{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Calcolo-della-dispersione-in-pandas\" data-toc-modified-id=\"Calcolo-della-dispersione-in-pandas-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Calcolo della dispersione in pandas</a></span><ul class=\"toc-item\"><li><span><a href=\"#Indici-di-dispersione\" data-toc-modified-id=\"Indici-di-dispersione-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Indici di dispersione</a></span></li><li><span><a href=\"#Box-plot\" data-toc-modified-id=\"Box-plot-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Box plot</a></span></li><li><span><a href=\"#Diagrammi-Q-Q\" data-toc-modified-id=\"Diagrammi-Q-Q-1.3\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>Diagrammi Q-Q</a></span></li><li><span><a href=\"#Simmetria,-distribuzioni-approssimativamente-normali-e-regola-empirica\" data-toc-modified-id=\"Simmetria,-distribuzioni-approssimativamente-normali-e-regola-empirica-1.4\"><span class=\"toc-item-num\">1.4&nbsp;&nbsp;</span>Simmetria, distribuzioni approssimativamente normali e regola empirica</a></span></li><li><span><a href=\"#Una-nota-sulla-produzione-dei-grafici-*\" data-toc-modified-id=\"Una-nota-sulla-produzione-dei-grafici-*-1.5\"><span class=\"toc-item-num\">1.5&nbsp;&nbsp;</span>Una nota sulla produzione dei grafici <sup>*</sup></a></span></li></ul></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "header": true
   },
   "source": [
    "<div class=\"header\">\n",
    "D. Malchiodi, Superhero data science. Vol 1: probabilità e statistica: Indici di dispersione.\n",
    "</div>\n",
    "<hr style=\"width: 90%;\" align=\"left\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div id=\"h-0\"></div>\n",
    "\n",
    "# Calcolo della dispersione in pandas\n",
    "\n",
    "<div id=\"h-1\"></div>\n",
    "\n",
    "## Indici di dispersione\n",
    "\n",
    "Gli oggetti di tipo serie messi a disposizione da pandas permettono di calcolare facilmente i principali indici di dispersione. Importiamo, come al solito, il nostro dataset e impostiamo lo stile per i grafici."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.constants import golden\n",
    "\n",
    "plt.style.use('fivethirtyeight')\n",
    "plt.rc('figure', figsize=(5.0, 5.0/golden))\n",
    "\n",
    "\n",
    "heroes = pd.read_csv('data/heroes.csv', sep=';', index_col=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gli indici di dispersione di un oggetto di tipo serie si calcolano invocando su quest'ultimo degli appositi metodi. In particolare:\n",
    "\n",
    "- `var` restituisce la varianza campionaria;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "388.76870505203914"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "year = heroes['First appearance']\n",
    "year.var()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `std` restituisce la deviazione standard campionaria;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19.717218491766"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "year.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `describe` calcola i principali indici descrittivi di centralità e dispersione (quelli relativi a media, deviazione standard, minimo, primo quartile, mediana, terzo quartile e massimo), unitamente al numero di osservazioni nella serie, che utilizza per popolare un nuovo oggetto di tipo serie;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count     367.000000\n",
       "mean     1979.855586\n",
       "std        19.717218\n",
       "min      1933.000000\n",
       "25%      1965.000000\n",
       "50%      1979.000000\n",
       "75%      1994.000000\n",
       "max      2099.000000\n",
       "Name: First appearance, dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "year.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `quantile` restituisce il quantile corrispondente al livello specificato come argomento."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1963.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "year.quantile(.15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Va sottolineato come l'eventuale calcolo di percentili, quartili o decili campionari deve essere fatto utilizzando opportunamente il metodo `quantile`, tenendo conto delle ovvie relazioni tra l'indice che si vuole calcolare e il corrispondente quantile. Per esempio, il $35$-esimo percentile si otterrà invocando `quantile(.35)`, così come il terzo quartile verrà restituito invocando `quantile(.75)` (sebbene in quest'ultimo caso si possa utilizzare anche il metodo `describe` introdotto nel punto precedente.\n",
    "\n",
    "<div id=\"h-2\"></div>\n",
    "\n",
    "## Box plot\n",
    "\n",
    "Un _box plot_ (o _box and whiskers plot_, o ancora un _diagramma a scatola_) è una rappresentazione grafica che riassume le principali caratteristiche di un campione di dati. Tale rappresentazione contiene due componenti principali:\n",
    "\n",
    "- una _scatola_, intesa come un rettangolo che evidenzia il primo e il terzo quartile campionario dei dati, che corrispondono alle due basi, e la mediana, indicata tramite un segmento parallelo alle basi stesse;\n",
    "- due _baffi_, che si estendono dagli estremi della scatola fino a raggiungere il minimo e il massimo valore osservato.\n",
    "\n",
    "A titolo di esempio la cella seguente visualizza il box plot relativo all'anno di prima apparizione."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "year.plot.box(whis='range')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si verifica visualmente come questo grafico metta in evidenza:\n",
    "\n",
    "- la centralità delle osservazioni, tramite il segmento che individua la mediana campionaria;\n",
    "- la loro dispersione, sia in termini di range interquartile (l'altezza della scatola) e di intervallo di variazione dei dati (la distanza tra gli estremi dei baffi).\n",
    "\n",
    "Vale la pena sottolineare che la presenza di eventuali valori mancanti non influisce sulla generazione del grafico. È inoltre stato necessario specificare l'argomento opzionale `whis` (abbreviazione di _whiskers_). In caso contrario viene visualizzata una versione leggermente diversa di box plot, in cui le osservazioni vengono preliminarmente analizzate in modo da evidenziare eventuali _outlier_ marcandoli con dei cerchi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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wCm4REYNRcIuIGIyuDihdiumto1ew9V6Qf2XaN3V3uSLtStekqwOKtJKu4CedhZZKREQMRsEtImIwCm4REYNRcIuIGIyCW0TEYBTcIiIGo+AWETEYBbeIiMG0Krg//vhj7r//fsLDwzGZTGRmZjqdr6qqYtasWQwbNgw/Pz/uvfdeDh486FQTGxuLyWRyuk2dOtWppra2lsTERAIDAwkMDCQxMZHa2tp2DlFEpGtpVXDX19czfPhwlixZQs+ePZ3O2e12HnroIQ4dOkRmZia5ubkEBARw1113UV9f71T70EMPYbVaHbeXXnrJ6fz06dMpKSnhvffeIysri5KSEmbOnNnOIYqIdC2tulbJxIkTmThxIgCzZ892Onfw4EH27t1LXl4eERERAKxcuZKhQ4eSnZ3NlClTHLW9evXC19e3xeewWq387W9/Y/v27YwePRqAl156iZiYGMrKyggNDW376EREuqB2r3GfPn0agB49evyv0auuwt3dnYKCAqfa7OxsgoODGTNmDE8//TQnTpxwnCsqKsLT09MR2gBjxozBw8ODwsLC9nZTRKTLaPfVAYcOHUpAQADPPfccr7zyCh4eHrz66qscPXqUyspKR91vf/tbAgICGDBgAF999RXPPvssX375JR988AFwdp3cy8sLF5f/XSXNxcWF/v37U1VVdcHnLysra+8QRFqpl95v8rO42ApDu4O7W7du/OUvf+Gxxx7j6quvxtXVlfHjx/Ob3/zGqe6RRx5x/HzNNdcQFBREdHQ0xcXFREZGAjiF9jl2u73F4+doCUV+NvlH9X6TTuGybAeMjIwkPz+fw4cPY7Vayc7O5j//+Q+DBw++4GOuvfZaXF1dOXToEAA+Pj4cP34cu/1/V5m12+1UV1fj7e19ObopItIlXNZ93H369KF///4cPHiQzz//nNtvv/2Ctfv376exsdHxYaXZbMZms1FUVOSoKSoqor6+3mndW0Tkl65VSyU2m80xM25qauLIkSOUlJTQt29fAgIC+OCDD+jXrx+BgYHs37+flJQUYmNjiYqKAuDbb79l06ZNTJw4kX79+mG1Wnn66acZMWIEY8aMASAsLIxbbrmFefPmsWrVKux2O/PmzePWW2/Vr6ciIudp1Tfg5OXlcccddzQ7/sADD/Daa6+xbt06Vq9eTVVVFb6+vtx///0sWLCA7t27A3DkyBESExM5cOAA9fX1DBo0iIkTJ5KSkkLfvn0d7dXU1JCcnMy2bdsAiImJYdmyZZhMpss1XpFLpm/Akc5CX10m0koKbuksdK0SERGDUXCLiBiMgltExGAU3CIiBqPgFhExGAW3iIjBKLhFRAxGwS0iYjAKbhERg1Fwi4gYjP7kXX6xMjIyWLp06RVpOzk5mdTU1CvStoiCW6SV9N2n0lloqURExGAU3CIiBqPgFhExGAW3iIjBKLhFRAxGu0pERAxGM24REYNRcIuIGIyCW0TEYBTcIiIGo+CWKy4xMZEHH3ywo7sh0mVoV4m026xZs3j33XebHc/NzWXEiBHU1dVht9sxmUyX/ByJiYnYbDbeeeed9nRVpEtw6+gOSNcwfvx4/vjHPzod8/LyAqBPnz4/+diGhga6d+9+xfpmJHotpDW0VCKXhbu7O76+vk43N7ez84IfL5XcdtttPPnkk6SlpRESEkJsbCwAb7zxBtdddx0+Pj6EhIRw77330tTURHp6Ops2bWLr1q2YTCZMJhMFBQUt9mPfvn1MnjyZ4OBgAgMDiYmJ4dNPP3WcP3PmDCaTifXr1xMXF4efnx8RERFkZWU5ag4dOoTJZCI7O5tbb70VX19fRo8eze7du52eq7S0lLi4OPz9/RkyZAgzZsygqqqqzX158803eeCBBxg4cCAvvPACP/zwA3PmzGHEiBEMGDCAUaNGsXr1auz2//1yfO41XbNmDcOGDSMoKIjHHnuM77//3lHT1NTEqlWrHK/pNddcQ3p6uuP8kSNHeOSRRxg8eDBBQUHEx8fz7bffturfWzqWgls6xLvvvoubmxvbt29nzZo17Nu3j5SUFNLS0ti3bx+bN29mwoQJADzxxBPceeed3HLLLVitVqxWK9dff32L7dpsNh544AG2bdvGzp07GT58OHFxcdTW1jrVPf/889xxxx3k5eXx8MMPk5iYSElJiVPNwoULmT17Nnl5eYwdO5YHH3yQyspKAP71r38RGxvLiBEj2LVrF5s3b6auro6HH37YEbCt7UtGRga33347n3zyCQkJCTQ2NuLv78+GDRsoLCwkLS2NZcuWNVuOys/P5+DBg1gsFt544w3++te/8vrrrzvO/+EPf+Cll15i/vz5FBYW8uabb+Ln5+fo26RJk/D09OTDDz/ko48+wsvLi7vuussp/KVz0hq3tNusWbPYtGkTPXr0cBy78cYbHbPYH69P33bbbdTX15OXl+eo37x5M/PmzePLL7/E09Oz2XNc6hq33W5nyJAhLFu2jHvvvZczZ87Qv39/pk6dysqVKx11sbGxBAYG8tprr3Ho0CGuu+46Fi1axBNPPAGcnb1ed911xMfHk5qaynPPPUdxcTHvv/++o43q6mpCQkLYvXs3kZGRre7LrFmzyMjI+MlxPP300xw4cIDs7GzH61FQUEBxcTGurq4AzJ49m8rKSrKzs6mrqyM0NJTly5czZcqUZu1t2LCBtWvXUlRUhIuLC3D2N4Dg4GDWrFnDnXfe2abXWX5eWuOWy+Kmm25i1apVjvvnh3hLrr32Wqf70dHR+Pn5MXLkSKKjo5kwYQJ33HFHiyH+U6qqqnj++efJz8/nu+++o7GxkZMnT3LkyBGnuhtuuMHpvtls5h//+McFa6666ipGjRqF1WoFoLi4mLy8PAYNGtSsD+Xl5URGRra6Lz9+LQBef/11MjMzqaio4NSpU/zwww9cffXVTjXh4eGO0Abw8/Pjyy+/BOCrr76ioaGBcePGtfg6FRcXc+jQIfz9/Z2Onzx5kvLy8hYfI52Hglsui169ehEcHNym+vP17t2bvLw88vPz2b17NytWrCA9PZ1du3bh6+vb6nYTExOpq6sjIyODgIAA3N3dmTRpEg0NDa1uozWampq47bbbePbZZ5ud8/HxaVNffvxabNq0iWeeeYb09HSuv/56evfuzbp169i5c6dT3bnPEM5xcXGhqakJwGk9/EL9j4yMdFpaOadfv34/+VjpeFrjlk7Dzc2N8ePHs2jRIvLz86mrq+Ojjz4CoFu3bjQ2Nl60jT179jBz5kwmTpxIeHg4vXr1cqxLn2/fvn1O9/fu3cvQoUMvWNPU1MRnn33mqBk5ciRfffUVgYGBBAcHO93O/ZbQ2r60NAaz2cz06dOJjIwkODi4zR8ahoeH0717d3Jzc1s8P3LkSA4ePEj//v2b9b892zbl56Hglk7hww8/ZN26dZSUlPDPf/6T9957j5MnTxIWFgZAYGAg+/fv55tvvqG6upozZ8602E5ISAgbN27EarXy6aefMnXqVNzd3ZvVffDBB/z5z3/mm2++4cUXX+Tjjz/m0Ucfdap5/fXXsVgsfP311yQnJ/Pvf/+bqVOnAmdn09XV1UybNo1PP/2U8vJycnJymDt3ruPDvdb2paUxFBcX8/e//52DBw+SkZFBYWFhm17PPn36MGPGDBYuXMg777xDeXk5+/bt46233gIgPj6evn378uCDD/LJJ59QXl5Ofn4+qampWioxAAW3dAomk4ktW7Zw1113YTabee2111i7di1msxmAhIQEQkJCGD9+PCEhIezdu7fFdl599VXq6uoYN24c06dPJyEhocV16NTUVDZv3szYsWP505/+xLp165p9oLho0SJeeeUVxo4dy+7du8nMzGTAgAEADBo0iB07dtDY2Mg999zDmDFjePLJJ+nZsyfdunVrU19+bPr06UyaNImEhASioqI4duxYs/9UWmPx4sXMnTuXJUuWcMMNN/DII49w7NgxADw9Pdm2bRv+/v5MmTIFs9nMnDlzsNlsF913Lx1Pu0rkF+XcTo63336bSZMmtVhzblfJub/8FOlsNOMWETEYBbeIiMFoqURExGA04xYRMRgFt4iIwSi4RUQMRsEtImIwCm4REYNRcIuIGMz/A7vi2yG4OZd2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "year.plot.box()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sebbene i box plot che abbiamo ottenuto fossero visualizzati in un sistema di riferimento bidimensionale, le informazioni salienti venivano tutte reperite leggendo l'asse delle ordinate. Specificando l'argomento opzionale `vert` è possibile ottenere un diagramma equivalente visualizzando le informazioni sull'asse delle ascisse. In questo caso i valori per i quartili si leggeranno ovviamente in corrispondenza di segmenti paralleli alle altezze della scatola."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "year.plot.box(vert=False, whis='range')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div id=\"h-3\"></div>\n",
    "\n",
    "## Diagrammi Q-Q\n",
    "\n",
    "Un _diagramma Q-Q_ (o _diagramma quantile-quantile_) è una rappresentazione grafica che considera due campioni al fine di valutare la validità dell'ipotesi che i campioni stessi seguano una medesima distribuzione. Questi diagrammi si basano sul fatto (che non dimostreremo) che i quantili campionari rappresentano l'approssimazione di quantili teorici che, considerati tutti insieme, individuano univocamente la distribuzione dei dati.\n",
    "\n",
    "Pertanto, se due campioni hanno un'uguale distribuzione, allora estraendo da entrambi il quantile di un livello fissato si dovranno ottenere due numeri molto vicini (in quanto essi rappresentano approssimazioni diverse di uno stesso valore).\n",
    "\n",
    "Se consideriamo per esempio le altezze di due campioni di supereroi Marvel e DC, escludendo eventuali _outlier_ (limitando per la precisione la scelta a valori compresi tra 150 e 200 centimetri), i corrispondenti quantili di livello $0.2$ assumeranno i seguenti valori."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(170.186, 170.456)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marvel = heroes.loc[(heroes['Publisher']=='Marvel Comics') & \\\n",
    "                    (heroes['Height'].between(150, 200))]\n",
    "\n",
    "dc = heroes.loc[(heroes['Publisher']=='DC Comics') & \\\n",
    "                (heroes['Height'].between(150, 200))]\n",
    "\n",
    "marvel_sample = marvel['Height'].sample(120)\n",
    "dc_sample = dc['Height'].sample(120)\n",
    "\n",
    "(marvel_sample.quantile(.2), dc_sample.quantile(.2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Per ottenere il diagramma Q-Q ripetiamo ora questa operazione facendo variare i livelli in una discretizzazione che copra ragionevolmente l'intervallo $[0, 1]$ e visualizziamo sul piano cartesiano un punto per ogni coppia di quantili campionari che si riferiscono a uno stesso livello."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "levels = np.linspace(0, 1, 100)\n",
    "plt.plot(marvel_sample.quantile(levels),\n",
    "         dc_sample.quantile(levels),\n",
    "         'o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il fatto che in ogni coppia considerata i due quantili fossero molto simili tra loro fa sì che i punti ottenuti si allineino approssimativamente sulla bisettrice del primo e del terzo quadrante. Possiamo evidenziare tale fatto sovrapponendo al diagramma il grafico della retta."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([min(dc_sample), max(dc_sample)],\n",
    "         [min(dc_sample), max(dc_sample)])\n",
    "plt.plot(dc_sample.quantile(levels),\n",
    "         marvel_sample.quantile(levels),\n",
    "         'o')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In realtà non è necessario costruire \"a mano\" i diagrammi Q-Q: il package `statmodels` mette a disposizione un oggetto `api` su cui invocare il metodo `qqplot_2samples` a cui passare direttamente i due campioni, aggiungendo l'argomento opzionale `line='45'` nel caso in cui si vuole tracciare anche il riferimento della bisettrice. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "sm.qqplot_2samples(marvel_sample, dc_sample, line='45')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"bs-callout bs-callout-primary\">\n",
    "Il diagramma prodotto da `qqplot_2samples` scambia il ruolo degli assi rispetto al diagramma precedente: è per questo motivo che i due campioni sono stati passati come argomenti considerandoli in ordine inverso rispetto a quanto fatto finora.\n",
    "</div>\n",
    "\n",
    "In sintesi, il diagramma ottenuto ci permette di avvalorare l'ipotesi che l'altezza dei supereroi non segua una distribuzione diversa nei fumetti editi da DC e Marvel.\n",
    "\n",
    "Chiaramente, non è detto che due campioni seguano necessariamente una medesima distribuzione. In tal caso, i punti ottenuti non si disporranno vicino alla bisettrice. È questo il caso della distribuzione del peso tra supereroine e supereroi."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "female = heroes.loc[(heroes['Gender']=='F') & \\\n",
    "                    (heroes['Weight'].between(50, 100))]\n",
    "\n",
    "male = heroes.loc[(heroes['Gender']=='M') & \\\n",
    "                (heroes['Weight'].between(50, 100))]\n",
    "\n",
    "female_sample = female['Weight'].sample(100)\n",
    "male_sample = male['Weight'].sample(100)\n",
    "sm.qqplot_2samples(female_sample, male_sample, line='45')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La tecnica del Q-Q plot permette quindi in casi come questo di confutare l'ipotesi di partenza.\n",
    "\n",
    "Si nota infine che una standardizzazione dei dati permette di confinare il grafico ottenuto in prossimità dell'origine. In tal modo diventa più facile accorgersi di eventuali valori fuori scala."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.qqplot_2samples((marvel_sample-marvel_sample.mean())/marvel_sample.std(),\n",
    "                   (dc_sample-dc_sample.mean())/dc_sample.std(),\n",
    "                   line='s',\n",
    "                   xlabel='DC', ylabel='Marvel')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sm.qqplot_2samples((female_sample-female_sample.mean())/female_sample.std(),\n",
    "                   (male_sample-male_sample.mean())/male_sample.std(),\n",
    "                   line='45',\n",
    "                   xlabel='Male', ylabel='Female')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div id=\"h-4\"></div>\n",
    "\n",
    "## Simmetria, distribuzioni approssimativamente normali e regola empirica\n",
    "\n",
    "Alcuni dei grafici finora visti possono essere utili per mettere in evidenza una proprietà interessante di un campione di dati legata alla simmetria delle corrispondenti frequenze. Quando le frequenze, visualizzate a seconda dei casi tramite un grafico a barre o un istogramma, tendono a distribuirsi in modo simmetrico rispetto al valore della media campionaria si dice che il campione segue una distribuzione _approssimativamente simmetrica_. Il grafico qui sotto affianca l'istogramma e il box plot di un siffatto campione. La simmetria è visibile in entrambe le rappresentazioni: l'istogramma è approssimativamente simmetrico rispetto alla sua parte centrale e nel box plot i baffi hanno all'incirca la stessa lunghezza, così come la mediana si posiziona verso il centro della scatola."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "sample = pd.Series(norm.rvs(24, 2, size=1000), name='')\n",
    "f, (h, b) = plt.subplots(2, 1, gridspec_kw = {'height_ratios':[4, 3]})\n",
    "f.set_figheight(6)\n",
    "\n",
    "h.yaxis.label.set_visible(False)\n",
    "\n",
    "sample.plot.hist(bins=20, ax=h)\n",
    "sample.plot.box(vert=False, whis='range', ax=b, widths=.4, label=None)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'asimmetria in una distribuzione si può invece presentare in due diverse modalità:\n",
    "\n",
    "- tende a essere presente una \"coda\" nella parte destra della distribuzione delle frequenze, evidenziata da valori più bassi delle frequenze nella parte destra dell'istogramma e da un baffo destro sensibilmente più lungo nel box plot, come esemplificato nella coppia di diagrammi qui sotto; in questo caso si parla quindi di distribuzione asimmetrica a destra (utilizzando a volte la terminologia inglese e dicendo che è presente uno _skew_ a destra);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWUAAAF9CAYAAADcAHlNAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAGaRJREFUeJzt3XtMVAca9/EfL9a76RCdTrdVNKsoQrTeVqjWpUVFDatYbaPum+2G1Ct2U9pV0e5qE2JFxRsmrDfUmK0btYbkXe1Ws5vSbPGC/aMGs7Z2CNF6hUAcI1q3K8z7h9lhKbUijHOeGb6fhKScOXPm4Zh+OZw5MxPl8/n8AgCY8H+cHgAA0IgoA4AhRBkADCHKAGAIUQYAQ4gyABhClAHAkIiKstfrdXoEM9gXjdgXjdgXjazui4iKMgCEO6IMAIYQZQAwhCgDgCFEGQAMIcoAYEgHpwcId669V1t1P1/m80GeBEAk4EgZAAwhygBgCFEGAEOIMgAYQpQBwBCiDACGEGUAMIQoA4AhRBkADCHKAGAIUQYAQ4gyABhClAHAEKIMAIYQZQAwhCgDgCEtivKJEyc0e/ZsDR48WC6XS/v3729y+6JFi+RyuZp8TZgwock6//73v7V06VL9/Oc/13PPPafZs2fr6tXWvUE8AESqFkX5zp07SkhI0Nq1a9WlS5cfXefll1/WhQsXAl8fffRRk9tXrFihI0eOaPfu3frb3/6m27dva9asWaqvr2/7TwEAEaJFHweVlpamtLQ0SVJWVtaPrtOpUyd5PJ4fve3WrVv685//rMLCQr3yyiuSpB07dmjIkCH67LPPNH78+NbMDgARJ2if0Xfq1CkNGDBATz/9tMaOHauVK1fK7XZLks6ePav//Oc/Sk1NDazfu3dvDRo0SGVlZQ+Nstfrfew5WnOftunaqnuFYs7Q7wu72BeN2BeNnNgXcXFxP3l7UKI8YcIETZ06VX379tW3336r1atXa9q0afrss8/UqVMnVVdXKzo6Wj179mxyP7fbrerq6lYP/0Ner/ex79Nmpa07L/6k53RkXxjFvmjEvmhkdV8EJcozZ84M/HdiYqKGDRumIUOG6Pjx45o2bdpD7+f3+xUVFRWMEcIOn4IN4Mc8kUvifvazn+m5555TZWWlJOmZZ55RfX29amtrm6xXU1MTOMUBAHhCUa6trdX169cDT/wNGzZMTz31lEpKSgLrXL16VRcuXFBSUtKTGAEAwlKLTl/U1dUFjnobGhp05coVlZeXKyYmRjExMVq7dq2mTZsmj8ejb7/9Vrm5uXK73frVr34lSXr66af1m9/8RqtWrZLb7VZMTIz+8Ic/KDExUS+//PIT++EAINy0KMpffvmlpk6dGvg+Ly9PeXl5mjNnjjZt2qTz58/rwIEDunXrljwej8aNG6e9e/eqR48egfusWbNG0dHRyszM1L179/TLX/5S27dvV3R0dPB/KgAIUy2K8rhx4+Tz+R56e3Fx8SO30blzZ+Xn5ys/P7/l0wFAO8N7XwCAIUQZAAwhygBgCFEGAEOIMgAYQpQBwBCiDACGEGUAMIQoA4AhRBkADCHKAGAIUQYAQ4gyABhClAHAEKIMAIYQZQAwhCgDgCFEGQAMIcoAYAhRBgBDiDIAGEKUAcCQDk4PYIVr71WnRwAAjpQBwBKOlMNMy4/ou0qlTdf1ZT4f/IEABBVHygBgCFEGAEOIMgAYQpQBwBCiDACGEGUAMIQoA4AhRBkADCHKAGAIUQYAQ4gyABhClAHAEKIMAIYQZQAwhCgDgCEtivKJEyc0e/ZsDR48WC6XS/v3729yu9/vV15enuLj4/Xss88qPT1dX331VZN1fD6f5s+fr9jYWMXGxmr+/Pny+XzB+0kAIAK0KMp37txRQkKC1q5dqy5dujS7vaCgQIWFhVq3bp0+/fRTud1uvfrqq7p9+3Zgnblz56q8vFwfffSRDh8+rPLyci1YsCB4PwkARIAWffJIWlqa0tLSJElZWVlNbvP7/dq2bZuys7OVkZEhSdq2bZvi4uJ0+PBhZWZm6sKFC/rHP/6hY8eOKSkpSZK0efNmTZkyRV6vV3FxccH8mQAgbLX546AuXbqkqqoqpaamBpZ16dJFY8aMUVlZmTIzM3XmzBl17949EGRJSk5OVrdu3VRWVvbQKHu93seepzX3eaBrK+8XPlq/b8Jfe/7Zf4h90ciJffGog9A2R7mqqkqS5Ha7myx3u926fv26JKm6ulo9e/ZUVFRU4PaoqCj16tVL1dXVD9324x5Bt+mouzTyP826vf5Fwl9jjdgXjazui6BdffG/wZUenNb4YYR/6IfrAEB71+YoezweSWp2xFtTUxM4en7mmWdUU1Mjv98fuN3v96u2trbZETYAtGdtjnLfvn3l8XhUUlISWHbv3j2dOnUqcA559OjRqqur05kzZwLrnDlzRnfu3GlynhkA2rsWnVOuq6tTZWWlJKmhoUFXrlxReXm5YmJi1KdPHy1atEgbN25UXFycBgwYoA0bNqhbt2567bXXJEmDBg3ShAkT9M4776igoEB+v1/vvPOOJk2aZPKcDgA4pUVR/vLLLzV16tTA93l5ecrLy9OcOXO0bds2vf322/ruu++0dOlS+Xw+jRw5UsXFxerRo0fgPrt27VJOTo5mzJghSZoyZYrWr18f5B8HAMJblM/n8z96tfDQlmdTXXsj/+oLX+bzTo/gCKvPsjuBfdHI6r5o8yVxCB+t/cXTXmMOOIE3JAIAQ4gyABhClAHAEKIMAIYQZQAwhCgDgCFEGQAMIcoAYAhRBgBDiDIAGEKUAcAQogwAhhBlADCEKAOAIUQZAAwhygBgCFEGAEOIMgAYQpQBwBCiDACGEGUAMIQoA4AhRBkADOng9ACIXK69V1t1P1/m80GeBAgfHCkDgCFEGQAMIcoAYAjnlPFIrT03DODxcaQMAIYQZQAwhCgDgCFEGQAMIcoAYEhEXX3xi9KuUilXCgAIXxwpA4AhRBkADCHKAGAIUQYAQ4gyABgSlCjn5eXJ5XI1+Ro4cGDgdr/fr7y8PMXHx+vZZ59Venq6vvrqq2A8NABElKAdKcfFxenChQuBr5MnTwZuKygoUGFhodatW6dPP/1Ubrdbr776qm7fvh2shweAiBC0KHfo0EEejyfw1atXL0kPjpK3bdum7OxsZWRkKCEhQdu2bVNdXZ0OHz4crIcHgIgQtBePXLx4UYMHD9ZTTz2lUaNGadWqVerXr58uXbqkqqoqpaamBtbt0qWLxowZo7KyMmVmZj50m16v9zGn6NrK6WHJ4/+7O7PNcMW+aOTEvoiLi/vJ24MS5VGjRulPf/qT4uLiVFNTo/z8fKWlpen06dOqqqqSJLnd7ib3cbvdun79+k9u91HDN8Or+SLCY/+7P4LX6w36NsMV+6KR1X0RlChPnDixyfejRo3SsGHD9Je//EW/+MUvJElRUVFN1vH7/c2WAUB790Quievevbvi4+NVWVkpj8cjSaqurm6yTk1NTbOjZwBo755IlO/duyev1yuPx6O+ffvK4/GopKSkye2nTp1SUlLSk3h4AAhbQTl98cc//lGTJ09W7969A+eU7969qzlz5igqKkqLFi3Sxo0bFRcXpwEDBmjDhg3q1q2bXnvttWA8PABEjKBE+dq1a5o7d65qa2vVq1cvjRo1Sn//+98VGxsrSXr77bf13XffaenSpfL5fBo5cqSKi4vVo0ePYDw8AESMKJ/P53d6iGDhU5cjgy/z+aBuz+qz7E5gXzSyui947wsAMIQoA4AhRBkADImoz+hDZGjLcwPBPh8NhBpHygBgCFEGAEOIMgAYQpQBwBCiDACGEGUAMIQoA4AhXKeMiPLj1zh3feSn0nB9M6zgSBkADCHKAGAIUQYAQ4gyABhClAHAEKIMAIYQZQAwhCgDgCFEGQAMIcoAYAhRBgBDeO8LQK3/XEDeMwPBxpEyABhClAHAEKIMAIZwThloA85FI9iIMuCA1sZcIuiRjtMXAGAIR8pAmOGUSWTjSBkADCHKAGAIUQYAQ4gyABjCE31AO/HgCcKuUunjPVHIE4ShxZEyABhClAHAEKIMAIaE/JxyUVGRtm7dqqqqKsXHxysvL09jxowJ9RgAWogXq4RWSKNcXFys5cuXa+PGjUpOTlZRUZFef/11nT59Wn369AnlKACesLa8v0drtfYXgaVfPCE9fVFYWKhf//rX+u1vf6tBgwYpPz9fHo9He/bsCeUYAGBWyI6Uv//+e509e1a/+93vmixPTU1VWVlZUB6DP5cAtFRcXFzgvy21I2RHyrW1taqvr5fb7W6y3O12q7q6OlRjAIBpIb/6Iioqqsn3fr+/2TIAaK9CFuWePXsqOjq62VFxTU1Ns6NnAGivQhbljh07atiwYSopKWmyvKSkRElJSaEaAwBMC+klcYsXL9aCBQs0cuRIJSUlac+ePbpx44YyMzNDOQYAmBXSc8ozZsxQXl6e8vPzNW7cOJ0+fVqHDh1SbGxsm7ZbVFSkoUOHyuPxKCUlRSdPngzSxOFj06ZNeuWVV9SnTx/1799fs2bN0vnz550ey4SNGzfK5XJp6dKlTo/iiBs3bmjhwoXq37+/PB6PkpKSVFpa6vRYjqivr9fq1asDvRg6dKhWr16t+/fvOz1aQMhf0Td37lzNnTs3aNvjBSkPlJaW6s0339SIESPk9/u1Zs0aTZ8+XWVlZYqJiXF6PMd88cUX2rdvnxITE50exRE+n0+TJk1ScnKyDh06pJ49e+rSpUvt9nmcLVu2qKioSNu2bVNCQoL+9a9/adGiRerYsaOWLVvm9HiSpCifz+d3eoi2GD9+vBITE7V169bAshEjRigjI0Pvv/++g5M5q66uTrGxsdq/f7+mTJni9DiOuHXrllJSUlRQUKD169crISFB+fn5To8VUrm5uTpx4oSOHz/u9CgmzJo1SzExMdq+fXtg2cKFC3Xz5k0dPHjQwckahfUbEv33BSmpqalNlgfzBSnhqq6uTg0NDXK5XE6P4pjs7GxlZGQoJSXF6VEc8/HHH2vkyJHKzMzUgAED9NJLL2nnzp3y+8P6WKzVkpOTVVpaqm+++UaS9PXXX+vzzz/XxIkTHZ6sUVi/yT0vSHm45cuXa8iQIRo9erTTozhi3759qqys1I4dO5wexVEXL17U7t27lZWVpezsbJ07d045OTmSpPnz5zs8XehlZ2errq5OSUlJio6O1v3797VkyZKgnlJtq7CO8n/xgpSm3nvvPZ0+fVrHjh1TdHS00+OEnNfrVW5urj755BN17NjR6XEc1dDQoOHDhwdO5b3wwguqrKxUUVFRu4xycXGxDhw4oKKiIsXHx+vcuXNavny5YmNj9cYbbzg9nqQwjzIvSGluxYoVKi4u1pEjR9SvXz+nx3HEmTNnVFtbqxdffDGwrL6+XidPntSePXt07do1derUycEJQ8fj8WjQoEFNlg0cOFBXrlxxaCJnrVq1Sm+99ZZmzpwpSUpMTNTly5e1efNmohwM//uClOnTpweWl5SUaNq0aQ5O5oycnBwVFxfr6NGjGjhwoNPjOCY9PV3Dhw9vsmzx4sXq37+/3n333XZ19JycnKyKioomyyoqKtrVlUn/6+7du83+eoyOjlZDQ4NDEzUX1lGWeEHKfy1ZskQHDx7Uhx9+KJfLpaqqKklSt27d1L17d4enCy2Xy9XsCc6uXbsqJiZGCQkJDk3ljKysLKWlpWnDhg2aMWOGysvLtXPnTq1cudLp0RwxefJkbdmyRX379lV8fLzKy8tVWFio2bNnOz1aQNhfEic9ePFIQUGBqqqqNHjwYK1Zs0Zjx451eqyQethVFjk5OVqxYkWIp7EnPT29XV4SJ0nHjx9Xbm6uKioq1Lt3b82bN08LFixol8+73L59Wx988IGOHj2qmpoaeTwezZw5U8uWLVPnzp2dHk9ShEQZACJFWF+nDACRhigDgCFEGQAMIcoAYAhRBgBDiDIAGEKUAcAQogwAhhBlADCEKAOAIUQZAAwhygBgCFEGAEOIMgAYQpQBwBCiDACGEGUAMIQoA4AhERVlr9fr9AhmsC8asS8asS8aWd0XERVlAAh3RBkADCHKAGAIUQYAQ4gyABhClAHAEKIMAIYQZQAwhCgDgCFEGQAMIcoAYAhRBgBDiDIAGEKUAcAQogwAhhBlADCEKAOAIUQZAAwhygBgCFEGAEOIMgAYQpQBwBCiDACGEGUAMIQoA4AhRBkADCHKAGAIUQYAQ4gyABhClAHAEKIMAIYQZQAwhCgDgCFEGQAMIcoAYAhRBgBDiDIAGEKUAcCQDk4PEKn67b8m3/f+oG/33af/nzbdymjBml2l0qtBf/yHcXWM0sX/+1zIHg+IVET5CfF975cv8/mgb/fOp3/VqhlZj1zP6/UqLi4u6I//MK69ofsFAEQyTl8AgCFEGQAMIcoAYAhRBgBDiDIAGEKUAcAQogwAhhBlADCEKAOAIUQZAAwhygBgCFEGAEMiKso7d+50egQA7UheXl7QtxlRUd61a5fTIwBoR9atWxf0bUZUlAEg3BFlADCEKAOAIUQZAAwhygBgCFEGAEOIMgAYQpQBwBCiDACGEGUAMIQoA4AhHZwe4Kd4vd7Hvo9r79UnMEnrtGb+R3nuMbb7JB7/4bqa2vdNdZVKrc4WauyLRsHZF4/7/1lcXNxP3h7l8/n8bRnIEpfLJZ/P5/QYkh78cvBlPh/07d75dLK6pR575Hper/eR//jB9KR+3mAI9b6wjH3RKBj74kk0h9MXAGAIUQYAQ4gyABhClAHAEKIMAIYQZQAwhCgDgCFEGQAMIcoAYAhRBgBDiDIAGEKUAcCQiIryvHnznB4BQDuSk5MT9G1GVJTnz5/v9AgA2pEVK1YEfZsRFWUACHdEGQAMIcoAYAhRBgBDiDIAGEKUAcAQogwAhhBlADCEKAOAIUQZAAwhygBgSAenB4hkrr1Xg77Nd5+epk0t2m5XqTT4j/8wro5RIXssIJIR5SfEl/n8E9pylla1YC2v16u4uLgnNAOAJ4XTFwBgCFEGAEOIMgAYQpQBwBCiDACGEGUAMIQoA4AhRBkADCHKAGAIUQYAQ4gyABhClAHAEKIMAIYQZQAwhCgDgCFEGQAMIcoAYAhRBgBDiDIAGEKUAcAQogwAhhBlADCEKAOAIUQZAAwhygBgCFEGAEOIMgAYQpQBwBCiDACGEGUAMIQoA4AhRBkADCHKAGAIUQYAQ4gyABhClAHAEKIMAIYQZQAwJMrn8/mdHgIA8ABHygBgCFEGAEOIMgAYQpQBwBCiDACGEGUAMCQiolxUVKShQ4fK4/EoJSVFJ0+edHqkkNu0aZNeeeUV9enTR/3799esWbN0/vx5p8cyYePGjXK5XFq6dKnTozjixo0bWrhwofr37y+Px6OkpCSVlpY6PZYj6uvrtXr16kAvhg4dqtWrV+v+/ftOjxYQ9lEuLi7W8uXL9fvf/17//Oc/NXr0aL3++uu6fPmy06OFVGlpqd58800dP35cf/3rX9WhQwdNnz5dN2/edHo0R33xxRfat2+fEhMTnR7FET6fT5MmTZLf79ehQ4dUVlam9evXy+12Oz2aI7Zs2aKioiKtW7dOZ86c0dq1a7Vr1y5t2rTJ6dECwv7FI+PHj1diYqK2bt0aWDZixAhlZGTo/fffd3AyZ9XV1Sk2Nlb79+/XlClTnB7HEbdu3VJKSooKCgq0fv16JSQkKD8/3+mxQio3N1cnTpzQ8ePHnR7FhFmzZikmJkbbt28PLFu4cKFu3rypgwcPOjhZo7A+Uv7+++919uxZpaamNlmempqqsrIyh6ayoa6uTg0NDXK5XE6P4pjs7GxlZGQoJSXF6VEc8/HHH2vkyJHKzMzUgAED9NJLL2nnzp3y+8P6WKzVkpOTVVpaqm+++UaS9PXXX+vzzz/XxIkTHZ6sUQenB2iL2tpa1dfXN/tTzO12q7q62qGpbFi+fLmGDBmi0aNHOz2KI/bt26fKykrt2LHD6VEcdfHiRe3evVtZWVnKzs7WuXPnlJOTI0maP3++w9OFXnZ2turq6pSUlKTo6Gjdv39fS5Ys0dy5c50eLSCso/xfUVFRTb73+/3NlrUn7733nk6fPq1jx44pOjra6XFCzuv1Kjc3V5988ok6duzo9DiOamho0PDhwwOn8l544QVVVlaqqKioXUa5uLhYBw4cUFFRkeLj43Xu3DktX75csbGxeuONN5weT1KYR7lnz56Kjo5udlRcU1PTbp/IWLFihYqLi3XkyBH169fP6XEccebMGdXW1urFF18MLKuvr9fJkye1Z88eXbt2TZ06dXJwwtDxeDwaNGhQk2UDBw7UlStXHJrIWatWrdJbb72lmTNnSpISExN1+fJlbd68mSgHQ8eOHTVs2DCVlJRo+vTpgeUlJSWaNm2ag5M5IycnR8XFxTp69KgGDhzo9DiOSU9P1/Dhw5ssW7x4sfr376933323XR09Jycnq6KiosmyiooK9enTx6GJnHX37t1mfz1GR0eroaHBoYmaC+soSw/+Z1uwYIFGjhyppKQk7dmzRzdu3FBmZqbTo4XUkiVLdPDgQX344YdyuVyqqqqSJHXr1k3du3d3eLrQcrlczZ7g7Nq1q2JiYpSQkODQVM7IyspSWlqaNmzYoBkzZqi8vFw7d+7UypUrnR7NEZMnT9aWLVvUt29fxcfHq7y8XIWFhZo9e7bTowWE/SVx0oMXjxQUFKiqqkqDBw/WmjVrNHbsWKfHCqmHXWWRk5OjFStWhHgae9LT09vlJXGSdPz4ceXm5qqiokK9e/fWvHnztGDBgnb5vMvt27f1wQcf6OjRo6qpqZHH49HMmTO1bNkyde7c2enxJEVIlAEgUoT1dcoAEGmIMgAYQpQBwBCiDACGEGUAMIQoA4AhRBkADCHKAGDI/wdiuNOe2v0XKQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import gamma\n",
    "sample = pd.Series(gamma.rvs(2, size=1000), name='')\n",
    "f, (h, b) = plt.subplots(2, 1, gridspec_kw = {'height_ratios':[4, 3]})\n",
    "f.set_figheight(6)\n",
    "\n",
    "h.yaxis.label.set_visible(False)\n",
    "\n",
    "sample.plot.hist(bins=20, ax=h)\n",
    "sample.plot.box(vert=False, whis='range', ax=b, widths=.4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- viceversa, è possibile che la coda della distribuzione sia a sinistra, come nel grafico sottostante, e quindi si parla di asimmetria (o _skew_) a sinistra."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "hide_input": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import beta\n",
    "sample = pd.Series(beta.rvs(20, 2, size=1000), name='')\n",
    "f, (h, b) = plt.subplots(2, 1, gridspec_kw = {'height_ratios':[4, 3]})\n",
    "f.set_figheight(6)\n",
    "\n",
    "h.yaxis.label.set_visible(False)\n",
    "\n",
    "sample.plot.hist(bins=20, ax=h)\n",
    "sample.plot.box(vert=False, whis='range', ax=b, widths=.4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consideriamo per esempio il BMI dei supereroi nei soli casi in cui il relativo valore è inferiore a $100$, e visualizziamo separatamente i corrispondenti istogramma e box plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample = heroes['Weight'] / (heroes['Height']/100) **2\n",
    "sample = sample[sample < 100]\n",
    "\n",
    "sample.name = 'BMI'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample.plot.hist(bins=20)\n",
    "plt.ylabel('')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample.plot.box(vert=False, whis='range', widths=.4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si vede chiaramente la presenza di un'asimmetria a destra. Se invece consideriamo l'altezza, restringendosi ai casi in cui il corrispondente valore è compreso tra $150$ e $220$, otteniamo una distribuzione approssimativamente simmetrica."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample = heroes[(heroes['Height'].between(150, 220))]['Height']\n",
    "sample.plot.hist(bins=20)\n",
    "plt.ylabel('')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Rn3/+qYiICEn+mzk9PV2ffPKJcnJy1KZNG9dyd8578+bN9ccff8jp/OfrQ6fTqXPnzvllZnfUtuP8t4qKCo0ePVpHjx7Vp59+qsaNG3tkZsLvA0FBQXrsscdUVFRUafmxY8dks9kk3QhA3bp1tWvXLtfjxcXFri/K/GXt2rUKDw/XE088UWl5RESEQkNDK817+fJl5eXl+WXea9eu6dq1a1U+MQUGBrp+46qtx1iSQkJC1LRpU/3888/Kz89X3759Jfln5mnTpik7O1s5OTmKjY2t9Jg7571r164qLy/XwYMHXescPHhQFy5c8MvM7qhtx1m68Z5OSUnR0aNHtXXrVtcPXU/MzKUeDykvL9fx48cl3bi0c+bMGRUUFKhRo0ay2WwaP368UlJS1KNHDyUmJmrPnj3atGmT677ukJAQvfDCC5ozZ46aNWumRo0aaebMmerQoUOV6PpiXunGLWUbN27U+PHjq/zqaLFYNHbsWC1ZskQxMTGKjo7W4sWLFRwcrEGDBnl8Xndm7tmzpzIyMhQcHCybzaZ9+/Zpw4YNysjIkOT7Y+zOzFu2bFHjxo0VHh6uo0ePavr06UpOTnZ9YefrmSdPnqyPP/5Y69atk9VqdV3TDw4OVsOGDd0673FxcerVq5cmTpyozMxMOZ1OTZw4Ub179/bKHT13mlmSSktLdfr0aZWVlUmSTpw4oZCQEIWGhio0NLTWHeeKigqNGjVK+fn5Wr9+vSwWi2ud//znP6pfv/49zcztnB6yZ88e9evXr8ryYcOGacWKFZKkrKwsLV26VMXFxYqMjNSkSZMqRfLy5cuaPXu2srOzdfnyZSUmJmrJkiVq3bq1X+Zdt26dJkyYoCNHjqhly5ZV1nU6nZo/f77WrFkju92uzp07a/HixWrfvr3H53Vn5pKSEmVkZGjXrl0qLS2VzWbTyJEjNW7cONcPLl8eY3dmXrlypZYtW6azZ88qNDRUQ4cO1dSpUxUUFORa15cz3+qukmnTpik9PV2Se+e9tLRU06ZN0xdffCFJSkpK0sKFC2t0p40nZ87KytLLL79823Vq03E+deqUHnnkkWrXWb58ueuW4LudmfADgGG4xg8AhiH8AGAYwg8AhiH8AGAYwg8AhiH8AGAYwg8AhiH8AGAYwg8Ahvl/J7SJ5kxl+QsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x222.492 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample.plot.box(vert=False, whis='range', widths=.4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tra le distribuzioni approssimativamente simmetriche, un ruolo particolare spetta alle cosiddette distribuzioni _approssimativamente normali_, in cui la simmetria è accompagnata da una forma \"a campana\" del grafico delle frequenze. In questo tipo di distribuzioni i dati si concentrano attorno alla media campionaria secondo la seguente _regola empirica_:\n",
    "\n",
    "- approssimativamente il 68% delle osservazioni dista dalla media campionaria non più di una deviazione standard campionaria;\n",
    "- approssimativamente il 95% delle osservazioni dista dalla media campionaria non più di due deviazioni standard campionarie;\n",
    "- approssimativamente il 99.7% delle osservazioni dista dalla media campionaria non più di tre deviazioni standard campionarie.\n",
    "\n",
    "Siccome il grafico delle frequenze dell'altezza ha approssimativamente un andamento a campana, possiamo controllare numericamente se questa regola empirica risulti verificata."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "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>%</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.672269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.947479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.993697</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          %\n",
       "1  0.672269\n",
       "2  0.947479\n",
       "3  0.993697"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def check_empirical_rule(n):\n",
    "    within = len(sample[np.abs(sample - sample.mean()) < n*sample.std()])\n",
    "    return  within / len(sample)\n",
    "\n",
    "pd.DataFrame([check_empirical_rule(n) for n in range(1, 4)], columns=['%'],\n",
    "             index=range(1, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I risultati ottenuti sono altamente in accordo con le percentuali sopra indicate, e quindi l'ipotesi iniziale che le altezze considerate fossero distribuite in modo approssimativamente normale risulta validata.\n",
    "\n",
    "<div id=\"h-5\"></div>\n",
    "\n",
    "## Una nota sulla produzione dei grafici <sup>*</sup>\n",
    "\n",
    "I lettori più curiosi si saranno probabilmente chiesti come mai gli esempi riportati all'inizio del paragrafo precedente affiancassero istogrammi e box plot, mentre quando è stato mostrato come analizzare lo stato di simmetria della distribuzione di un campione questi due grafici sono stati costruiti separatamente. Ciò è dovuto al fatto che l'utilizzo di `subplot` permette di creare più grafici in una stessa figura, con il vincolo che le loro dimensioni devono essere uguali. Questo avrebbe avuto come effetto quello di ottenere un istogramma con delle barre molto basse, o in alternativa un box plot con un'altezza troppo elevata. In entrambi i casi si sarebbe quindi generato un grafico non particolarmente agevole da leggere. Una soluzione a questo problema, non introdotta prima per non complicare inutilmente la spiegazione, consiste nell'utilizzare come nella cella seguente il metodo `plt.subplots`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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F3hcRDwDvB65o433u627gvLZ8AY+dSdvLniLiJOC5wA7gGZm5F4ZPkMDxbbNe9Tanp3F61RMs2NdFDGe8cAR9GVTLbw1wLMPDD78HXN9mIdPyHrE38dhsCvrf11uAd2TmicA7gKvbeJ/7ugh4a0TcwfBQzCNtvHc9RcRTgM8Cl2bmDxfadJ6xkr1NY08wvq+IeBfwKHDt7NA8N1+wr1Jn/U2J3cANOTwYe1tE/BT4BabgPWLt7QOvA543Mtz3vjYDl7TlvwA+3pZ721dm3sPw9QEi4lnAa9pVveopIp7M8Inv2sy8oQ3vi4gNmbm3HdqbPbTei97G9DROL3qC8X1FxGbgtcC57TkRjqAvZ1TL7y+Bc+DQk8TRwPeBrcAbI+KYiDgZmAFu66zKI/My4J7M3D0y1ve+HgRe0pbPAWYPaW4FfqudTXYWcHD2kFN1EXF8+/kk4PeBj7arerOv2lGIq4FdmfmBkau2MvzjgvbzxpHx0vtrgZ7G6cX+GtdXRLwSuAw4LzN/PHKTxffV9Rkjfb4wPAS2F/gXhn8lXMwwmP6M4esEdwLnjGz/LoZnuNxLO9Os4mW+vtr4J4E3z7N9b/sCzgbuYHgW0g7geW3bYPhJ/t8Gvs7I2ViVLmN6uoThmVffAq6kvbG/Z/vqbIaHg+4CdrbLq4GnA9sY/kGxDTiuL/trgZ5+ve27h4F9wBf7tL8W6Os+hq9FzY599Ej7KvXJFJIkzeWhP0lSaQaVJKk0g0qSVJpBJUkqzaCSJJVmUEmSSjOoJEmlGVSSpNIMKklSaQaVJKk0g0qSVJpBJUkqzaCSJJVmUEmSSjOoJEml9eqr6A8ePOiXZ0nSlFu3bl2MrjujkiSVZlBJkkozqFbQYDDouoQVYV/9Mo19TWNPYF/jGFSSpNIMKklSaQaVJKk0g0qSVJpBJUkqzaCSJJVmUEmSSjOoJEmlGVSSpNIMKklSaQaVJKk0g0qSVJpBJUkqzaCSJJVmUEmSSjOoJEmlGVSSpNIMKklSaQaVJKk0g0qSVJpBJUkqzaCSJJVmUEmSSjOoJEmlGVSSpNIMKklSaQaVJKk0g0qSVJpBJUkqzaCSJJVmUEmSSjOoJEmlGVSSpNIMKklSaQaVJKm0NV0XID2Rk659kAOP5AQeaS1s37Oke3jnuhv5wMFNy1TP4Vt/dHD/bz5z4o8rTYJBpfIOPJIcuHDjij/OYDBgZmZmSffxT3+7lXe/7neWqaLDt/6apQWsVJmH/iRJpRlUkqTSDCpJUmkGlSSpNINKklSaQSVJKs2gkiSVZlBJkkozqCRJpRlUkqTSDCpJUmmrMqje8573dF2CJE2VlXxeXZVBddVVV3VdgiRNlZV8Xl2VQSVJ6g+DSpJUmkElSSrNoJIklWZQSZJKM6gkSaUZVJKk0gwqSVJpTxhUEfGPc9Z/OyI+/AS3OS8iLn+CbX41Ij4/5rpLI2LtE9UmSZp+KzKjysytmXnlEu7iUsCgkiQtLagi4hcj4rMRcXu7vLCNH5p1RcQvRcSt7fr/NmeG9pSI+ExE3BMR18bQ7wLPBG6OiJuXUp8kqf/WHMY2Px8RO0fWjwO2tuUPAn+Umdsj4l8DXwSePef2HwQ+mJmfiog3z7nuucAvAw8C/wd4YWZ+KCLeCbw0M78/rqjBYHAYpY+3/po9S7r94VkL2yfxOJM2+b6Wur8n9TjPXIb7ODJrF/idnsbfw2nsCfre10K/+0/0/2JmZmbsdYcTVP+cmafNrkTEbwNntNWXAc+JiNmrnxYRT51z+xcA57flPwfeP3LdbZm5u93vTuAkYPth1LRgU4fjwIUbl3T7wzEYDJZcZ0WT7mv9NXsm8njL0dc/PbD0380jsn3P2N/pafw9nMaeoN99rX/H+N/9pfZ1OEG1kCcBL8jMfx4dHAmuJ/LwyPJPlqEeSdKUWerJFF8C3ja7EhGnzbPNrcDr2/IbD/N+fwTMnZlJklahpQbV7wJnRMRdEfFNYO5rUDA8g++dEXEbsAE4eBj3+zHgC55MIUl6wkNtmfmUOeufBD7Zlr8P/Pt5bnNoG2APcFZmZkS8Efhq2+YW4JaR27xtZPlPgD85/DYkSdNqEq8JPQ/4cAxfuDoAXDSBx5QkTYkVD6rM/N/AqSv9OJKk6eRn/UmSSjOoJEmlGVSSpNIMKklSaasyqC677LKuS5CkqbKSz6urMqiuuOKKrkuQpKmyks+rqzKoJEn9YVBJkkozqCRJpRlUkqTSDCpJUmkGlSSpNINKklSaQSVJKs2gkiSVZlBJkkozqCRJpU3iq+ilJVt/zZ4JPMpa2L60x3nnuvP4wERq/Vnrj46JP6Y0KQaVyjtw4caJPM5gMGBmZmaJ9/I7vHtZqpE0y0N/kqTSDCpJUmkGlSSpNINKklSaQSVJKs2gkiSVZlBJkkozqCRJpRlUkqTSDCpJUmkGlSSpNINKklSaQSVJKs2gkiSVZlBJkkozqCRJpRlUkqTSDCpJUmkGlSSpNINKklSaQSVJKs2gkiSVZlBJkkozqCRJpRlUkqTSDCpJUmkGlSSpNINKklSaQSVJKs2gkiSVZlBJkkozqCRJpRlUkqTSDCpJUmkGlSSptMjMrms4bAcPHuxPsZKkI7Ju3boYXXdGJUkqzaCSJJXWq0N/kqTVxxmVJKk0g0qSVJpBtQQR8YmI2B8Rd88Zf3tE3BsR34iI946MXxER97Xrfm3yFR+e+fqKiOsiYme73B8RO0eu63Nfp0XEra2vr0bEmW08IuJDra+7IuL07iofb0xPp0bEVyLi6xHxVxHxtJHr+rKvToyImyNiV/t/dEkbPy4iboqIQft5bBsvv78W6OmCtv7TiDhjzm3K768F+npfRNzT9sfnImL9yG0W11dmejnCC/Bi4HTg7pGxlwJ/AxzT1o9vP58DfA04BjgZ+DZwVNc9HG5fc67/Q+Dd09AX8CXgVW351cAtI8tfAAI4C9jRdf2L6Ol24CVt+SLgD3q4rzYAp7flpwLfavW/F7i8jV8OXNWX/bVAT88GTgFuAc4Y2b4X+2uBvl4BrGnjV43sq0X35YxqCTLzy8AP5gy/BbgyMx9u2+xv45uAT2fmw5n5XeA+4MyJFbsIY/oChn+5Am8APtWG+t5XArMzjnXAg215E/CnOXQrsD4iNkym0sM3pqdTgC+35ZuA17flPu2rvZl5Z1v+EbAL2Miwhy1tsy3A+W25/P4a11Nm7srMe+e5SS/21wJ9fSkzH22b3Qqc0JYX3ZdBtfyeBbwoInZExN9FxPPb+EbggZHtdrexvnkRsC8zB229731dCrwvIh4A3g9c0cb73NfdwHlt+QLgxLbcy54i4iTgucAO4BmZuReGT5DA8W2zXvU2p6dxetUTLNjXRQxnvHAEfRlUy28NcCzDww+/B1zfZiExz7Z9fG/Am3hsNgX97+stwDsy80TgHcDVbbzPfV0EvDUi7mB4KOaRNt67niLiKcBngUsz84cLbTrPWMneprEnGN9XRLwLeBS4dnZonpsv2Nea5SpSh+wGbsjhwdjbIuKnwC+08RNHtjuBxw4z9UJErAFeBzxvZLjvfW0GLmnLfwF8vC33tq/MvIfh6wNExLOA17SretVTRDyZ4RPftZl5QxveFxEbMnNvO7Q3e2i9F72N6WmcXvQE4/uKiM3Aa4Fz23MiHEFfzqiW318C58ChJ4mjge8DW4E3RsQxEXEyMAPc1lmVR+ZlwD2ZuXtkrO99PQi8pC2fA8we0twK/FY7m+ws4ODsIafqIuL49vNJwO8DH21X9WZftaMQVwO7MvMDI1dtZfjHBe3njSPjpffXAj2N04v9Na6viHglcBlwXmb+eOQmi++r6zNG+nxheAhsL/AvDP9KuJhhMP0Zw9cJ7gTOGdn+XQzPcLmXdqZZxct8fbXxTwJvnmf73vYFnA3cwfAspB3A89q2AXyk9fV1Rs7GqnQZ09MlDM+8+hZwJe0TaHq2r85meDjoLmBnu7waeDqwjeEfFNuA4/qyvxbo6dfbvnsY2Ad8sU/7a4G+7mP4WtTs2EePtC8/QkmSVJqH/iRJpRlUkqTSDCpJUmkGlSSpNINKklSaQSVJKs2gkiSV9v8B51uUeeIoWQ4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (h, b) = plt.subplots(2, 1, gridspec_kw = {'height_ratios':[4, 3]})\n",
    "f.set_figheight(6)\n",
    "\n",
    "h.yaxis.label.set_visible(False)\n",
    "\n",
    "sample.plot.hist(bins=20, ax=h)\n",
    "sample.plot.box(vert=False, whis='range', ax=b, widths=.4)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vediamo nell'ordine quali sono i punti interessanti nel codice che ha prodotto questo grafico:\n",
    "\n",
    "1. il metodo `plt.subplots` accetta due argomenti il cui significato è lo stesso di quelli di `plt.subplot`: pertanto nella prima riga si genera una figura con due righe, ognuna contenente un asse;\n",
    "2. lo stesso metodo restituisce dei riferimenti alla figura e ai due assi;\n",
    "3. l'argomento opzionale `gridspec_kw` permette di specificare un dizionario con informazioni addizionali: nel nostro caso le altezze relative dei due assi;\n",
    "4. usando il riferimento alla figura è possibile invocare il metodo `set_figheight` al fine di impostare l'altezza globale della figura;\n",
    "5. analogamente, tramite il riferimento agli assi è possibile disattivare la visualizzazione dell'etichetta sull'asse delle ascisse dell'istogramma (tale etichetta conterrebbe il testo `'Frequency'`, dunque non sarebbe particolarmente informativa);\n",
    "6. l'invocazione dei metodi `hist` e `box` viene fatta specificando per l'argomento opzionale `ax` i riferimenti agli assi restituiti da `plt.subplots`;\n",
    "7. infine, nella creazione del box plot viene specificato un valore per l'argomento opzionale `width` che permette di ottenere un grafico in cui la scatola ha un'altezza più alta di quella predefinita, al fine di migliorare la leggibilità del risultato."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "footer": true
   },
   "source": [
    "<hr style=\"width: 90%;\" align=\"left\" />\n",
    "<span style=\"font-size: 0.8rem;\">D. Malchiodi, Superhero data science. Vol 1: probabilità e statistica: Indici di dispersione, 2017.</span>\n",
    "<br>\n",
    "<span style=\"font-size: 0.8rem;\">Powered by <img src=\"img/jupyter-logo.png\" style=\"height: 1rem; display: inline; margin-left: 0.5ex; margin-top: 0;\" alt=\"Jupyter Notebook\"></span>\n",
    "<div style=\"float: left; margin-top: 1ex;\">\n",
    "<img src=\"http://mirrors.creativecommons.org/presskit/icons/cc.large.png\" style=\"width: 1.5em; float: left; margin-right: 0.6ex; margin-top: 0;\">\n",
    "<img src=\"http://mirrors.creativecommons.org/presskit/icons/by.large.png\" style=\"width: 1.5em; float: left; margin-right: 0.6ex; margin-top: 0;\">\n",
    "<img src=\"http://mirrors.creativecommons.org/presskit/icons/nc.large.png\" style=\"width: 1.5em; float: left; margin-right: 0.6ex; margin-top: 0;\">\n",
    "<img src=\"http://mirrors.creativecommons.org/presskit/icons/nd.large.png\" style=\"width: 1.5em; float: left; margin-right: 0.6ex; margin-top: 0;\">\n",
    "<span style=\"font-size: 0.7rem; line-height: 0.7rem; vertical-align: middle;\">Quest'opera è distribuita con Licenza <a rel=\"license\" href=\"http://creativecommons.org/licenses/by-nc-nd/4.0/\">Creative Commons Attribuzione - Non commerciale - Non opere derivate 4.0 Internazionale</a></span>.\n",
    "</div>"
   ]
  }
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