXCtcbHUUEgMfm3o/VrHl9MnRUeGTQLL1xJZhMffvyeHs9FB07TMqNDxucbORJW/UEp1orqOioMTqKCDOyJjMpczwWsz6CZOjo3SaDJikllWtvvo3W5g9HeQqPHMQxdhaO3AkGJhthrHYcU67hucJXjU4iggkTX5j/GZxW7cAuQ0uFRwbVvMXLcCck4fP2AhAKBjm0bzcpNz9mcLKRI3PlY1R31lHWWm50FBGuHbuADFeq0TFkBFLhkUHlcLq4YdUa2j+y+/Kp4kJCzhQSZl5nYLIRwmzFOv1anjv+mtFJRHDbXDw2736cNqfRUWQEUuGRQTd99jwys3Lp7jq7s280GmXHts2k3fQIZleiseHiXPqND9Hc20ZhU6nRUUT43Ox7tKOyGEaFRwadxWrlpjvW0tPZSTQaBaC1qYEzp8pIvekRQ7PFO/ucFTx3XHN3xHiTM67i2rELsWsZuhhEhUeGxLhJU5g4bSatzU19tx3cuxPHVXNxjplhYLL4lbb8fjoDHg7VFxodRUY4i9nC/1j0iHZUFkOp8MiQMJlM3LzmHqKRCIGAHzg7gXn3u9tIX/0VnaY+COwLb+P5Qs3dEePdNWUlKa5ko2PICKfCI0MmNT2D62+9k9amD0d5qstP0dLRQfLSuw1MFn+SF92JNxJiT81ho6PICJedOIq102/VMnQxnAqPDKl5S5aRnZtPZ3tb3227391G0oLV2DLyDUwWX5yL7+KFwvV9c6ZEjPKVhZ/DatYIrhhPhUeGlMVq5bZ7HsDr8fSds9Xr6eHQ3t1k3PVXoK3mr1jSnJsJWSzsqNxndBQZ4W6deD3j0wq0o7LEBL0LZcjljh7DwuU30tJY33db6YmjdPhCpFx3v4HJ4oNr+X28eGID4WjE6CgyguUn5/DQ1Wtx2nQpS2KDCo8YYumKlbgTk+j19PTd9t6Wt0mYfTPOMdMNTDa8JUy/FhwutpXvNjqKjGBWs5W/WfpFLUGXmKLCI4ZwutysuuczdLS2Enn/0pbP28uOrW+TseYbmB1ugxMOTwk3PsRfit4kGAkZHUVGsM/MvIsMdxpmXcqSGKJ3oxhmwpTpLFh2A00NH17aqq0sp6KigrRVTxqYbHhyTZiHJSGZt0+/Z3QUGcFmZk3h5onLdHyExBwVHjHU9bfeTvqoLLo62vtu27/rPUw5E3XW1iVKvOURXit5G384YHQUGaES7Ql8ffHjuFR2JAap8Iih7A4na+7/HL0eD8HA2Q/qcDjEtrffJO2Wx7CmZhuccHhwFEzHlpzJm2XbjI4iI9iTCx7GrbIjMUqFRwyXnT+aG1ffRUtTQ9++Me0tzRzZv5fMe/8Ok7ajv6jk277AxrJt9Aa9RkeREerOyTcxI3syNqsmKktsUuGRmDB/6XWMnTjlY2dtFR8/QlN7F+mrNZ/nQuw5V2FPz2X9yXeMjiIj1PRRk7h35h247S6jo4iclwqPxASLxcLqez6D2WzG2+vpu33nts2QM5nE+bcZmC62pa76ElvO7KTb33PxO4sMsDRXCt9c+oTm7UjMU+GRmJGSls6d9z9Me2sL4dDZZdWhUJDNGzeQsvwBnAXTDE4Ye6wZ+dizxvBK8Sajo8gIZDNb+dtrv4LTqrIjsU+FR2LKxGkzWXbzKprq6/rm83R3dvDu5k1k3v03WJIzDU4YW9JWP8nOygO0+zqNjiIj0JcWfJbshAzsmrcjw4AKj8ScpStu5aop02hpbOi7ra6qgmNHDjPqvr/XJOb3WZMzsedN4KXiN4yOIiPQ7ZNWMDdnBgnOBKOjiPSLCo/EHIvFwu2f/iwJSUkf25/nxJGDNLZ3k/GpvwKT3rpptz/JgdqjNHtajY4iI8z8vKu5d8btJLkSjY4i0m/61JCYlJCYxD2fewK/34fP++FS6x1b38HrHkXarV8wMJ3xzO4U7GOm8+KJ142OIiPMpIzxPLXwc1qRJcOOCo/ErKzcfO68/3O0NTf1TWKORMJsfmM9pjFXk7z0HoMTGidj9Zc53lBCXXej0VFkBMlLyuZvr30Su9WOyWQyOo7IJVHhkZg2ZeZslq9cTWN9LZFIBIBgMMBbG17BPe82Eq++0eCEQ89sd2O/ajYvnFhvdBQZQdKcKXxr+f/AglmbC8qwZDU6gMSWZ555hk2bNpGWlsaoUaNYsWIFv/jFL0hLS8PpdPKrX/2Kf/3Xf2Xfvn2Ew2HuvvtuHnnkEQB+8Ytf8OabbxIOh1m2bBlPP/00tbW1PPXUU0yaNIni4mIyMjL48Y9/TGpqar8zLV1xK10d7Rw7sJec/NGYTCa8Hg+b1r/C6rWfI+zpwHv68CD9i8SetFVf5GRrOZUdNUZHkRHCZXPyD8ufwoaVBJcmKcvwpBEe6bNlyxYOHjzIhg0b+MUvfkFRUREA5eXl/OAHP+A3v/kN69atA+Dll1/mpZdeYvPmzRw4cIB3332XwsJCXnrpJV555RUaGxt57bXXACgpKeHRRx9lw4YNJCcns379pY1MmM1mVt51HxOnzqCpoa7v9q6ONja/uYGMNd/AkTthgP4VYpzVjmPKQp4vfM3oJDJCWM1Wnl7yJRItblKTUoyOI3LZNMIjfXbt2sWqVauw2+3Y7XZuvvlmADIyMhg9ejQAu3fvpri4mD179gDQ29tLaWkpNTU1HDt2jLvvvhsAn89HXl4e8+fPJyMjg+nTpwMwadIkOjsvfc8Yq83GnQ88zPO/+iktTQ1kZp09VLS5oY4dW95m2ae/ReMf/5FgS/UV/zvEssyVj1HVWUdZa7nRUWQEsJjMfO2aR8hxjyIjJd3oOCJXRIVH+pjN5r55Mh/ldH64i2o4HObpp59m5cqVALS1tZGQkMAzzzzD5z//eR599FEAurq6sFgstLe343A4+h5vMpn6NhS8VA6ni3s+9wX+8PMf09HWSmp6BgDVFafZs9PG4oe+Q+MfvxO/pcdsxTb9Wp7b9Qujk8gIYDGZ+dqixxifVEBmSobRcUSumC5pSZ+lS5fy1ltvEQgE6OnpYdu2bdTV1X3sPosXL2bdunUEg0E8Hg8PPvggR44cYfHixbz66qt4PB5CoRBf/epX2bRp4I87SExO4dOPPokJ6O76cKSovKyEPTt3kP3Qd7BlFgz468aC9BWfpam3jRNNpUZHkTj3QdkZ484jK22U0XFEBoRGeKTPDTfcwOHDh1m7di0pKSlkZWV9bHQG4IEHHqCyspK1a9cSCoW4++67WbRoEXB2rs6nP/1pwuEwy5cvZ+3atdTW1g54zvTMUdz32JP86ec/xmI2405MAs6WHiBuR3rss2/kT/v+y+gYEuc+KDv5jixyM7K1/Fzihil6udcXJO4cPnyYiooK1q5dSzAY5P777+d73/seU6dONTraOVWXn+aFX/+UhMTEvtIDMH7SVBZfuyyuSk/adffjnX0933jzO0ZHkTj2QdnJs48if1QeVqv+Jpb4oUta0mf8+PFs2LCBNWvWcPfdd3P77bfHbNkBKBg/gfsf/wqenh56e7r7bo/Hy1v2Bbfx/HGtzJLBo7Ij8U4jPDLsXXikZznNL34Pf90pAxNemeRFa2DJHXz19W9f9oRvkQuxW2x8Y9HjjLKmqexI3NIIjwx7FxrpeW/bZkbd/21cE+YZmPDKOJes4fnC9So7MiiS7An843XfICWSoLIjcU2FR+LC+UpPTcUZ3n79VdLv/BqJs1cYmPDyJM25hZDZws7K/UZHkTg0yp3Od2/8G7xtHsbnj1PZkbimwiNx44PS0+vxfGzJektjPW+8vI6E5Z8hZdl9Bia8dK7r7uPFExsIRz+5P5LIlRiXOprvrnia6vIqpk+cprIjcU+FR+JKwfgJPPTlrxMJheloa+27vaujndf//AKWadeTvurLYIr9t37C9GuJ2h1sK99tdBSJM7Oyp/K/rvsaJ0+eZMHV81V2ZESI/d/6IpcoJ7+Az37lr3C63LQ2Nfbd7u318MbLL+LLnEDmPX+Lyea8wLMYL+HGh3i5aCPBSMjoKBJHlo+9hq8tfJRTp06xaM5CLBaL0ZFEhoQKj8Sl9MxRPPTlr5OZk0tTfW3fhN9gMMDbG16hOWQj55F/wZqWY3DSc3NNmIfZnczbp98zOorECbPJzOdn38sDU++kuqaGebPmalNBGVG0LF3imt/nZf0Lv+dUcSHZeaMxmz/s+FNmzmbewkW0vvZjvGeOGJjyk0Z9+Se8XnuQvxS/aXQUiQNJjkS+uegLmL1gNVmYNH6i0ZFEhpxGeCSuOZwuPvXgo8y+ZikNNdWEQsG+75UWHmXzxtdJu/NrJC+928CUH+cYMx1bcgZvntpqdBSJA+PTCvj+TX9Hc2UDSa4ElR0ZsTTCIyNCJBJh7/Z32LZxPWkZmbjcCX3fcycksuK2O7B11tK6/idEAz4Dk8KoJ37IOy3FPHf8VUNzyPC3fMw1PDLnPt55dzPLF15LZnqm0ZFEDKMRQjsj0QAADqpJREFUHhkRzGYzS25cyacfe5L/v707i43ruu84/r2zr1xmIWdIifsmUbQWU9ZCW1JUeYscb43dOK0LJw8FjKKtkaDOU4oWCQLUyEOTPDRFkKQOjMauE8uWZdOLRIna952UREoURYrbkEPOcDZyttsHqrZpKbKtiBxy+P8ABGd4h/f878Nwfjzn3HOikci0O7iikTDvb3sTX9KI54VX0Du8GavT4KnA4PCy49LOjNUg5j+tRssLy5/h2dqttOzdzSMbH5awIxY86eERC47fN8S2137NmH8Et8c7beJm9dIGGtc2EWj5HeEzu2a9toLv/Dt7Q7389+n/nfW2RXbw2gr4pzXfJTIaIjAWoGn1+mlz14RYqORdIBYcZ0Ehf/PiS1TXNzBwvYdk4tN5PZ3t52h++02Ma57G9Zc/QGO2zVpdOmcx+oIS3rn44ay1KbLLX5Q38ePN/8yZ46cx6ow8sOZ+CTtC3CA9PGLBSqfTHN3Xwp7m7eTmO7BYPw03Go2We9c1UVlZhf/dnzPRfW7G63E//2OOJUb55fHXZrwtkV3sBisvNj5PocHJhy0f8+TD35AhLCE+RwKPWPC6Oi7w7u9fJZlM4iwonDbE5V1cygObHyLWtpfAntcgNTOLAOpyXBS++Au+1/xvDEdHZ6QNkZ3uKVzC36/+W06cPsnwyAhPPfI4JuPcXlRTiEyQwCMEEAoG+OCt17l8sQ13oRe9wfDJMaPJzP1f24LDZmZ0+38Q91276+27n/sXzmri/OzIb+76uUV2MmoNPLfsCdYVr+LN7X9g9fJGVtQvl8UEhfgTJPAIcUM6neb0kQPs2rENg9FInsM57XhVXT2r199P+PQugvveQE3G70q7Gksu3n/4JS9/9BMGQkNf/AtiwVvhqefvVj1H19WrnDl/hqcffQpnviPTZQkxp0ngEeJzhgf72f773zHiG8Tt8U7ba8hksbC2aSOFhQWMNf/yrqzQ7H7mB1yymHjlwH/+2ecS2S3XlMN3VzxLdV4Zb77zR2oqqtm0boPshyXElyCBR4hbiMcn2f9xM0f3tZCTm4/Vbp92vKikjPUbN5O8foHAx78mFQneUTsagwXPS7/ihy0/5Vqg726ULrKQgsLmiia+vewJDp84wokzJ/n2k9+ipHhxpksTYt6QwCPEbXRf7qD5D//DeDCAu9CDVqf75JhWp2Pl6rVU19UT2PMa4dO7gK/2dnI+8RI9Lhc/av35Xa5cZIviHA8v3vs8hqSO1996g9qqGh7Z9DBmk0xMFuKrkMAjxBeIT05weM9ODu3ZiclkItfhnDYxNN/ppmnTZkxqguDO3zLR2/7lTqwzUPS93/Cj1l/Q6b86Q9WL+cputPHs0q00lazm/Z3NXO3p5luPP0vpopJMlybEvCSBR4gvaaj/Oh9se4P+nm5cBYUYPnfrb3lNHY1rmkgOXSG461USo/23PZ/r6y8ysKicH7b8dCbLFvOMXqtna/VmHq99kFPnT/Pxnp1sbtpEU+N69Hp9pssTYt6SwCPEV5BKpTh77DC7338bVVVvWrdHo9WytGElDasaiVw4QHDv66Sj4zefSKPD+/3f8sqB/6LN1zGLVyDmKgWF+0tX89cNT9I/MMBbO96mwOnmm1ufkkUEhbgLJPAIcQeCY6Psfv8dLp47hdVmx56bNy34GE0mljeuoapmCeNHtjN+9N1pt7E7tnyHQM1yXv7oJ5koX8wx9QW1vLD8mygJ2Pbe2wwN+3hm69Oyro4Qd5EEHiHukKqqXO/uYteOtxjs671pewoAe24ejWvX4/EUETy0jfCpj1CTcTzff5WfHX2VUwPnM1S9mAuWuKt4duljeCxu3vuomTPtZ3l44xbuv+9+LGZzpssTIqtI4BHiz5ROp+loO8uuHW8RGg/idBVgMBqnvcbhKmBF42pcBYWkR3oJujy81PyvmSlYZFx9QQ1/tfQbuM0Odu5t4ciJo6xddR8PbthCfm5epssTIitJ4BHiLonHJzl77DB7P3qPZDKJy10w7Tb2y9e6CGjg5X98mXyXm+bOPTR37iYcj2SwajFbFBQai+/h6bpHyNHZaT3Yyv4jB6irruPxBx+jqNCb6RKFyGoSeIS4yyLhEEdbWzh+sBUFcLgLUDQaduxvoaiqhtLScvJz87l3xSqqy6to7T7M+5278UVGMl26mAF6rZ6mkkaerHkINaGy9+BeDp88SlGhl6cffZKqskqZpyPELJDAI8QMCY6NcvxgKycP7sM35ueCf4iNmx5C0Xz64WazWFl5z0qW1S7l8ug1mi/v5tRgG/K2nP8KbW4ertzAxrK1DPqG2H94P6fPn6XI4+WxLV9nSVUdGo0m02UKsWBI4BFiho0Hxnh3+x850H4ao8mEy+nCaJg+x0en1VJbWUtDfQNmi4kPr7TScvUQ45OhDFUt7oSiKKzyNvBo5SYqHCWcv9DG3sP76BvsY3HRYrZufpTayhoJOkJkgAQeIWbJeGicQyeP0HJgNxOTkzjy8rFarDe9zuMupKG+geqyKk4NnOeDK61cGrmSgYrFl5VnyuFr5et5qGID0UiEM+fOcvD4ISKxKDUV1Ty0YYsMXQmRYRJ4hJhl0ViMk+dOsnN/C4FgEJPJiCPPcdN//SajkaU1S1m2pB6NXsv+nmPs6zlKb/D2KziL2WHVW7hv0Qo2lqyhLH8xHVc7OXbyGG0dF9AoCiuXrWTTugdY5F0kQUeIOUACjxAZkkqluHKti9bD+2jraEejaHA6HDcNdwG4nW5qq2qoq6olnIiyr/co+3uOMRzxZ6Dyhcug1XNvUQMbFq9haWEN3X3X6Ojo4Pi5E4RCIXLsuWxu2sSqZSvIsedkulwhxGdI4BFiDvCP+Tl25gSth/cSjcWwWW3k5eTesmeg2FNEbVUtNRVVDIVH2Nd7jJMD5xgMD2eg8uxn1ploKKxjbfFKVhU10D88QGdnJ20d7fQPDZBOpamrqmXTug1Ul1eh1WozXbIQ4hYk8Agxh8QTcS5evsSeQ3vp6pnaQT3XnoPNarsp/Gg0GkqLS6isqKR8cRmTqTgnB85zYvAc7cOdJFKJTFxCVliU42WldxmNngbKnSVcH+qju7ubto52rg/0kUgksJgtNDWu474Vjbid7kyXLIT4AhJ4hJijRgNjtHde4MCxgwz6BkFRyM/Nw2K23PL1boeL8pIySkpK8TgLuDR8heOD5zgz2C69P1/AojezxF3NvZ4GVhXVo6QVrvZ0093TzdXebnwjPibjcQx6A433rGJVw0rKF5dJb44Q84gEHiHmOFVVGfYPc+5iGweOH2J0bBSNRkNOTg5Ws+WWw15Gg5GyRaWUlJRQWlyCVqulY6SLC/7LXPJfoWu0h0Q6mYGrmRsKbW5qXRUscVZR56zEaXPQ7xvgWs81rvZ0MzTiIzgeYGJiEq1Oyz1LGrhveSOVZRUY9IZMly+EuAMSeISYR1RVpW+wj/OX2jnddobB4SEUwGQykWvPRfeZrSw+y261UeQpwlvowevx4spz0Rvo46L/Ch3+q/QE+xgMD5NW07N7QbMg12hnUW4RFfklLHVWUe0qJ51K0zfUz+DgIP2DA/j8PkKRMMFgEAC9Xs+y2qWsqF9OVVmVbOQpRBaQwCPEPDYWDNDV08WZtnO0d14gmUqiUW7f+wOg1+nwuD0UebwUFBTidDjJsdgZCg3TG+zn2ngfvcF+eoP9+CJ+VOb+nwmrwcLinCIW5xZRklNEaW4xxbketIoG39gIIyMjDAwO0D/YTygSJpFIEAyNMzk5gaqCp6CQlctWUFtRwyJv8Z8Mj0KI+UkCjxBZIpFI0DtwnYuXOzh74SxDw0OgKKCqWK1WbBbbbT/EdTodzjwHLocLR74Dh9OBK9+J1WQlEA3ij44xEhtlODrKSGx06nl0DH90jGgiNqPXptPocJjzcFrycFrycZrzcZsduC1OnJZ8HJY8dBotvsAIfr+fsbExRkb9+Mf8RKIRVFUlNhEjFA6RTKYAMBqN1FbWsHxJA+Ul5bJLuRBZTgKPEFkqGosx4Bugp6+Xi5cv0tXTTTKVRFVVDHoDFrMZs9mMVnP7ibd6nQ67zY7dap/6brNhtdmw2WzkWO3kWO0YdAYmkpPE4hNMJCaIJSaIJmJEkzEiiRjxVIK0mkZFJaWmUVUVraJBURS0igatosWiN2PRmbHozZj1pk++TAYjCgqhWJjxcIhQOEQkHCEcDhOKTD0PRcJEY1FgatgvnogTjUWJRmMoCqTTKm6ni7qqWqrKKikq9OLMd8oWD0IsIBJ4hFggUqkUPv8w/UP9XO7uoqevh0HfIGlVRWEqFBhNRiwmM2aT+SuFAUVRMOgNGA0GDAYjRoMBo8F442dGtDotCgoajYKCAoqCqqqoN8JPOj0VUibjk0zG48TjU4///2epVOqmNlVVJZFIEJ2IEo3FUNPqVLhRVXLtORR7i6koKae0uISiQu8tt/EQQiwcEniEWMBSqRSB8QD+sVF8/mGuXb9Gb/91fCM+VKaCDCqk1TQajWYq0NwIMTqdbsZ6SFRVJZVKEU/Eb4SeOIlEHEXRTAUmpkKS1WplsbeYkuJSij1enPkOnPkuzCbTjNQlhJi/JPAIIW6SSqWIRCOMh0OEI1NDSaOBUXwjw/gDfkbHxojGIiRTKTQazSfBaCqLTD1QVXXqOVMB5rMUlE8nVCtTAQb1xtRoVUVVVYzGqTvPnPkO3A4XbpebXHvOjeE1GzarDZNRgo0Q4suRwCOEuGPJZPKTHpjJ+OS0oahkMnljuGpq7o6qqmhuzNtRFAWNRntjCMzw6XCY3oDRODUUJhtuCiHuJgk8QgghhMh6couCEEIIIbKeBB4hhBBCZD0JPEIIIYTIehJ4hBBCCJH1JPAIIYQQIutJ4BFCCCFE1pPAI4QQQoisJ4FHCCGEEFlPAo8QQgghsp4EHiGEEEJkPQk8QgghhMh6EniEEEIIkfUk8AghhBAi60ngEUIIIUTWk8AjhBBCiKwngUcIIYQQWU8CjxBCCCGy3v8BLOepBVcm4HIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig1, ax1 = plt.subplots(figsize=(10,6))\n",
    "ax1.pie(freq, explode=(0, 0, 0), labels=values, autopct='%1.1f%%', shadow=True, startangle=90)\n",
    "ax1.axis('equal')  # Equal aspect ratio ensures that pie is drawn as a circle.\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Média e Mediana"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A média e mediana são medidas de tendência central usadas para dados quantitativos. Assim, a média:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: [1, 1, 1, 2, 2, 3, 4, 5, 5, 5]\n",
      "A média: 2.9\n"
     ]
    }
   ],
   "source": [
    "import numpy as np \n",
    "X = [1,1,1,2,2,3,4,5,5,5]\n",
    "mx = np.mean(X)\n",
    "print('X:', X)\n",
    "print('A média:', mx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No caso da mediana:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: [1, 1, 1, 2, 2, 3, 4, 5, 5, 5]\n",
      "A mediana: 2.5\n"
     ]
    }
   ],
   "source": [
    "md = np.median(X)\n",
    "print('X:', X)\n",
    "print('A mediana:', md)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Se adicionarmos um valor extremo aos dados, vejamos como a média e a mediana se comportam:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X2: [1, 1, 1, 2, 2, 3, 4, 5, 5, 100]\n",
      "A nova média: 12.4\n",
      "A nova mediana: 2.5\n"
     ]
    }
   ],
   "source": [
    "X2 = [1,1,1,2,2,3,4,5,5,100]\n",
    "print('X2:', X2)\n",
    "print('A nova média:', np.mean(X2))\n",
    "print('A nova mediana:', np.median(X2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ou seja, a média é altamente sensível a valores extremos, enquanto que a mediana é mais robusta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos considerar uma distribuição de probabilidades. Os dados são gerados a partir de distribuições normal e exponencial."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para a distribuição normal, a média é indicada pela linha contínua e a mediana, pela tracejada."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt #biblioteca gráfica para mostrar os gráficos\n",
    "\n",
    "mu = 0 # Média da distribuicao normal\n",
    "sigma = 10 #desvio padrão da distribuição normal\n",
    "Y = np.random.normal(mu, sigma, 500)\n",
    "plt.hist(Y, density=True, bins=50,lw=0,alpha=.8)\n",
    "\n",
    "m = np.mean(Y)\n",
    "md = np.median(Y)\n",
    "plt.vlines(m,0,0.05)\n",
    "plt.vlines(md,0,0.05, linestyles = 'dashed')\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.xlabel(\"x\",fontsize = 20) \n",
    "plt.ylabel(\"p(x)\", fontsize = 20) \n",
    "plt.show(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para a distribuição exponencial, a média é indicada pela linha contínua e a mediana, pela tracejada."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt #biblioteca gráfica para mostrar os gráficos\n",
    "\n",
    "lbda = 100 # taxa da distribuição exponencial\n",
    "beta = 1.0/lbda\n",
    "\n",
    "Y = np.random.exponential(beta, 500)\n",
    "plt.hist(Y, density=True, bins=50,lw=0,alpha=.8)\n",
    "\n",
    "m = np.mean(Y)\n",
    "md = np.median(Y)\n",
    "plt.vlines(m,0,lbda)\n",
    "plt.vlines(md,0,lbda, linestyles = 'dashed')\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.xlabel(\"x\",fontsize = 20) \n",
    "plt.ylabel(\"p(x)\", fontsize = 20) \n",
    "\n",
    "plt.show(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notamos que a média é similar à mediana se a distribuição é praticamente simétrica em relação à média. Caso a distribuição não seja simétrica, o mais adequado é usar a mediana como medida central."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quantis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# biblioteca para mostrar os gráficos\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "\n",
    "data = pd.read_csv('data/iris.csv', header=(0))\n",
    "plt.figure(figsize=(8, 8))\n",
    "# mostra o boxplot\n",
    "sns.boxplot(x=\"species\", y=\"petal_length\", data=data)\n",
    "plt.xlabel('Espécie', fontsize=18)\n",
    "plt.ylabel('Comprimento da pétala', fontsize=16)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Medidas de dispersão"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As medidas de dispersão mais usadas são a variância e o desvio padrão. A distância interquantil (IQR) também é bastante usada e quantifica a diferença entre o terceiro e primeiro quantil. Já a amplitude simplesmente mede a diferença entre os valores máximo e mínimo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: [0, 0, 1, 1, 18]\n",
      "Média de X: 4.0\n",
      "Variância de X: 61.5\n",
      "IQR de X: 1.0\n",
      "Amplitude de X: 18\n",
      "\n",
      "\n",
      "Y: [4, 4, 4, 4, 4]\n",
      "Média de Y: 4.0\n",
      "Variância de Y: 0.0\n",
      "IQR de Y: 0.0\n",
      "Amplitude de Y: 0\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import iqr\n",
    "\n",
    "def variancia(X):\n",
    "    m = np.mean(X)\n",
    "    N = len(X)\n",
    "    s = 0\n",
    "    for i in np.arange(0, len(X)):\n",
    "        s = s + (X[i]-m)**2\n",
    "    s = s/(N-1)\n",
    "    return s\n",
    "\n",
    "X = [0,0,1,1,18]\n",
    "Y = [4, 4, 4, 4, 4]\n",
    "mx = np.mean(X)\n",
    "my = np.mean(Y)\n",
    "print('X:', X)\n",
    "print('Média de X:', mx)\n",
    "print('Variância de X:', variancia(X))\n",
    "print('IQR de X:', iqr(X))\n",
    "print('Amplitude de X:', np.max(X)-np.min(X))\n",
    "\n",
    "print('\\n')\n",
    "print('Y:', Y)\n",
    "print('Média de Y:', my)\n",
    "print('Variância de Y:', variancia(Y))\n",
    "print('IQR de Y:', iqr(Y))\n",
    "print('Amplitude de Y:', np.max(Y)-np.min(Y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notem que os dados acima possuem a mesma média, mas a variância é bastante diferente."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Resumo descritivo"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para obtermos um resumo das medidas estatística dos dados:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "      <td>150.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>5.843333</td>\n",
       "      <td>3.054000</td>\n",
       "      <td>3.758667</td>\n",
       "      <td>1.198667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.828066</td>\n",
       "      <td>0.433594</td>\n",
       "      <td>1.764420</td>\n",
       "      <td>0.763161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>4.300000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>5.100000</td>\n",
       "      <td>2.800000</td>\n",
       "      <td>1.600000</td>\n",
       "      <td>0.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>5.800000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>4.350000</td>\n",
       "      <td>1.300000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>6.400000</td>\n",
       "      <td>3.300000</td>\n",
       "      <td>5.100000</td>\n",
       "      <td>1.800000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>7.900000</td>\n",
       "      <td>4.400000</td>\n",
       "      <td>6.900000</td>\n",
       "      <td>2.500000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       sepal_length  sepal_width  petal_length  petal_width\n",
       "count    150.000000   150.000000    150.000000   150.000000\n",
       "mean       5.843333     3.054000      3.758667     1.198667\n",
       "std        0.828066     0.433594      1.764420     0.763161\n",
       "min        4.300000     2.000000      1.000000     0.100000\n",
       "25%        5.100000     2.800000      1.600000     0.300000\n",
       "50%        5.800000     3.000000      4.350000     1.300000\n",
       "75%        6.400000     3.300000      5.100000     1.800000\n",
       "max        7.900000     4.400000      6.900000     2.500000"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd # biblioteca pandas\n",
    "data = pd.read_csv('data/iris.csv', header=(0)) # lê os dados a partir do arquivo\n",
    "\n",
    "data.describe() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Correlação"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlação de Pearson"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos considerar alguns casos para vermos como se comporta o coeficiente de correlação de Pearson de acordo com diferentes tendências entre as variáveis $X$ e $Y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import pearsonr\n",
    "\n",
    "N = 100\n",
    "X = np.linspace(-1,1, N)\n",
    "erro = np.random.uniform(-1,1,N) # ruído a ser incluído na relação linear.\n",
    "for sigma in np.arange(0,2,0.2):\n",
    "    Y = -0.8*X + erro*sigma\n",
    "    plt.plot(X,Y, 'ro')\n",
    "    corr, p_value = pearsonr(X, Y) # calcula a correlação\n",
    "    corr = int(corr*100)/100\n",
    "    string = 'corr = '+ str(corr)\n",
    "    plt.xlim(-1.5,1.5)\n",
    "    plt.ylim(-2, 2)\n",
    "    plt.text(0.6,1.7, string, fontsize=15)\n",
    "    plt.show(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A medida de correlação é importante para analisar a relação entre as variáveis. Se duas variáveis são altamente correlacionadas, é adequado remover uma delas, de modo a reduzir informação redundante nos dados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos considerar a base de dados da flor Iris:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd # biblioteca pandas\n",
    "data = pd.read_csv('data/iris.csv', header=(0)) # lê os dados a partir do arquivo\n",
    "\n",
    "corr = data.corr()\n",
    "#Plot Correlation Matrix using Matplotlib\n",
    "plt.figure(figsize=(7, 5))\n",
    "plt.imshow(corr, cmap='Blues', interpolation='none', aspect='auto')\n",
    "plt.colorbar()\n",
    "plt.xticks(range(len(corr)), corr.columns, rotation='vertical')\n",
    "plt.yticks(range(len(corr)), corr.columns);\n",
    "plt.suptitle('Correlation between variables', fontsize=15, fontweight='bold')\n",
    "plt.grid(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos mostrar a mesma tabela usando a biblioteca Searborn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "plt.figure(figsize= (6, 6))\n",
    "sns.heatmap(data.corr())\n",
    "plt.show(sns)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlação de Spearman"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Além do coeficiente de Pearson, podemos considerar o coeficiente de correlação de Spearman:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import pearsonr, spearmanr\n",
    "\n",
    "N = 100\n",
    "x = np.linspace(1, 50000, N) \n",
    "z = np.log(x)\n",
    "\n",
    "plt.plot(x, z) \n",
    "plt.xlabel(\"x\",fontsize = 20) \n",
    "plt.ylabel(\"Log(X)\", fontsize = 20) \n",
    "corr, p_value = pearsonr(x, z)\n",
    "corrs, p_values = spearmanr(x, z)\n",
    "corr = int(corr*100)/100\n",
    "corrs = int(corrs*100)/100\n",
    "string = 'Pearson corr. = '+ str(corr)\n",
    "plt.text(20000,3, string, fontsize=15)\n",
    "string = 'Spearman corr. = '+ str(corrs)\n",
    "plt.text(20000,1, string, fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notem que nesse caso, os coeficientes de Spearman e Pearson são diferentes. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementação das correlações de Pearon e Spearman"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos considerar um exemplo numérico para obtermos mais intuição sobre o cálculo dessas medidas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y')"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = [0.9,0.5, 0.3, 0.1, 1.0]\n",
    "y = [0.5, -0.1, 0.3, 0.1, 0.8]\n",
    "plt.plot(x, y, 'bo') \n",
    "plt.xlabel(\"x\",fontsize = 20) \n",
    "plt.ylabel(\"y\", fontsize = 20) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O coeficiente de correlação de Pearson:\n",
    "$$\n",
    "\\rho ={\\frac {\\sum _{i=1}^{n}(x_{i}-{\\bar {x}})(y_{i}-{\\bar {y}})}{{\\sqrt {\\sum _{i=1}^{n}(x_{i}-{\\bar {x}})^{2}}}\\cdot {\\sqrt {\\sum _{i=1}^{n}(y_{i}-{\\bar {y}})^{2}}}}}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos implementar uma função para calculá-lo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uma função para calcular a variância:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valor calculado pela função: 0.3440930106817051\n",
      "Valor calculado com o Numpy: 0.3440930106817051\n"
     ]
    }
   ],
   "source": [
    "def std(x):\n",
    "    n = len(x)\n",
    "    xm = 0\n",
    "    for i in range(0,n):\n",
    "        xm = xm + x[i]\n",
    "    xm = xm/n\n",
    "    std = 0\n",
    "    for i in range(0,n):\n",
    "        std = std + (x[i]-xm)**2\n",
    "    std = np.sqrt(std/(n))\n",
    "    return std\n",
    "    \n",
    "print(\"Valor calculado pela função:\", std(x))\n",
    "print(\"Valor calculado com o Numpy:\", np.std(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "E o coeficiente de Pearson:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valor calculado pela função: 0.7516412406984152\n",
      "Valor calculado usando o pacote statistics: 0.7516412406984154\n"
     ]
    }
   ],
   "source": [
    "from scipy.stats import pearsonr, spearmanr\n",
    "\n",
    "def Pearson(x,y):\n",
    "    n = len(x)\n",
    "    # averages\n",
    "    xm = 0\n",
    "    ym = 0\n",
    "    for i in range(0,n):\n",
    "        xm = xm + x[i]\n",
    "        ym = ym + y[i]\n",
    "    xm = xm/n\n",
    "    ym = ym/n\n",
    "    r = 0\n",
    "    for i in range(0,n):\n",
    "        r = r + (x[i]-xm)*(y[i]-ym)\n",
    "    r = r/n\n",
    "    r = r/(std(x)*std(y))\n",
    "    return r\n",
    "print(\"Valor calculado pela função:\", Pearson(x,y))\n",
    "print(\"Valor calculado usando o pacote statistics:\", pearsonr(x, y)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No caso do coeficiente de Spearman, vamos obter a ordem dos valores de x e y."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x: [0.9, 0.5, 0.3, 0.1, 1.0]\n",
      "Sorted x: [4, 3, 2, 1, 5]\n",
      "y: [0.5, -0.1, 0.3, 0.1, 0.8]\n",
      "Sorted y: [4, 1, 3, 2, 5]\n"
     ]
    }
   ],
   "source": [
    "print('x:', x)\n",
    "print('Sorted x:', [sorted(x).index(i)+1 for i in x])\n",
    "print('y:', y)\n",
    "print('Sorted y:', [sorted(y).index(i)+1 for i in y])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valor calculado pela função: 0.6999999999999998\n",
      "Valor calculado usando o pacote statistics: 0.7\n"
     ]
    }
   ],
   "source": [
    "xr = [sorted(x).index(i)+1 for i in x]\n",
    "yr = [sorted(y).index(i)+1 for i in y] \n",
    "print(\"Valor calculado pela função:\", Pearson(xr,yr))\n",
    "print(\"Valor calculado usando o pacote statistics:\", spearmanr(xr, yr)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Logo, vemos que o coeficiente de Spearman nada mais é do que o coeficiente de Pearson aplicado à ordem dos valores."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercícios de fixação"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1 - Gere dados a partir de uma distribuição de Poisson. Varie a taxas $\\lambda$ no intervalo [1,10] e mostre o gráfico da média em função da variância."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2 - Considere os dados da Iris. Calcule a média, variância e IQR para cada atributo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3 - Obtenha o boxplot de todas as variáveis da flor Iris, para cada espécie."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4 - Para a função log(), investigue como as correlações de Pearson e Spearman variam de acordo com o intervalo dos dados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5 - Considere o código acima que mostra como a correlação de Pearson muda com a inclusão de ruídos. Modifique a função para $Y = 0.5*X +$ ruído. Varie o ruído e calcule os coeficientes de Pearson e Spearman, mostrando os respectivos scatterplots com os valores dos coeficientes (como feito no exemplo)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6- Considere os dados abaixo, chamado quarteto de Ascomb. Calcule a média, variância, correlação de Pearson e Spearman entre as variáveis x e y. O que você pode dizer sobre esses dados?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "x = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n",
    "y1 = [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68]\n",
    "y2 = [9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74]\n",
    "y3 = [7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73]\n",
    "x4 = [8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8]\n",
    "y4 = [6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89]\n",
    "\n",
    "datasets = {\n",
    "    'I': (x, y1),\n",
    "    'II': (x, y2),\n",
    "    'III': (x, y3),\n",
    "    'IV': (x4, y4)\n",
    "}\n",
    "\n",
    "fig, axs = plt.subplots(2, 2, sharex=True, sharey=True, figsize=(10, 5),\n",
    "                        gridspec_kw={'wspace': 0.08, 'hspace': 0.08})\n",
    "\n",
    "for ax, (label, (x, y)) in zip(axs.flat, datasets.items()):\n",
    "    ax.text(0.1, 0.9, label, fontsize=20, transform=ax.transAxes, va='top')\n",
    "    ax.tick_params(direction='in', top=True, right=True)\n",
    "    ax.plot(x, y, 'o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
