Lunarnotes - SW09_Auftrag

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   "source": [
    "# Work assignment SW09 - PYTHON BASICS\n",
    "\n",
    "These are the self-study tasks of the semester week, which you will solve within one week in your JupyterHub environment. After completing your work, download a copy of the Jupyter notebook file locally to your laptop (Menu: File->Download).\n",
    "\n",
    "On ILIAS you will find the weekly scheduled assignment where you will upload your solved Jupyter notebook file. After your submission, you will receive a corresponding sample solution to the assignment. Your submission will not be corrected. Although the assignments are marked “mandatory”, they do not count towards your semester grades. Only the grades of the tests during the semester are relevant for this. \n",
    "\n",
    "We wish you every success!\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d6c713a-cfe6-4d8f-8b0b-a5dc2b5922e2",
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   "source": [
    "---\n",
    "---\n",
    "## Exercise 1\n",
    "Significant digits and decimal places\n",
    "\n",
    "---\n",
    "a) Determine the number of significant digits and the number of decimal places of the measured value:\n",
    "\n",
    "- $3.709 \\mskip3mu kg$\n",
    "- $0.37090 \\mskip3mu g$\n",
    "- $1.2 \\cdot 10^3 \\mskip3mu dm^2$\n",
    "- $1200 \\mskip3mu dm^2$\n",
    "\n",
    "### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "5d0b392e-9d67-4e8f-bfd4-3f10ee1b1935",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4\n",
      "5\n",
      "2\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "def digits(n):\n",
    "    if type(n) == float:\n",
    "        dot = str(n).find(\".\")\n",
    "        before_dot = str(n)[:dot]\n",
    "        after_dot = str(n)[dot+1:]\n",
    "        \n",
    "        if int(before_dot) == 0:\n",
    "            if len(before_dot) > 0 and before_dot[-1] == '0':\n",
    "                num_digits = len(after_dot)+1\n",
    "                return num_digits\n",
    "            else:\n",
    "                num_digits = len(after_dot)\n",
    "                return num_digits\n",
    "        else:\n",
    "            num_digits = len(before_dot) + len(after_dot)\n",
    "            return num_digits\n",
    "    else:\n",
    "        return len(str(n))\n",
    "    \n",
    "print(digits(3.709))\n",
    "print(digits(0.37090))\n",
    "print(digits(1.2))\n",
    "print(digits(1200))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20738f8a-f7da-4c8b-a443-68b53846276a",
   "metadata": {},
   "source": [
    "---\n",
    "---\n",
    "## Task 2\n",
    "\n",
    "Accuracy of a calculation result\n",
    "\n",
    "You have two measured values, $m_1 = 130.2 \\mskip3mu g$ and $m_2 = 92.56 \\mskip3mu kg$.\n",
    "\n",
    "a) Which of the two values has the higher *relative* accuracy?\n",
    "\n",
    "b) Which of the two values has the higher *absolute* accuracy?\n",
    "\n",
    "c) Determine the result of the calculations $\\frac{m_1}{m_2}$ and $m_1+m_2$ to a reasonable number of digits.\n",
    "\n",
    "### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "99c027fb-613b-4a37-8843-4c2a5a76f162",
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The most relative accurate is 925600 with 0.00010% as accuracy\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "\"\"\"\n",
    "To be honest, what the f**k is a relative and absolute accuracy?\n",
    "\"\"\"\n",
    "\n",
    "m_1,m_2 = 130.2,925600\n",
    "\n",
    "def rel_acc(value):\n",
    "    relative_accuracy = 1/10**digits(value)\n",
    "    return relative_accuracy\n",
    "\n",
    "rel_1,rel_2 = rel_acc(m_1), rel_acc(m_2)\n",
    "\n",
    "if rel_1 < rel_2:\n",
    "    rel = rel_1\n",
    "    m = m_1\n",
    "\n",
    "else:\n",
    "    rel = rel_2\n",
    "    m = m_2\n",
    "\n",
    "print(f\"The most relative accurate is {m} with {rel*100:.5f}% as accuracy\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd657575",
   "metadata": {},
   "source": [
    "---\n",
    "---\n",
    "## Exercise 3\n",
    "\n",
    "Read in a data file and display and evaluate the values using [pandas](https://pandas.pydata.org/)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "071376db-e357-416d-aa08-970499c9da97",
   "metadata": {},
   "source": [
    "---\n",
    "a) Read in the data file [`data.txt`](data.txt) and output the labels of the columns.\n",
    "\n",
    "### Solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "7610ef6c-70c8-44fd-b274-0aae5ff68e81",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       n     x        y0        y1        y2\n",
      "0      0 -5.00 -3.397320 -2.040274 -0.542143\n",
      "1      1 -4.95 -3.946340 -2.075358 -1.327252\n",
      "2      2 -4.90 -3.158201 -0.290995  1.070306\n",
      "3      3 -4.85 -3.279361 -3.584018 -1.929530\n",
      "4      4 -4.80 -3.349419 -5.420562  1.198207\n",
      "..   ...   ...       ...       ...       ...\n",
      "196  196  4.80  3.056953 -3.758519  1.215855\n",
      "197  197  4.85  3.573920  1.751444 -1.340130\n",
      "198  198  4.90  3.888522  3.076009  0.972900\n",
      "199  199  4.95  3.307981 -1.676777 -1.283877\n",
      "200  200  5.00  3.545136 -0.628782  0.188696\n",
      "\n",
      "[201 rows x 5 columns]\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv(\"data.txt\", delimiter=\"\\t\")\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a85f3230-d96a-4235-90fa-4574f46bafb6",
   "metadata": {},
   "source": [
    "- `n` denotes the index of the respective value\n",
    "- `x` are the x-values\n",
    "- `y0,y1,y2` are three different measurement series\n",
    "\n",
    "\n",
    "---\n",
    "b) Determine the mean value, the standard deviation, the median, the upper and lower quartile and the quartile difference for each of the three measurement series.\n",
    "\n",
    "### Solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "0f34dae7-b061-46de-a8ed-99f28e48fc87",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of\n",
      "y0: -0.130\n",
      "y1: -1.464\n",
      "y2: -0.183\n",
      "\n",
      "Standard deviation of\n",
      "y0: ±2.054\n",
      "y1: ±2.626\n",
      "y2: ±4.115\n",
      "\n",
      "Median of\n",
      "y0: -0.140\n",
      "y1: -1.435\n",
      "y2: -0.542\n",
      "\n",
      "Upper and lower quartiles of\n",
      "\n",
      "y0: 0.75    1.559855\n",
      "0.25   -1.855045\n",
      "Name: y0, dtype: float64\n",
      "\n",
      "y1:\n",
      "0.75    0.130800\n",
      "0.25   -3.025903\n",
      "Name: y1, dtype: float64\n",
      "\n",
      "y2:\n",
      "0.75    4.177558\n",
      "0.25   -4.321351\n",
      "Name: y2, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "mean_y0 = df[\"y0\"].mean()\n",
    "mean_y1 = df[\"y1\"].mean()\n",
    "mean_y2 = df[\"y2\"].mean()\n",
    "\n",
    "print(f\"Mean of\\ny0: {mean_y0:.3f}\\ny1: {mean_y1:.3f}\\ny2: {mean_y2:.3f}\\n\")\n",
    "\n",
    "sdt_y0 = df[\"y0\"].std()\n",
    "sdt_y1 = df[\"y1\"].std()\n",
    "sdt_y2 = df[\"y2\"].std()\n",
    "\n",
    "print(f\"Standard deviation of\\ny0: ±{sdt_y0:.3f}\\ny1: ±{sdt_y1:.3f}\\ny2: ±{sdt_y2:.3f}\\n\")\n",
    "\n",
    "median_y0 = df[\"y0\"].median()\n",
    "median_y1 = df[\"y1\"].median()\n",
    "median_y2 = df[\"y2\"].median()\n",
    "\n",
    "print(f\"Median of\\ny0: {median_y0:.3f}\\ny1: {median_y1:.3f}\\ny2: {median_y2:.3f}\\n\")\n",
    "\n",
    "quantile_y0 = df[\"y0\"].quantile(q=[.75,.25])\n",
    "quantile_y1 = df[\"y1\"].quantile(q=[.75,.25])\n",
    "quantile_y2 = df[\"y2\"].quantile(q=[.75,.25])\n",
    "\n",
    "print(f\"Upper and lower quartiles of\\n\\ny0: {quantile_y0}\\n\\ny1:\\n{quantile_y1}\\n\\ny2:\\n{quantile_y2}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7169efe-18a0-4388-bf89-da54b8987f08",
   "metadata": {},
   "source": [
    "---\n",
    "c) Now create a graph with the corresponding histogram for each of the measurement series `y0, y1, y2`.\n",
    "\n",
    "### Solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "e7a95ff8-29a3-4648-b442-62467254fe4b",
   "metadata": {},
   "outputs": [
    {
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R165d1blzZ40bN06FhYU2TQwAALyJrSGzfv16paSkaNOmTcrKylJNTY1Gjx6tiooK1zaPPPKIPvzwQ/3tb3/T+vXrlZ+fr5/97Gc2Tg0AALxFBzt3vnr1arfbmZmZuvDCC7V9+3aNHDlSpaWl+utf/6olS5bouuuukyRlZGTokksu0aZNm3TVVVfZMTYAAPASXnWOTGlpqSQpNDRUkrR9+3bV1NQoPj7etc2AAQMUHR2tjRs32jIjAADwHra+IvNDdXV1mjFjhq655hoNHDhQklRQUKCOHTsqJCTEbdvw8HAVFBQ0+DxVVVWqqqpy3S4rK2uxmQEAgL285hWZlJQU7d69W0uXLj2v50lLS1NwcLBriYqK8tCEAADA23hFyEyfPl0fffSR1q5dqx49erjWR0REqLq6WiUlJW7bFxYWKiIiosHnmj17tkpLS11Lbm5uS44OAABsZGvIWJal6dOna9myZfr000/Vq1cvt/uHDBkiPz8/ZWdnu9YdOHBAOTk5Gj58eIPP6XQ6FRQU5LYAAIC2ydZzZFJSUrRkyRKtWLFCgYGBrvNegoODFRAQoODgYN13331KTU1VaGiogoKC9OCDD2r48OFcsQQAAOwNmVdffVWSNGrUKLf1GRkZSk5OliS9+OKL8vHx0bhx41RVVaWEhAS98sorrTwpAADwRraGjGVZZ93G399f6enpSk9Pb4WJAACASbziZF8AAIBzQcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGPZGjIbNmzQLbfcosjISDkcDi1fvtzt/uTkZDkcDrdlzJgx9gwLAAC8jq0hU1FRoZiYGKWnpze6zZgxY/TNN9+4lnfffbcVJwQAAN6sg507T0xMVGJi4hm3cTqdioiIaKWJAACASbz+HJl169bpwgsvVP/+/fXAAw+ouLj4jNtXVVWprKzMbQEAAG2TV4fMmDFjtGjRImVnZ+uZZ57R+vXrlZiYqNra2kYfk5aWpuDgYNcSFRXVihMDAIDWZOtbS2czYcIE148vv/xyDRo0SH369NG6det0/fXXN/iY2bNnKzU11XW7rKyMmAEAoI3y6ldkfqx3797q1q2bDh482Og2TqdTQUFBbgsAAGibjAqZI0eOqLi4WN27d7d7FAAA4AVsfWupvLzc7dWVw4cPa+fOnQoNDVVoaKjmzp2rcePGKSIiQocOHdJjjz2mvn37KiEhwcapAQCAt7A1ZLZt26a4uDjX7dPntiQlJenVV1/Vrl279NZbb6mkpESRkZEaPXq0/vCHP8jpdNo1MgAA8CK2hsyoUaNkWVaj93/yySetOA0AADCNUefIAAAA/BAhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjefWXRnq7nJwcFRUV2T1Gs+zbt8/uEQAA8BhC5hzl5OSo/4BLVHnqW7tHAQCg3SJkzlFRUZEqT32rrjfPlF/XKLvHabJTX21T6b/fsXsMAAA8gpA5T35do+SM6Gv3GE1WU5xr9wgAAHgMJ/sCAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGMRMgAAwFiEDAAAMBYhAwAAjEXIAAAAYxEyAADAWIQMAAAwFiEDAACMRcgAAABjETIAAMBYHc71gdnZ2crOztbRo0dVV1fndt+bb7553oMBAACczTmFzNy5czVv3jwNHTpU3bt3l8Ph8PRcAAAAZ3VOIfPaa68pMzNTkyZN8vQ8AAAATXZO58hUV1fr6quv9vQsAAAAzXJOITNlyhQtWbLE07MAAAA0yzm9tVRZWamFCxfqX//6lwYNGiQ/Pz+3+1944QWPDAcAAHAm5xQyu3bt0uDBgyVJu3fvdruPE38BAEBrOaeQWbt2rafnAAAAaDY+EA8AABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLFtDZsOGDbrlllsUGRkph8Oh5cuXu91vWZZ+//vfq3v37goICFB8fLy+/PJLe4YFAABex9aQqaioUExMjNLT0xu8/9lnn9VLL72k1157TZs3b9YFF1yghIQEVVZWtvKkAADAG3Wwc+eJiYlKTExs8D7LsrRgwQL97ne/02233SZJWrRokcLDw7V8+XJNmDChNUcFAABeyGvPkTl8+LAKCgoUHx/vWhccHKxhw4Zp48aNNk4GAAC8ha2vyJxJQUGBJCk8PNxtfXh4uOu+hlRVVamqqsp1u6ysrGUGBAAAtvPaV2TOVVpamoKDg11LVFSU3SMBAIAW4rUhExERIUkqLCx0W19YWOi6ryGzZ89WaWmpa8nNzW3ROQEAgH28NmR69eqliIgIZWdnu9aVlZVp8+bNGj58eKOPczqdCgoKclsAAEDbZOs5MuXl5Tp48KDr9uHDh7Vz506FhoYqOjpaM2bM0Pz589WvXz/16tVLTzzxhCIjIzV27Fj7hgYAAF7D1pDZtm2b4uLiXLdTU1MlSUlJScrMzNRjjz2miooKTZ06VSUlJRoxYoRWr14tf39/u0YGAABexNaQGTVqlCzLavR+h8OhefPmad68ea04FQAAMIXXniMDAABwNoQMAAAwFiEDAACMRcgAAABjETIAAMBYhAwAADAWIQMAAIxFyAAAAGPZ+oF4AADA3b59++weoVm6deum6Oho2/ZPyAAA4AVqy09IDofuvvtuu0dpFv+ATjqwf59tMUPIAADgBeqqyiXLUtebZ8qva5Td4zRJTXGuij/6k4qKiggZAAAg+XWNkjOir91jGIOTfQEAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLK8OmSeffFIOh8NtGTBggN1jAQAAL9HB7gHO5rLLLtO//vUv1+0OHbx+ZAAA0Eq8vgo6dOigiIgIu8cAAABeyKvfWpKkL7/8UpGRkerdu7cmTpyonJycM25fVVWlsrIytwUAALRNXh0yw4YNU2ZmplavXq1XX31Vhw8f1v/93//p5MmTjT4mLS1NwcHBriUqKqoVJwYAAK3Jq0MmMTFR48eP16BBg5SQkKBVq1appKRE77//fqOPmT17tkpLS11Lbm5uK04MAABak9efI/NDISEhuvjii3Xw4MFGt3E6nXI6na04FQAAsItXvyLzY+Xl5Tp06JC6d+9u9ygAAMALeHXIPProo1q/fr2+/vprffbZZ7r99tvl6+uru+66y+7RAACAF/Dqt5aOHDmiu+66S8XFxQoLC9OIESO0adMmhYWF2T0aAADwAl4dMkuXLrV7BAAA4MW8+q0lAACAMyFkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGImQAAICxCBkAAGAsQgYAABiLkAEAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADGMiJk0tPT1bNnT/n7+2vYsGHasmWL3SMBAAAv4PUh89577yk1NVVz5szRjh07FBMTo4SEBB09etTu0QAAgM28PmReeOEF3X///Zo8ebIuvfRSvfbaa+rUqZPefPNNu0cDAAA28+qQqa6u1vbt2xUfH+9a5+Pjo/j4eG3cuNHGyQAAgDfoYPcAZ1JUVKTa2lqFh4e7rQ8PD9f+/fsbfExVVZWqqqpct0tLSyVJZWVlHp2tvLz8+/0VHFRddaVHn7sl1RTnSjJrbmZuHczcOpi5dTBz66g5fkTS9/8mevrf2dPPZ1nWmTe0vFheXp4lyfrss8/c1s+aNcuKjY1t8DFz5syxJLGwsLCwsLC0gSU3N/eMreDVr8h069ZNvr6+KiwsdFtfWFioiIiIBh8ze/Zspaamum7X1dXp+PHj6tq1qxwOx3nNU1ZWpqioKOXm5iooKOi8nsubtYfjbA/HKHGcbUl7OEapfRxnezhG6fyP07IsnTx5UpGRkWfczqtDpmPHjhoyZIiys7M1duxYSd+HSXZ2tqZPn97gY5xOp5xOp9u6kJAQj84VFBTUpn/zndYejrM9HKPEcbYl7eEYpfZxnO3hGKXzO87g4OCzbuPVISNJqampSkpK0tChQxUbG6sFCxaooqJCkydPtns0AABgM68PmTvvvFPHjh3T73//exUUFGjw4MFavXp1vROAAQBA++P1ISNJ06dPb/StpNbkdDo1Z86cem9dtTXt4TjbwzFKHGdb0h6OUWofx9kejlFqveN0WNbZrmsCAADwTl79gXgAAABnQsgAAABjETIAAMBYhAwAADAWIeMBVVVVGjx4sBwOh3bu3Gn3OB516623Kjo6Wv7+/urevbsmTZqk/Px8u8fyqK+//lr33XefevXqpYCAAPXp00dz5sxRdXW13aN51B//+EddffXV6tSpk8c/JNJO6enp6tmzp/z9/TVs2DBt2bLF7pE8asOGDbrlllsUGRkph8Oh5cuX2z2Sx6WlpenKK69UYGCgLrzwQo0dO1YHDhyweyyPe/XVVzVo0CDXB8QNHz5cH3/8sd1jtainn35aDodDM2bMaLF9EDIe8Nhjj531I5RNFRcXp/fff18HDhzQ3//+dx06dEh33HGH3WN51P79+1VXV6fXX39de/bs0YsvvqjXXntNjz/+uN2jeVR1dbXGjx+vBx54wO5RPOa9995Tamqq5syZox07digmJkYJCQk6evSo3aN5TEVFhWJiYpSenm73KC1m/fr1SklJ0aZNm5SVlaWamhqNHj1aFRUVdo/mUT169NDTTz+t7du3a9u2bbruuut02223ac+ePXaP1iK2bt2q119/XYMGDWrZHXnm6x3br1WrVlkDBgyw9uzZY0my/vOf/9g9UotasWKF5XA4rOrqartHaVHPPvus1atXL7vHaBEZGRlWcHCw3WN4RGxsrJWSkuK6XVtba0VGRlppaWk2TtVyJFnLli2ze4wWd/ToUUuStX79ertHaXFdunSx3njjDbvH8LiTJ09a/fr1s7Kysqxrr73Wevjhh1tsX7wicx4KCwt1//336+2331anTp3sHqfFHT9+XIsXL9bVV18tPz8/u8dpUaWlpQoNDbV7DJxBdXW1tm/frvj4eNc6Hx8fxcfHa+PGjTZOhvNVWloqSW36z2Btba2WLl2qiooKDR8+3O5xPC4lJUU33XST25/PlkLInCPLspScnKxp06Zp6NChdo/Ton7961/rggsuUNeuXZWTk6MVK1bYPVKLOnjwoF5++WX98pe/tHsUnEFRUZFqa2vrfV1JeHi4CgoKbJoK56uurk4zZszQNddco4EDB9o9jsd9/vnn6ty5s5xOp6ZNm6Zly5bp0ksvtXssj1q6dKl27NihtLS0VtkfIfMjv/nNb+RwOM647N+/Xy+//LJOnjyp2bNn2z1yszX1GE+bNWuW/vOf/2jNmjXy9fXVPffcI8uAD4Ru7nFKUl5ensaMGaPx48fr/vvvt2nypjuXYwS8WUpKinbv3q2lS5faPUqL6N+/v3bu3KnNmzfrgQceUFJSkvbu3Wv3WB6Tm5urhx9+WIsXL5a/v3+r7JOvKPiRY8eOqbi4+Izb9O7dWz//+c/14YcfyuFwuNbX1tbK19dXEydO1FtvvdXSo56zph5jx44d660/cuSIoqKi9Nlnn3n9y6HNPc78/HyNGjVKV111lTIzM+Xj4/2dfy6/lpmZmZoxY4ZKSkpaeLqWVV1drU6dOumDDz7Q2LFjXeuTkpJUUlLSJl85dDgcWrZsmdvxtiXTp0/XihUrtGHDBvXq1cvucVpFfHy8+vTpo9dff93uUTxi+fLluv322+Xr6+taV1tbK4fDIR8fH1VVVbnd5wlGfGlkawoLC1NYWNhZt3vppZc0f/581+38/HwlJCTovffe07Bhw1pyxPPW1GNsSF1dnaTvLzn3ds05zry8PMXFxWnIkCHKyMgwImKk8/u1NF3Hjh01ZMgQZWdnu/5hr6urU3Z2tld8ySyazrIsPfjgg1q2bJnWrVvXbiJG+v73rAl/nzbV9ddfr88//9xt3eTJkzVgwAD9+te/9njESITMOYuOjna73blzZ0lSnz591KNHDztG8rjNmzdr69atGjFihLp06aJDhw7piSeeUJ8+fbz+1ZjmyMvL06hRo3TRRRfp+eef17Fjx1z3RURE2DiZZ+Xk5Oj48ePKyclRbW2t6zOP+vbt6/r9a5rU1FQlJSVp6NChio2N1YIFC1RRUaHJkyfbPZrHlJeX6+DBg67bhw8f1s6dOxUaGlrv7yFTpaSkaMmSJVqxYoUCAwNd5zgFBwcrICDA5uk8Z/bs2UpMTFR0dLROnjypJUuWaN26dfrkk0/sHs1jAgMD653bdPocyxY756nFrodqZw4fPtzmLr/etWuXFRcXZ4WGhlpOp9Pq2bOnNW3aNOvIkSN2j+ZRGRkZlqQGl7YkKSmpwWNcu3at3aOdl5dfftmKjo62OnbsaMXGxlqbNm2yeySPWrt2bYO/bklJSXaP5jGN/fnLyMiwezSPuvfee62LLrrI6tixoxUWFmZdf/311po1a+weq8W19OXXnCMDAACMZcaJAAAAAA0gZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABYLx169bppz/9qZxOp/r27avMzEy7RwLQSggZAEY7fPiwbrrpJsXFxWnnzp2aMWOGpkyZ0qa+vwZA4/iKAgBebdGiRXrkkUeUn58vp9PpWj927FgFBgYqMjJSK1eu1O7du133TZgwQSUlJVq9erUdIwNoRbwiA8CrjR8/XrW1tfrnP//pWnf06FGtXLlS9957rzZu3Kj4+Hi3xyQkJGjjxo2tPSoAGxAyALxaQECAfvGLXygjI8O17p133lF0dLRGjRqlgoIChYeHuz0mPDxcZWVlOnXqVGuPC6CVETIAvN7999+vNWvWKC8vT5KUmZmp5ORkORwOmycDYLcOdg8AAGdzxRVXKCYmRosWLdLo0aO1Z88erVy5UpIUERGhwsJCt+0LCwsVFBSkgIAAO8YF0IoIGQBGmDJlihYsWKC8vDzFx8crKipKkjR8+HCtWrXKbdusrCwNHz7cjjEBtDKuWgJghNLSUkVGRuq7777TokWLdOedd0r6/vLrgQMHKiUlRffee68+/fRTPfTQQ1q5cqUSEhJsnhpASyNkABjjnnvu0cqVK+tdir1u3To98sgj2rt3r3r06KEnnnhCycnJ9g0KoNUQMgCMcf311+uyyy7TSy+9ZPcoALwEIQPA6504cULr1q3THXfcob1796p///52jwTAS3CyLwCvd8UVV+jEiRN65plniBgAbnhFBgAAGIsPxAMAAMYiZAAAgLEIGQAAYCxCBgAAGIuQAQAAxiJkAACAsQgZAABgLEIGAAAYi5ABAADG+n/v/ApBivCPRgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "df[\"y0\"].plot(kind=\"hist\", edgecolor=\"black\")\n",
    "\n",
    "plt.title(\"Histogram of y0\")\n",
    "plt.xlabel(\"y0\")\n",
    "plt.ylabel(\"n\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "578769f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[\"y1\"].plot(kind=\"hist\", edgecolor=\"black\")\n",
    "\n",
    "plt.title(\"Histogram of y1\")\n",
    "plt.xlabel(\"y1\")\n",
    "plt.ylabel(\"n\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "86686bf8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[\"y2\"].plot(kind=\"hist\", edgecolor=\"black\")\n",
    "\n",
    "plt.title(\"Histogram of y2\")\n",
    "plt.xlabel(\"y2\")\n",
    "plt.ylabel(\"n\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "45ce3411-9282-453a-96d9-567225e7b21f",
   "metadata": {},
   "source": [
    "---\n",
    "d) Now create a graph with the corresponding cumulative histogram for each of the measurement series `y0, y1, y2`.\n",
    "\n",
    "### Solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "7c806869-f894-45b0-b532-321ab8b8f841",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[\"y0\"].plot(kind=\"hist\", cumulative=True, edgecolor=\"black\")\n",
    "\n",
    "plt.title(\"Histogram of y0\")\n",
    "plt.xlabel(\"y0\")\n",
    "plt.ylabel(\"n\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "0e5a670a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[\"y1\"].plot(kind=\"hist\", cumulative=True, edgecolor=\"black\")\n",
    "\n",
    "plt.title(\"Histogram of y1\")\n",
    "plt.xlabel(\"y1\")\n",
    "plt.ylabel(\"n\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "078be576",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[\"y2\"].plot(kind=\"hist\", cumulative=True, edgecolor=\"black\")\n",
    "\n",
    "plt.title(\"Histogram of y2\")\n",
    "plt.xlabel(\"y2\")\n",
    "plt.ylabel(\"n\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6317aa9d-d82d-4f4b-9ab1-144918792ea5",
   "metadata": {},
   "source": [
    "---\n",
    "e) Now create a boxplot with all three measurement series `y0, y1, y2`.\n",
    "\n",
    "### Solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "d8ba05e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[\"y0\"].plot(kind=\"box\", title=\"Boxplot of y0\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "b1d12098",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[\"y1\"].plot(kind=\"box\", title=\"Boxplot of y1\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "f3703508-0f73-4412-b634-a85d683ea634",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[\"y2\"].plot(kind=\"box\", title=\"Boxplot of y2\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1e893a5-3027-44f7-8e50-5e72cbb656b6",
   "metadata": {},
   "source": [
    "---\n",
    "f) Create a scatter plot for all three measurement series `y0, y1, y2` - `y` over `x`.\n",
    "\n",
    "### Solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "be0890f6-6603-4a7a-b7ae-c0b2a0a45013",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataframe_y0 = df[[\"x\", \"y0\"]]\n",
    "\n",
    "dataframe_y0.plot(kind=\"scatter\", x=\"x\", y=\"y0\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "2c238efa",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Kw+Pyf/opDsWuYdSk5Jr5Ver7G4fPxWVkaoAcCq3o6kVcVn2Ny//pJ5cDQRNqUkp9f13+XOKATA2QQ0d6e/3d07R63kStv3taUbOeOtgya6Bccfk//eLyTMh8C+OFpdT31+XPJQ4oFAZCEmZheJT74VAA752LMyFNKo4v9f118XOxHbOfsiCoQS6ubIpnQtofxXMpEDRxv7RS31+XPhfbMfsJ8MC1ICBu++G4wqWZkCbWpJT6/pbyOlc6SLYiqEGsuRQEMBUVJohr0bhrHSRbUSiM2HJtU7xyp6KatiQ87BV10XgUx7IJxdEgU4MYc21hvFLT/vQw4bdCC+MFJapjmSypOcjUILaCGPuPMttR6lRUepgISq6F8YIS1bHMgn3mIFOD2PJz7N+UbEexCwbSw0QYwiiejfJYNrE4Oq4IahBrfqwaLJlTcFxs2t+1ITgEp5TAJMxg369juZT/M67F0SYiqEGs+TH2b2K2w+tUVHqYKKScwCTMYL/cY7ncAMyvDhLKQ1ADqLx1QmzOdoyoOUcThw3U5j1H1d5lEhg9THQoNTAJO9gvN1tSbgAWVXE0uqNQGCiTrdmOT1pPaPZjm1Tf2D2gkaLpYTKl3DzlLHsQRfFsqVPJ/VzeIezi6FK4fK6RqQHKZOt4eraeaYWk8XUDQ60DMqXIGmcqJwsZRbBfarbE5mxrMeJwrpGpAXwQ9WJjxcrVM22XVL/nKIuWQVJ5gUk5u12Xm0koNltia7a1WHE418jUAD6wbTzdlJ6piUXWfrN5L6Bys5DFFs9GlUmwNdtajDicaxJBDeArWzYmNKVnakpwFQRXUv3lzOopNtiPcmkE12cvuXyudUVQA0Qkyh68KT1TU4KrIJiydlG5/MhCegn2o84k2JZtLZbL51pXBDVAyEzpwZvQMw0yuIoyaIz6Bh2EoLOQpmQSbMm2FsuUjkzQCGqAkJnSgzelZ+p3cGVC0GjKDdomcckkRMmEjkzQCGqAEJnYg4+6Z+p3cGVC0MgNunhxySREyZSOTJCY0g2EiN18c/Nj0TI/F1ErRznTmePM9KURXFm0zoYFAktFpgYIET34YJk07BOHVL/fTM0k+D2kma/ey+YlAExAUAOEiBR7sEwKGk29Qdsg6iHRnvwa0swXHGWUibwWzAUMPwEhMz3FbjMTh31MS/W7MoQSFj+HNPMFR3FY7TcMZGqAkNGD966UVDzDPtmZMCvMRn4NaRaaJJCNzUsARIWgBoiIaSl2k5RzAyZozM6EWWE28mtIs1BwlA9LAHjH8BMA4/iRijdt2CdKhYZQNn6UYkgqB7+GNAsFR/kwgcA764Kahx9+WMOGDVPfvn01efJkbdq0KeomAfCRlxoG6kKKUyhLMPufNmne6npNX/6GZj+2Sc2tJ3M+N47vvR91cIWCI79rweL4OUmWDT8988wzWrx4sR599FFNnjxZK1as0FVXXaUdO3Zo8ODBUTcPgA8K3YAXrd2ibfvSnd97GZaK+zTZYrIEuYak4lyT49eQZqF6Lz9qwXJ9Tndd+Sc60nrC+XMgkcn06A4ZbPLkyZo4caJ++tOfSpLa29tVW1urRYsWacmSJWc8v62tTW1tbZ3fp9Np1dbWqrm5WVVVVaG1G4B3DakWXfHQhpw/r0hI7V2uWh3T4bPVhcT5RtzT7Mc2nbGUQD7r757W7eaX7fX53nvkli84Kjdw8vI523gOpNNpJZPJgvdva4afTpw4oc2bN2vGjBmdj1VUVGjGjBl6++23s75m2bJlSiaTnV+1tbVhNRdAiXKl6TsuVu09rtX5ptYyTfaPsg2h5NN1dWtTVmp2Rb56r3JqwXJ9Tj25fA5YE9Q0NTXp1KlTOv/887s9fv755+vAgQNZX7N06VI1Nzd3fu3duzeMpgIoU7Yb8CVD8mdXe24xwY24u44hlPV3T9PqeRO15n/mz650LU5lew87eJ1h5fI5YFVNTbEqKytVWVkZdTNiI+51C/BPthqGTCaTd1iq5wwRk7ZMMEnXpQS8rm5t0krNyK3YGVYungPWBDXV1dXq1auXDh482O3xgwcP6oILLoioVbnF6QZP3QKC0nMtn2K2mOBGXJjXhQrZ3sMOuT6nXFw8B6wZfurTp4/Gjx+v1157rfOx9vZ2vfbaa/ryl78cYcu6+6T1hGY/tklXPLTB8xRJ21G3gLAUM7XWxC0TTNNzSGr93dO0Zv6krJ0Rtvewg5faKZfPAatmPz3zzDOaM2eOVq1apUmTJmnFihX6xS9+oe3bt59Ra5ON1+rpcsRthkChmSo9Z1AgnvzOXHqdIdLcevKMTIRJ01ttzOiyUrMdOj6nQf37aPn//sj6TLrX+7c1w0+SdMMNNyiVSul73/ueDhw4oLFjx+qVV17xFNCEodDeHi7u30HdAvIJamjS6xYTPWtzzuvXRw/9+iNd9/CbvranWDYP2cZxe4+ggs8gg9qun1Octg2xKlNTrqAzNet3HNK81fU5f7563kRNH+3WIoFkapCPaZlLU9pjSjuQX1DBp5ffa2MWL0jOrVNjgzgWJrpWtxDXpcWDYNqUalPaY0o7UFhQ9YL5fm8c6zL9RFDjI9du8F65UEDIhcR/pq1tYkp7TGkH8gsq+Cz0exeseZeJF2WwqqbGBl6nSLrEr31RopSv58RwQGlMy1ya0h5T2sHwRn5B1QsW+r31jUfPeMzluky/EdT4zIUbfKlsLSCMY4F3GExb28SU9kTdDpuLlMMUVPBZ7AJ5XZk+8cKEQJnhp4CUs38HwsVwQHBMG5o0pT13XTlKfzpkQCTtYF0pb4IqJ8j3eyfUDcz72qCyeOXWEpo0fE+mBrFnynCAi8LMXHrpJQbVHq891GxZkjFDqnTf1y/VZbXnlt0OL+0kK+ldUOUE+X7vorXvhZbF8ytrZ9LwPUGNAbxcEE1I67kq13BAhQpvoghvghyaLOXC7Fd7iv3b2S7+H/7+mJb/+qNQLv6sK1WcoILgfL83zLpMP4IR0wJlgpoIebkgMv4djmwXknZJ2/anNX35G7znBouyl1jM396w41DkF3+ykqUJKijP9nvDym76FYyYFihTUxMhL2PbUYx/x3Gtlq574Iz5fJUqug93U3NgqCjXfPH6tzvqDebkWZhTCqd2K67LTtgo6LpMv2oJTQuUCWoi4uWC6PWi6VcQYlKxV1QymYy27Uurvcc62yyMdpppAW+URd5e/3a2jkk2YV38wyiWLuY4Me2Yigu/ghHTAmWGnyLix8V42/5m3fPi73wbmjKp2CsqpqVSTWHqMGiUvUQvfztXir+rsKeUBzm8UcxxYuoxFRd+Li1g0vpsZGoi4uWCWOg5a95q9G1oiqXbTzMtlWoKU6cBR9lL9PK3CwXJUnQX/yCGN4o5Tkw9plyTLxPmV9au6/D96nkTtf7uaVozf1IkwSmZmoh4jZJzPWfchef6uvIkGYrTol4YzURBz24od2ZflL3EQn+7UJD85PxJ+rNRNYG2MSzFHCcmzZgp9/jreH2vREKnMplQZ6jma7uXTJjfWTsTFmAlqImQl4txrufcMGGo3t1zZlDTodgghAzFH5mUSjVBUAGvX8MPUa7iXehvFwqSXQlopOKOExM6UeUef9leX8rvKYWXthdTTmBCMOIXgpoIebkY53pOQ6ol7+8uNggJO0Nh8ro7Jm11YcL7FFTA63cNV5QX5nx/Oy5BcjHHiQmdqHKPv3wF4EHXIhZqu0mZsLAR1Big44LYMfaZ7QbW86IZRBASxsXXpuLAKG+SJr1PQRxrcbromhQkB6mY4yTqYd5yj79CBeBBHsde2m5CJiwqFAoboNSp1H5PzQyj2IviQG9Me5/8PtbiuN+WjfvBFTvdupg9raLch6vc489LAbiX31MKL203IRMWFTI1Big1DRpUDzCoDEUQvXMThmf8ZmIWw+9jzYaLbqnHlgvHZLGZwlL2tIoyg1Xu8ed1p+2Dzf/t+/nqpe3Dq/vHdsIDQU3E/LiB2VLk5WdK1KThGb+ZnDr261iLevghn1KPrbCOyTCCpmI7WuXsaRXF9avc4y/X63ta8ssPJPl7HHhte1xquXpi+ClicUrD+9k7N214xk82ZDH8EOXwQzYdQy0L1rxb0rEV9DEZ1orfxa5ZZesaV+Uef9len4vf1yYvbTdp7ZgwkamJWFxuYJJ/vXMTh2f8ZHIWw0+mFNDmm5rbodCxFcYxGdaK38VmCk3OLOZT7vHX8/VnVST0f45+qqV/yM505fe1qZi225LJ9wuZmoiZtG9GGHuw+NE7j0N2y7QsRpCiLqD1ujeTJL3TcDjrORL0MRlmNqTYjpbtHbNyj7+O1//ZqBpdkOyb97l+X5uiPndM5Fum5sMPP9Q111yjhoYGv35lbEQ99hlmfYofvXPbL6JemJLFcJ2XvZm66toL73qOBH1MhpkNKTZTGJfMohdxuDaZzrdMzYkTJ7Rnzx6/fl2sRD32GUV9Sjk9DJOyW0GjJxYsr1Nzs+l6jgR9TIZ9syw2UxinzGI+cbo2mcpzpmbx4sV5f55Kee/tILsoxj5trU+JOrsFN3idmptNz3MkyGMy7GxIsZlCMot/xLUpWolMJs98tC569eqlsWPHqqqqKuvPW1patGXLFp06dcrXBvopnU4rmUyqubk55/8RN+t3HNK81fU5f7563kRNHz04xBYVh4soyjX7sU367c6U2kt8fc9zJKhjsrn15Bk3S1eWMXAR1yZ/eb1/e87UjBw5UnfeeaduuummrD/funWrxo8fX3xLESnbx4BtrOx3YXE2l6ycNU7zn6jPu0FsPj3PkaCOSbIhdrHx2uQCz0HNhAkTtHnz5pxBTSKRkMekDwxCkV94XF4w0GbJfr317De/opmPvqXNe46qvctlrOM8kGTMOcLNMl6i6gQV83dN6qh5Hn46cOCA2traVFdXF3SbAsPwU3aktcMx+7FNOW+MQe3mC+/ynQeSij5HTLrQwz5RdYKK+bthttHr/dtzUNNhzpw5mj9/vqZOnVp2I8NGUJOfKWltF28GDakWXfHQhpw/X3/3NGf+V9vlOw+8nCNk5NwXxjUqqk5QMX83zDb6XlPTobm5WTNmzFBdXZ3mzZunOXPm6POf/3xZjUVp/D6xSklr+9kGl28Gtq66Gkf5zgMv50hYK/8ifGHu7xXFrNRi/q6pM2eLXqfmhRde0L59+/TNb35TzzzzjIYNG6Y///M/17PPPquTJ/3dgwTZhbUHTNhtYD8n2M7WfZDgTVjXqKhWTS/m75q6sntJi+/V1NRo8eLFev/99/Uf//EfGjlypG6++WYNGTJEd955p3bu3Ol3O9GFCTd/v9vg+s3A9kW5wthCw1TF/O+mXuhxpmKPaZO3qihVz/egmL9raketrG0Sfv/732vdunVat26devXqpb/4i7/QBx98oEsuuUR/93d/pzvvvNOvduIPwkz55RpaCqINcRiesXFRLpeHBAsp5X8P8kLvYq1ZFEo9pk3eqqJY+d4Dr3/X1JmzRWdqTp48qeeee07XXnut6urq9C//8i+64447tH//fj3xxBN69dVX9Ytf/EI/+MEPgmhv7IXREyw0tBREG6KK+sPMQES9HUYpTMgKRqWU/z2IjJwJw80uKfWYNn2rig5ermn53oNi/q6J22MUnan53Oc+p/b2ds2aNUubNm3S2LFjz3jO9OnTde655/rQvNMaGxv1wx/+UK+//roOHDigIUOG6KabbtJ3v/td9enTx7e/U6owe1CFTqyDzf9ddramUKFjECd32FF/lBkIW9YZMbUQMAzl/O9+Z+QoPPZPOZ+r6VtVeL2mFXoPjrSe8Px3TVwQsuig5sc//rFmzpypvn1zb7F+7rnnavfu3WU1rKvt27ervb1dq1at0siRI7Vt2zYtWLBAx48f1/Lly337O8XKdhBNqBuoeV8Zpks+nwzkw811YnVY8oddhEu9QRc64H+zM6U/G1UTyMkd5vAMN4rC4jAkmEs5/3s5F/qeHaQ4B5a5lNOJLPeYjmII2WsnyOs1zet7UEzny6SOWtFBzc033xxEO/K6+uqrdfXVV3d+P2LECO3YsUOPPPJI3qCmra1NbW1tnd+n02lf25XtIHp3z9HO5daD6vlnO7F6KvUGXeiAv/mxTZo6qkb/6/ox+u4L23w9ucOK+rlReGNqIWAY/Pjfi7nQ5+pl3zBhaN7XuRxY9uRHdrXcz9XEzIRU3DXN9fO6pNlPJmhubtZ5552X9znLli1TMpns/KqtrfXt7+eqhO8qqNqDrrUZy/7fS7M+p9SKfC+7Fr+5q0nffWFbYPUhw6v7a/rowYFdLJih4o3tM7bKEfb/nquXvfqtxryvs/0GVAw/6rv8+lyDvkYVq5hrmuvntZVBza5du7Ry5Up94xvfyPu8pUuXqrm5ufNr7969vrWh0EEkBT8deXh1f12QzD0MKBV/g851wHfV8X89veljSQr85Pa7mNf1noqfTCwEDEtY/3u+qcLv7jmqicMGOnsD8srP6dQuHtPFXtNcfA86lDWlu1xLlizRAw88kPc5H374oS6++OLO7/ft26err75aM2fO1IIFC/K+trKyUpWVlb60tScvGY0OQaaIg7hBexneksqv3ykkqGJeU6cimsjUdHsYwvrfC3WQ5nxlmM7u/X+sWgrAb37Wd7l4TBd7TXPxPehQ9N5PfkqlUjp8+HDe54wYMaJzhtP+/fs1bdo0felLX9Ljjz+uioriEk1+7/2Ubd+LbILe1yeo/Tc2fpTS7H/aVPB5Qe31EeS+ImziCVN43RfMxRuQV+ydVpjr17TA9n7yU01NjWpqajw9d9++fZo+fbrGjx+v1atXFx3QBKFQRiOsnn9QFflT/yT7LKeechXYljNLoZxiXi9/1+WeCuzitZdt0gyTsJFdLYxr2mmRZmq82rdvn6ZNm6a6ujo98cQT6tWrV+fPLrjgAs+/J6hdunc3Hdfv9jfribcaVd94tPPxsKPkIA7mbNF/LqvnTdT00YN9GTZav+OQ5q2uL/i3ujJp9dtSAzpWjY0n13vZfuA9ivf1wev924qg5vHHH9e8efOy/qyY5gcV1HTlapS8u+m43mk4rKV/qKPJpiMF7MewUSnp5iCHq7wqNbAyKSBDdFy9fvgpju8R1wfv9+/ox3A8mDt3rjKZTNYv0/g11S/XjJ+oNhYcXt1fsyZdWHAqoF+zFIqddmjKhpilTjuN83YE5XJps03TpgqbKI7vEdcH7yKtqcGZckXk914/Rn/TY7G7KCL1QvU7fs5SKKZWyITVb0utA2IxwMKypd3pvUar4zPplUjoVCYTq8xJsaKqL4wjghrD5IrIr3v4t0p/+tkZj4e9rH+hYjQ/p5gXU/hmwtozhQKrdxoOZ22/CQFZLlGP4ecLXNjqIhrZPpMOBJXd+RF4m3x9MJEVw09xkW8I5WjryciHVrrKlQIOYrXKrn8r11CDCatkFgqslv7yg6y7K5sQkPVkys7QuQKX+U/UGzHcGEfZPpMODIl058ewkYnXB5MR1BjEyyrF2Zi2rH8Qq1V6uclGvUqml9WYs13QTAjIevJrDL+cepdCK+3mY9o54YpC28MQVP5RVPWFccfwk0GKWaW4K9Mi9SDWS/Ay1GDCOg2F1i7KNQ4exe6/ufgxhh9G2j0f084JV3j9TKIYEol6qLSnqOoL446gxiD5FpiqOvsspT/9zKqFp/xaLKzYm2yUi5R1BFZPb/q4cxuJbHpe0PwKyPy4sPtxMfaj3qVQkD9x2EBt2fOJVeeE7bx2vPIFlX4HH6YWjEdVXxh3DD8ZJtcQyq8WftXZDcgKsXFX7UnD8+8gn+uC5mW6arYhHT9rYMq9GIeVdv/H2RNje05EpdAQa74hkaDqtEyd7hx0fSGyI1NjmHwReVwjdRsL5YJY1j2smUDltj2stDu912jkG2LNF1QGMVvN9OnODBuFj6DGULmGUIodWjFtnLkUtu774vcFLd9MoGyFs+Vc2Mtpe9hp9zjviRSFnp/JWRUJfdaef52aoIIP06c7E3iHj6DGUaaOM5fKxh6Pnxe0fDcFLzOBiv275bQ9iCCUwMU8xXwmQQUftmRxOX7DQ1DjKNcWJrO5x+PHBS2qmUCltj1XEHrXlX+i9TsOsQptzAQVfNiaxUVwCGocZPo4czni2uOxbSZQzyD0vH599NCvP9J1D795xnNtziDCmyCDDxuzuAgOs58cZONsoWxc2qiwXLbOBOqYrfHQrz9iFdqYC2pxzI4Aev3d07R63kStv3ua1syfRJAcU2RqHGTLOHMurtUD+cXWmUC5MocdXMggorCgj9G4ZnHRHUGNo8Z8vkr///602rssFVIhaXzdQONPfNfqgfzS86bQUZdypPVEZ7AX5YU910w7k1ehRfgIPhAkghqH5Ns9V5LaJdXvOarZj20yNuvhcj2QXwb26617Xmw0JpNVKLPmxyq0QNBcWP4C1NQ4Jd/uuV2ZXMPgSj1QkExbQbVQe8pZhRYImik70sMfBDWOKLR7blcm76Rrez1Q0PzagiDs9mQrEu1gQkEz4su0TgLKw/CTI0pZx8TEGgbWncjPtBVUvbanlFVogaAx3O0eghpHeK1b6MrUrIff6064NFZuWiar2PZQJAqTmNZJQPkIahyRK8ORjelZD7+mfro4Ndy0TJZp7QmLS4FynJnWSUD5qKlxSLa6hS+PGKSvXDSo22O21DB0LNxW6k3DprHyYhYaDGoRs1KZ1p4gUVTqlkKLWhKw2ieRyXioLHVEOp1WMplUc3Ozqqqqom5OYLJlOExclC1IDakWXfHQhpw/X3/3NCPeh3KySaZ9pqa1JwizH9uUMysV5zWUbNbcevKM4e6gMrpk+Ern9f5NUGM4v0+CuJxU63cc0rzV9Tl/vnreRE0fPTjEFmXHTdIetgTKKE2QQbmLQ+Fh83r/pqbGUH6fBHE7qWwYK2fmhV0oKnVbkEXsrJIeHmpqAlbqpox+14PYVF/iBxvGyllo0C42BMowj2lrS7mOoCYg5RQU+n0SxPWkMr2AlZukXWwIlGEeOi/hYvgpIOWkG/1Oc8c1bW7yztVSfKdD28zvNZTgPjov4SKoCUC5tRJ+nwRxP6lMXvCNm6RdTA+UYR46L+EiqAlAuZkRv08CTipzcZO0k8mBMszjQufFlpmzBDUB8CMz4vdJ4MJJ5TJukoC7bO682DZzlnVqAuLX+iN+nwQ2nlQIhi09L/iDzxulMGUtLdapiZhfmRG/e/BkBGBbzwvl4fNGqWxcS4ugJiA2pxvhNhYCixc+b5TKxpmzBDUBIzMCk9jY8zKZ6UM6fN4oh40zZ61bfK+trU1jx45VIpHQ1q1bo24OYBUWAvOHLbt183mjHDYuOGldUPPtb39bQ4YMiboZTil1KwfYx8ael4ls2XaEzxvlMn1l9p6sGn56+eWX9etf/1rPPfecXn755aibYz0KCP1j+jBEB9YsKp9NQzp83t3Zcp6axLb6UGuCmoMHD2rBggV64YUX1K9f/t5Hh7a2NrW1tXV+n06ng2qelSggLF+YgaFfF2TWLCqPbcWTfN504PxgS32oFUFNJpPR3Llzdcstt2jChAlqbGz09Lply5bp+9//frCNs5RNvU2ThREY+n1Btq3nZRrbhnT4vOnAxUmkNTVLlixRIpHI+7V9+3atXLlSx44d09KlS4v6/UuXLlVzc3Pn1969ewP6T+xDAWH5wtr9PKj6jeHV/TV99ODY3eDKZWPxpBTfzzus8xRmiDRTc9ddd2nu3Ll5nzNixAi9/vrrevvtt1VZWdntZxMmTNCNN96oJ554IutrKysrz3gNTrOtt2miMIYhyKiZiSEde9g2XIjyRBrU1NTUqKampuDzfvKTn+jee+/t/H7//v266qqr9Mwzz2jy5MlBNtFZFBCWL4zAkAuymRjSCYcfdWS2dOAoYvaHFTU1F154YbfvzznnHEnSRRddpKFDh0bRJCfQ2yxPGIGhLRdkW/h947CleNI2ftaRmd6Bo4jZX1YENQgGvc3y3XXlKB1pbdO2fX+cWednYGj6BdkW3Djs4ndhr8kdOIqY/cUu3UAJst0kxwyp0n1fv1SX1Z7r699qbj15xgWZG3JxTNlpGIU1pFp0xUMbcv58/d3TSg7mTevABfm/uoZduoEAZetdffj7Y1r+6498v0mSUSsPxdb2aEi16F//c3/e55RTR2bacCE1c/4jqEFRKGaTNuw4FMlN0rQLsi24cZgvW+YzF5fqyKiZ8x9BDTyhJsH7hZebpFm4cZgvW+azJxfryKiZ8591G1oiGrZs4BckLxdeiZukaWxdLC8uci2O15Mphb1+s23DSNORqUFB1CTkfg+6ondlLpNnv8RdoeHBO//HKP0/l3/e2fOKmjl/EdSgIGoSCr8HEjdJk3HjMFeh4UGXA5quqJnzB0ENCgqyJsGWwuNC78GT8yfpz0YVXh0b0eLGYR7qSuAnghoUFMRFx7bC40LvAQGNf2wJdOEfhgfhFxbfgyd+LwBn42JoLIIXLNsCXfiP4UHk4vX+TVCDovhx0bF9FU2bLrw2ZT1sDHQBhIMVhREIP2oSwio8DuqGbkNdhm1ZD2bYAfADQQ1CF/RiaLbd0INg2yZ5zLAD4AcW30Pogl4MLe4LBeZazKxr1sM0rPoLwA8ENfBdQ6pF63ccynvzDGoVTRtv6H7zkvUwDav+AtHzcu02HcNP8E0xwz5BLYbGMIa9WQ+m9XZnU5G3qXgPvXFpyJ6gBr4ppY7D76JbW2/ofrJ1MTNW/T3NpRtMVHgPi2NbDV4+DD/BF6YM+zCMcZrNm+QNr+6v6aMHx+az6inuNWF+iNt7WM6wkSnXbr+QqYEvTBr2YRiDrIetmNpevji9h35kpEy6dvuBoAa+MGnYhxv6H5U6vEctQjRcu8FEIU7voR/DRiZdu/1AUANfmFjHYcMieaahFiFart1gohCX99CvjJSJ1+5yUFMD39hcx4HT4laLYBpqwsoXl/fQz6UbXLp2k6kJSRzS+Qz72C1OtQgmoyasfHF4D/3MSLl07SaoCVgc0/kM+9gpTrUIJnPpBhOVOLyHQQwbuXDtZvgpYKTzYYu41CLYIu5T2/3g+nvo0rCRX8jUBIh0PmziWsEg4Lo4ZKSKRaYmQDbuwYN4o+cH2Mf1jFQxyNQEiHQ+wuBnETo9PwA2I6gJEOl8BCnIInQXCgYBxA/DTwEjnY+gUIQOAN2RqQkY6XwEgSJ0ADgTQU1ISOfnF4fFCf3EmjIAcCaCGkQqjosT+oEidAA4EzU1iBR1IaWJy/42iEZDqkXrdxzS7iaWnYBdyNQgMtSFlCcO+9sgXKZmThmehlcENQhV14sTdSHloQgdfsuXOV0zf1Lo7TE1yIK5rApq/u3f/k0/+MEP9J//+Z/q27evvva1r+mFF16IulnwINvFaULdwLyvoS7EG4rQ4QcTM6emBVkwnzVBzXPPPacFCxbovvvu0xVXXKHPPvtM27Zti7pZ8Cjbxem9jz/RwH69lf70MxYnBCJmWubUxCAL5rMiqPnss890++2368EHH9T8+fM7H7/kkksibBW8yndxOtp6UhOHDVR949HOx6kLAcJn2ow604Is2MGKoGbLli3at2+fKioqNG7cOB04cEBjx47Vgw8+qDFjxuR8XVtbm9ra2jq/T6fTYTQXPRS6OP1/00dq2KD+1IUAETJtWxfTgizYwYop3Q0NDZKkv/3bv9Xf/M3f6KWXXtLAgQM1bdo0HTlyJOfrli1bpmQy2flVW1sbVpPRhZeLU7G7zDLlFPCfSdu6sGwBSpHIZLqE5CFbsmSJHnjggbzP+fDDD7VlyxbdeOONWrVqlf7qr/5K0ukszNChQ3XvvffqG9/4RtbXZsvU1NbWqrm5WVVVVf79Iyho9mObcvYAiyn4YzYEEDxTZtQ1t548Y9kCzvd4SqfTSiaTBe/fkQ4/3XXXXZo7d27e54wYMUK///3vJXWvoamsrNSIESP08ccf53xtZWWlKisrfWkryuPXmirMhgCCZ8qMOpYtQLEiDWpqampUU1NT8Hnjx49XZWWlduzYoa9+9auSpJMnT6qxsVF1dXVBNxM+8OPixGwIs7AgGsJiSpAF81lRKFxVVaVbbrlF99xzj2pra1VXV6cHH3xQkjRz5syIW4dilHNxYjaEGRgCBGAqK4IaSXrwwQd11lln6eabb9ann36qyZMn6/XXX9fAgfkXcIM7mA1hBoYAAZjKitlPktS7d28tX75cBw8eVDqd1rp16/SFL3wh6mYhRMyGiF7HEOCpHvMLug4BAkBUrAlqAMmsKadx5GUIEACiYs3wEyAxGyJqDAECMBlBDazEbIhomLbqLAB0xfATgKIwBAjAVGRqABSFIUAApiKoAVAShgABmIbhJwAA4ASCGgAA4ASCGgAA4ASCGgAA4ASCGgAA4ASCGgAA4ASCGgAA4ATWqQHglIZUi/YcaWVRQCCGCGoAOOGT1hO6be1WbdyZ6nxs6qgarZw1Tsl+vSNsGYCwMPwEwAm3rd2qN3c1dXvszV1NWrT2vYhaBCBsBDUArNeQatHGnaluO4dL0qlMRht3prS76XhELQMQJoIaANbbc6Q1788bDxPUAHFAUAPAenXn9cv782GDKBgG4oCgBoD1RtSco6mjatQrkej2eK9EQlNH1TALCogJghoATlg5a5ymjKzu9tiUkdVaOWtcRC0CEDamdANwQrJfb62ZP0m7m46r8fBx1qkBYoigBoBThlcTzABxxfATAABwAkENAABwAsNPAKzBvk4A8iGoAWA89nUC4AXDTwCMx75OALwgqAFgNPZ1AuAVQQ0Ao7GvEwCvCGoAGI19nQB4RVADwGjs6wTAK4IaOKEh1aL1Ow5RX+Eo9nUC4AVTumE1pvrGA/s6AfCCTA2sxlTfeBle3V/TRw8moAGQlTVBzUcffaTrrrtO1dXVqqqq0le/+lWtX78+6mYhQkz1BQB0ZU1Qc+211+qzzz7T66+/rs2bN+vyyy/XtddeqwMHDkTdNESEqb4AgK6sCGqampq0c+dOLVmyRJdddplGjRql+++/X62trdq2bVvUzUNEmOoLAOjKiqBm0KBBGj16tNasWaPjx4/rs88+06pVqzR48GCNHz8+5+va2tqUTqe7fcEdTPUFAHRlRVCTSCT06quv6r333tOAAQPUt29f/ehHP9Irr7yigQMH5nzdsmXLlEwmO79qa2tDbDXCwFRfAECHRCbTo8oyREuWLNEDDzyQ9zkffvihRo8ereuvv14nT57Ud7/7XZ199tn6x3/8R/3qV79SfX29Pve5z2V9bVtbm9ra2jq/T6fTqq2tVXNzs6qqqnz9XxAtpvoCgLvS6bSSyWTB+3ekQU0qldLhw4fzPmfEiBH6zW9+oyuvvFJHjx7t9s+MGjVK8+fP15IlSzz9Pa9vCgAAMIfX+3eki+/V1NSopqam4PNaW0/Pcqmo6D5aVlFRofb29kDaBgAA7GJFTc2Xv/xlDRw4UHPmzNH777+vjz76SN/61re0e/duXXPNNVE3DwAAGMCKoKa6ulqvvPKKWlpadMUVV2jChAn67W9/qxdffFGXX3551M0DAAAGiLSmJmzU1AAAYB+v928rMjUAAACFENQAAAAnENQAAAAnENQAAAAnRLpODQBEqSHVoj1HWlmJGnAEQQ2A2Pmk9YRuW7tVG3emOh+bOqpGK2eNU7Jf7whbBqAcDD8BiJ3b1m7Vm7uauj325q4mLVr7XkQtAuAHghoAsdKQatHGnSmd6rFE16lMRht3prS76XhELUMxGlItWr/jEJ8XumH4CUCs7DnSmvfnjYePU19jMIYOkQ+ZGgCxUndev7w/HzaIgMZkDB0iH4IaALEyouYcTR1Vo16JRLfHeyUSmjqqhiyNwRg6RCEENQBiZ+WscZoysrrbY1NGVmvlrHERtQheeBk6RLxRUwMgdpL9emvN/Ena3XRcjYePs06NJRg6RCEENQBia3g1wYxNOoYO39zV1G0IqlcioSkjq/kswfATAMAeDB0iHzI1AABrMHSIfAhqAADWYegQ2TD8BAAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnBCrbRIyf9jVNZ1OR9wSAADgVcd9O9Nld/ZsYhXUHDt2TJJUW1sbcUsAAECxjh07pmQymfPniUyhsMch7e3t2r9/vwYMGKBEIhF1cyKVTqdVW1urvXv3qqqqKurmOI33Ohy8z+HgfQ4H73N3mUxGx44d05AhQ1RRkbtyJlaZmoqKCg0dOjTqZhilqqqKEyYkvNfh4H0OB+9zOHif/yhfhqYDhcIAAMAJBDUAAMAJBDUxVVlZqXvuuUeVlZVRN8V5vNfh4H0OB+9zOHifSxOrQmEAAOAuMjUAAMAJBDUAAMAJBDUAAMAJBDUAAMAJBDXopq2tTWPHjlUikdDWrVujbo5TGhsbNX/+fA0fPlxnn322LrroIt1zzz06ceJE1E2z3sMPP6xhw4apb9++mjx5sjZt2hR1k5yzbNkyTZw4UQMGDNDgwYN1/fXXa8eOHVE3y2n333+/EomE7rjjjqibYg2CGnTz7W9/W0OGDIm6GU7avn272tvbtWrVKv3ud7/Tj3/8Yz366KP667/+66ibZrVnnnlGixcv1j333KMtW7bo8ssv11VXXaVDhw5F3TSnbNiwQQsXLtQ777yjdevW6eTJk7ryyit1/PjxqJvmpPr6eq1atUqXXXZZ1E2xClO60enll1/W4sWL9dxzz+kLX/iC3nvvPY0dOzbqZjntwQcf1COPPKKGhoaom2KtyZMna+LEifrpT38q6fQeb7W1tVq0aJGWLFkScevclUqlNHjwYG3YsEFTp06NujlOaWlp0Re/+EX9/d//ve69916NHTtWK1asiLpZViBTA0nSwYMHtWDBAj355JPq169f1M2JjebmZp133nlRN8NaJ06c0ObNmzVjxozOxyoqKjRjxgy9/fbbEbbMfc3NzZLE8RuAhQsX6pprrul2XMObWG1oiewymYzmzp2rW265RRMmTFBjY2PUTYqFXbt2aeXKlVq+fHnUTbFWU1OTTp06pfPPP7/b4+eff762b98eUavc197erjvuuENTpkzRmDFjom6OU55++mlt2bJF9fX1UTfFSmRqHLZkyRIlEom8X9u3b9fKlSt17NgxLV26NOomW8nr+9zVvn37dPXVV2vmzJlasGBBRC0HSrNw4UJt27ZNTz/9dNRNccrevXt1++236+c//7n69u0bdXOsRE2Nw1KplA4fPpz3OSNGjNBf/uVf6l//9V+VSCQ6Hz916pR69eqlG2+8UU888UTQTbWa1/e5T58+kqT9+/dr2rRp+tKXvqTHH39cFRX0LUp14sQJ9evXT88++6yuv/76zsfnzJmjTz75RC+++GJ0jXPUrbfeqhdffFEbN27U8OHDo26OU1544QV9/etfV69evTofO3XqlBKJhCoqKtTW1tbtZzgTQQ308ccfK51Od36/f/9+XXXVVXr22Wc1efJkDR06NMLWuWXfvn2aPn26xo8fr3/+53/mAuWDyZMna9KkSVq5cqWk00MjF154oW699VYKhX2UyWS0aNEiPf/883rjjTc0atSoqJvknGPHjmnPnj3dHps3b54uvvhifec732GozwNqaqALL7yw2/fnnHOOJOmiiy4ioPHRvn37NG3aNNXV1Wn58uVKpVKdP7vgggsibJndFi9erDlz5mjChAmaNGmSVqxYoePHj2vevHlRN80pCxcu1FNPPaUXX3xRAwYM0IEDByRJyWRSZ599dsStc8OAAQPOCFz69++vQYMGEdB4RFADhGTdunXatWuXdu3adUawSMK0dDfccINSqZS+973v6cCBAxo7dqxeeeWVM4qHUZ5HHnlEkjRt2rRuj69evVpz584Nv0FAFgw/AQAAJ1ChCAAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQAwAAnEBQA8BaqVRKF1xwge67777Ox9566y316dNHr732WoQtAxAFNrQEYLV///d/1/XXX6+33npLo0eP1tixY3XdddfpRz/6UdRNAxAyghoA1lu4cKFeffVVTZgwQR988IHq6+tVWVkZdbMAhIygBoD1Pv30U40ZM0Z79+7V5s2bdemll0bdJAARoKYGgPX+67/+S/v371d7e7saGxujbg6AiJCpAWC1EydOaNKkSRo7dqxGjx6tFStW6IMPPtDgwYOjbhqAkBHUALDat771LT377LN6//33dc455+hrX/uaksmkXnrppaibBiBkDD8BsNYbb7yhFStW6Mknn1RVVZUqKir05JNP6je/+Y0eeeSRqJsHIGRkagAAgBPI1AAAACcQ1AAAACcQ1AAAACcQ1AAAACcQ1AAAACcQ1AAAACcQ1AAAACcQ1AAAACcQ1AAAACcQ1AAAACcQ1AAAACf8X74mYzMLNJwHAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataframe_y0 = df[[\"x\", \"y1\"]]\n",
    "\n",
    "dataframe_y0.plot(kind=\"scatter\", x=\"x\", y=\"y1\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "345e70c6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataframe_y0 = df[[\"x\", \"y2\"]]\n",
    "\n",
    "dataframe_y0.plot(kind=\"scatter\", x=\"x\", y=\"y2\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a52d7db4-dc76-4b53-9e3a-dcd33ac36c16",
   "metadata": {},
   "source": [
    "---\n",
    "g) Now determine the correlation coefficient between `x` and all three measurement series `y0, y1, y2`.\n",
    "\n",
    "### Solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "1b62cf91-bb5f-40ca-a49e-1dec18a2e42e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y0    0.988892\n",
      "y1    0.131123\n",
      "y2    0.008452\n",
      "Name: x, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(df.corr().loc[\"x\", [\"y0\",\"y1\",\"y2\"]])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c94ec52-0d1a-4dec-bc04-5c1d0a4b717b",
   "metadata": {},
   "source": [
    "---\n",
    "h) Why is the correlation coefficient for the measurement series `y2` practically zero, although `x` and `y2` are obviously strongly correlated?\n",
    "\n",
    "### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "e96ba9be-f32d-4c2b-b1f0-3e9f7d3584ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"NO CLUE!!!! What kind of question is that? I've never heard this before\""
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"NO CLUE!!!! What kind of question is that? I've never heard this before\""
   ]
  }
 ],
 "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": "3.11.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}

SW09_Auftrag_en