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    "# Aggregation\n",
    "\n",
    "Aggregationen beziehen sich auf jede Datentransformation, die skalare Werte aus Arrays erzeugt. In den vorangegangenen Beispielen wurden mehrere von ihnen verwendet, darunter `count` und `sum`. Ihr fragt euch nun vielleicht, was passiert, wenn ihr `sum()` auf ein `GroupBy`-Objekt anwendet. Für viele gängige Aggregationen, wie die in der folgenden Tabelle, gibt es optimierte Implementierungen. Sie sind jedoch nicht auf diesen Satz von Methoden beschränkt.\n",
    "\n",
    "Funktionsname | Beschreibung\n",
    ":------------ | :-----------\n",
    "`any`, `all` | Gibt `True` zurück, wenn einer (ein oder mehrere Werte) oder alle Nicht-NA-Werte \"truthy\" sind\n",
    "`count` | Anzahl der Nicht-NA-Werte\n",
    "`cummin`, `cummax` | Kumuliertes Minimum und Maximum der Nicht-NA-Werte\n",
    "`cumsum` | Kumulative Summe der Nicht-NA-Werte\n",
    "`cumprod` | Kumulatives Produkt von Nicht-NA-Werten\n",
    "`first`, `last` | Erste und letzte Nicht-NA-Werte\n",
    "`mean` | Mittelwert der Nicht-NA-Werte\n",
    "`median` | Arithmetischer Median der Nicht-NA-Werte\n",
    "`min`, `max` | Minimum und Maximum der Nicht-NA-Werte\n",
    "`nth` | Abrufen des n-ten größten Wertes\n",
    "`ohlc` | Berechnung von vier *Open-high-low-close*-Statistiken für zeitreihenähnliche Daten\n",
    "`prod` | Produkt der Nicht-NA-Werte\n",
    "`quantile` | Berechnet das Stichprobenquantil\n",
    "`rank` | Ordinale Ränge von Nicht-NA-Werten, wie beim Aufruf von Series.rank\n",
    "`sum` | Summe der Nicht-NA-Werte\n",
    "`std`, `var` | Standardabweichung und Varianz der Stichprobe\n",
    "\n",
    "Ihr könnt eigene Aggregationen verwenden und zusätzlich jede Methode aufrufen, die auch für das gruppierte Objekt definiert ist. Zum Beispiel wählt die `Series`-Methode `nsmallest` die kleinste angeforderte Anzahl von Werten aus den Daten aus.\n",
    "\n",
    "Obwohl `nsmallest` nicht explizit für `GroupBy` implementiert ist, können wir es dennoch mit einer nicht optimierten Implementierung verwenden. Intern zerlegt `GroupBy` die `Series`, ruft `df.nsmallest(n)` für jeden Teil auf und fügt diese Ergebnisse dann im Ergebnisobjekt zusammen:"
   ]
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   "source": [
    "import pandas as pd"
   ]
  },
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   "source": [
    "df = pd.DataFrame(\n",
    "    {\n",
    "        \"Title\": [\n",
    "            \"Jupyter Tutorial\",\n",
    "            \"Jupyter Tutorial\",\n",
    "            \"PyViz Tutorial\",\n",
    "            None,\n",
    "            \"Python Basics\",\n",
    "            \"Python Basics\",\n",
    "        ],\n",
    "        \"2021-12\": [30134, 6073, 4873, None, 427, 95],\n",
    "        \"2022-01\": [33295, 7716, 3930, None, 276, 226],\n",
    "        \"2022-02\": [19651, 6547, 2573, None, 525, 157],\n",
    "    }\n",
    ")\n",
    "\n",
    "df"
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   "id": "e87f7e40",
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     "shell.execute_reply.started": "2026-05-21T16:38:57.445886Z"
    }
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   "outputs": [],
   "source": [
    "grouped = df.groupby(\"Title\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "de944585",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-21T16:38:57.447916Z",
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     "shell.execute_reply.started": "2026-05-21T16:38:57.447910Z"
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    {
     "data": {
      "text/plain": [
       "Title              \n",
       "Jupyter Tutorial  1    7716.0\n",
       "PyViz Tutorial    2    3930.0\n",
       "Python Basics     5     226.0\n",
       "Name: 2022-01, dtype: float64"
      ]
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "grouped[\"2022-01\"].nsmallest(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7dced4b7",
   "metadata": {},
   "source": [
    "Um eine eigene Aggregationsfunktionen zu verwenden, übergebt eine beliebige Funktion, die ein Array aggregiert, an die Methode `aggregate` oder `agg`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d99f985e",
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    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2021-12</th>\n",
       "      <th>2022-01</th>\n",
       "      <th>2022-02</th>\n",
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       "      <th>Title</th>\n",
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       "      <th></th>\n",
       "    </tr>\n",
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       "                  2021-12  2022-01  2022-02\n",
       "Title                                      \n",
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    "def minmaxrange(arr):\n",
    "    return arr.max() - arr.min()\n",
    "\n",
    "\n",
    "grouped.agg(minmaxrange)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "66e7a918",
   "metadata": {},
   "source": [
    "Ihr werdet feststellen, dass einige Methoden wie `describe` ebenfalls funktionieren, auch wenn es sich dabei streng genommen nicht um Aggregationen handelt:"
   ]
  },
  {
   "cell_type": "code",
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       "      <th colspan=\"8\" halign=\"left\">2022-02</th>\n",
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       "      <th></th>\n",
       "      <th>count</th>\n",
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       "    <tr>\n",
       "      <th>Python Basics</th>\n",
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       "<p>3 rows × 24 columns</p>\n",
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       "                 2021-12                                                    \\\n",
       "                   count     mean           std     min       25%      50%   \n",
       "Title                                                                        \n",
       "Jupyter Tutorial     2.0  18103.5  17013.696262  6073.0  12088.25  18103.5   \n",
       "PyViz Tutorial       1.0   4873.0           NaN  4873.0   4873.00   4873.0   \n",
       "Python Basics        2.0    261.0    234.759451    95.0    178.00    261.0   \n",
       "\n",
       "                                    2022-01           ...                     \\\n",
       "                       75%      max   count     mean  ...       75%      max   \n",
       "Title                                                 ...                      \n",
       "Jupyter Tutorial  24118.75  30134.0     2.0  20505.5  ...  26900.25  33295.0   \n",
       "PyViz Tutorial     4873.00   4873.0     1.0   3930.0  ...   3930.00   3930.0   \n",
       "Python Basics       344.00    427.0     2.0    251.0  ...    263.50    276.0   \n",
       "\n",
       "                 2022-02                                                 \\\n",
       "                   count     mean          std     min     25%      50%   \n",
       "Title                                                                     \n",
       "Jupyter Tutorial     2.0  13099.0  9265.927261  6547.0  9823.0  13099.0   \n",
       "PyViz Tutorial       1.0   2573.0          NaN  2573.0  2573.0   2573.0   \n",
       "Python Basics        2.0    341.0   260.215295   157.0   249.0    341.0   \n",
       "\n",
       "                                    \n",
       "                      75%      max  \n",
       "Title                               \n",
       "Jupyter Tutorial  16375.0  19651.0  \n",
       "PyViz Tutorial     2573.0   2573.0  \n",
       "Python Basics       433.0    525.0  \n",
       "\n",
       "[3 rows x 24 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9adf3b68",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "\n",
    "**Hinweis:**\n",
    "\n",
    "Benutzerdefinierte Aggregationsfunktionen sind im Allgemeinen viel langsamer als die optimierten Funktionen in der obigen Tabelle. Dies liegt daran, dass bei der Erstellung der Zwischendatensätze für die Gruppe ein gewisser Mehraufwand entsteht (Funktionsaufrufe, Umordnung von Daten).\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "668065b9",
   "metadata": {},
   "source": [
    "## Spaltenweise zusätzliche Funktionen\n",
    "\n",
    "Wie wir bereits gesehen haben, ist das Aggregieren einer `Series` oder aller Spalten eines `DataFrame` eine Frage der Verwendung von `aggregate` (oder `agg`) mit der gewünschten Funktion oder des Aufrufs einer Methode wie `mean` oder `std`. Es kommt jedoch häufiger vor, dass gleichzeitig mit einer anderen Funktion je nach Spalte oder mit mehreren Funktionen aggregiert werden soll."
   ]
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       "                  2021-12  2022-01  2022-02\n",
       "Title                                      \n",
       "Jupyter Tutorial  18103.5  20505.5  13099.0\n",
       "PyViz Tutorial     4873.0   3930.0   2573.0\n",
       "Python Basics       261.0    251.0    341.0"
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     "execution_count": 7,
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    "grouped.agg(\"mean\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd0c9405",
   "metadata": {},
   "source": [
    "Wenn ihr stattdessen eine Liste von Funktionen oder Funktionsnamen übergebt, erhaltet ihr einen `DataFrame` mit Spaltennamen aus den Funktionen zurück:"
   ]
  },
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       "                  2021-12                            2022-01                \\\n",
       "                     mean           std minmaxrange     mean           std   \n",
       "Title                                                                        \n",
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       "\n",
       "                              2022-02                           \n",
       "                 minmaxrange     mean          std minmaxrange  \n",
       "Title                                                           \n",
       "Jupyter Tutorial     25579.0  13099.0  9265.927261     13104.0  \n",
       "PyViz Tutorial           0.0   2573.0          NaN         0.0  \n",
       "Python Basics           50.0    341.0   260.215295       368.0  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
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    }
   ],
   "source": [
    "grouped.agg([\"mean\", \"std\", minmaxrange])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e6a9e80",
   "metadata": {},
   "source": [
    "Hier haben wir `agg` eine Liste von Aggregationsfunktionen übergeben, die unabhängig voneinander für die Datengruppen ausgewertet werden sollen."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b9a475d9",
   "metadata": {},
   "source": [
    "Ihr braucht die Namen, die `GroupBy` den Spalten gibt, nicht zu akzeptieren; insbesondere haben Lambda-Funktionen den Namen `<lambda>`, was ihre Identifizierung erschwert. Wenn ihr eine Liste von Tupels übergebt, wird das erste Element jedes Tuples als Spaltenname im `DataFrame` verwendet:"
   ]
  },
  {
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       "                    2021-12                                2022-01  \\\n",
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       "\n",
       "                                                2022-02                     \\\n",
       "                 Standardabweichung  Bereich Mittelwert Standardabweichung   \n",
       "Title                                                                        \n",
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       "\n",
       "                           \n",
       "                  Bereich  \n",
       "Title                      \n",
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       "PyViz Tutorial        0.0  \n",
       "Python Basics       368.0  "
      ]
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     "execution_count": 9,
     "metadata": {},
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   ],
   "source": [
    "grouped.agg(\n",
    "    [(\"Mean\", \"mean\"), (\"Standard deviation\", \"std\"), (\"Range\", minmaxrange)],\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb306ec2",
   "metadata": {},
   "source": [
    "Bei einem `DataFrame` habt ihr die Möglichkeit, eine Liste von Funktionen anzugeben, die auf alle Spalten oder auf verschiedene Funktionen pro Spalte angewendet werden. Nehmen wir an, wir möchten die gleichen drei Statistiken für die Spalten berechnen:"
   ]
  },
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       "                 2021-12                   2022-01                   2022-02  \\\n",
       "                   count     mean      max   count     mean      max   count   \n",
       "Title                                                                          \n",
       "Jupyter Tutorial       2  18103.5  30134.0       2  20505.5  33295.0       2   \n",
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       "\n",
       "                                    \n",
       "                     mean      max  \n",
       "Title                               \n",
       "Jupyter Tutorial  13099.0  19651.0  \n",
       "PyViz Tutorial     2573.0   2573.0  \n",
       "Python Basics       341.0    525.0  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats = [\"count\", \"mean\", \"max\"]\n",
    "evaluations = grouped.agg(stats)\n",
    "\n",
    "evaluations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "454dbc00",
   "metadata": {},
   "source": [
    "Wie ihr sehen könnt, hat der resultierende `DataFrame` hierarchische Spalten, genauso wie ihr sie bekommen würdet, wenn ihr jede Spalte separat aggregieren und [pandas.concat](https://pandas.pydata.org/docs/reference/api/pandas.concat.html) verwenden würdet, um die Ergebnisse zusammenzufügen, indem ihr die Spaltennamen als Schlüsselargument verwendet:"
   ]
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       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Jupyter Tutorial</th>\n",
       "      <td>2</td>\n",
       "      <td>18103.5</td>\n",
       "      <td>30134.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PyViz Tutorial</th>\n",
       "      <td>1</td>\n",
       "      <td>4873.0</td>\n",
       "      <td>4873.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Python Basics</th>\n",
       "      <td>2</td>\n",
       "      <td>261.0</td>\n",
       "      <td>427.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  count     mean      max\n",
       "Title                                    \n",
       "Jupyter Tutorial      2  18103.5  30134.0\n",
       "PyViz Tutorial        1   4873.0   4873.0\n",
       "Python Basics         2    261.0    427.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "evaluations[\"2021-12\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "245a9179",
   "metadata": {},
   "source": [
    "Wie zuvor kann eine Liste von Tupeln mit benutzerdefinierten Namen übergeben werden:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "e80c106a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-21T16:38:57.501147Z",
     "iopub.status.busy": "2026-05-21T16:38:57.501043Z",
     "iopub.status.idle": "2026-05-21T16:38:57.506419Z",
     "shell.execute_reply": "2026-05-21T16:38:57.506015Z",
     "shell.execute_reply.started": "2026-05-21T16:38:57.501140Z"
    }
   },
   "outputs": [
    {
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       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>Mean</th>\n",
       "      <th>Variance</th>\n",
       "      <th>Mean</th>\n",
       "      <th>Variance</th>\n",
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       "    <tr>\n",
       "      <th>Title</th>\n",
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       "                  2021-12               2022-01             \n",
       "                     Mean     Variance     Mean     Variance\n",
       "Title                                                       \n",
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     "execution_count": 12,
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   "source": [
    "tuples = [(\"Mean\", \"mean\"), (\"Variance\", \"var\")]\n",
    "\n",
    "grouped[[\"2021-12\", \"2022-01\"]].agg(tuples)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f9720af",
   "metadata": {},
   "source": [
    "Nehmen wir nun an, dass potenziell verschiedene Funktionen auf eine oder mehrere der Spalten angewendet werden sollen, dann übergeben wir dazu ein `dict` an `agg`, das eine Zuordnung von Spaltennamen zu einer der Funktionsspezifikationen enthält:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
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     "shell.execute_reply.started": "2026-05-21T16:38:57.507194Z"
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    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>2021-12</th>\n",
       "      <th>2022-01</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Title</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  <tbody>\n",
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       "      <td>261.0</td>\n",
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       "                  2021-12      2022-01\n",
       "Title                                 \n",
       "Jupyter Tutorial  18103.5  327142620.5\n",
       "PyViz Tutorial     4873.0          NaN\n",
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    "grouped.agg({\"2021-12\": \"mean\", \"2022-01\": \"var\"})"
   ]
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  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "01ce2021",
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     "shell.execute_reply.started": "2026-05-21T16:38:57.510957Z"
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    {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th colspan=\"4\" halign=\"left\">2021-12</th>\n",
       "      <th>2022-01</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>min</th>\n",
       "      <th>max</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>sum</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Title</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Jupyter Tutorial</th>\n",
       "      <td>6073.0</td>\n",
       "      <td>30134.0</td>\n",
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       "      <td>17013.696262</td>\n",
       "      <td>41011.0</td>\n",
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       "    <tr>\n",
       "      <th>PyViz Tutorial</th>\n",
       "      <td>4873.0</td>\n",
       "      <td>4873.0</td>\n",
       "      <td>4873.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3930.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Python Basics</th>\n",
       "      <td>95.0</td>\n",
       "      <td>427.0</td>\n",
       "      <td>261.0</td>\n",
       "      <td>234.759451</td>\n",
       "      <td>502.0</td>\n",
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      ],
      "text/plain": [
       "                 2021-12                                  2022-01\n",
       "                     min      max     mean           std      sum\n",
       "Title                                                            \n",
       "Jupyter Tutorial  6073.0  30134.0  18103.5  17013.696262  41011.0\n",
       "PyViz Tutorial    4873.0   4873.0   4873.0           NaN   3930.0\n",
       "Python Basics       95.0    427.0    261.0    234.759451    502.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
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   ],
   "source": [
    "grouped.agg({\"2021-12\": [\"min\", \"max\", \"mean\", \"std\"], \"2022-01\": \"sum\"})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "64c324f9",
   "metadata": {},
   "source": [
    "## Aggregierte Daten ohne Zeilenindizes zurückgeben\n",
    "\n",
    "In allen bisherigen Beispielen werden die aggregierten Daten mit einem Index zurückgegeben. Da dies nicht immer erwünscht ist, könnt ihr dieses Verhalten in den meisten Fällen deaktivieren, indem ihr `as_index=False` an `groupby` übergebt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "b8e1f80b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-05-21T16:38:57.515993Z",
     "iopub.status.busy": "2026-05-21T16:38:57.515883Z",
     "iopub.status.idle": "2026-05-21T16:38:57.519546Z",
     "shell.execute_reply": "2026-05-21T16:38:57.519279Z",
     "shell.execute_reply.started": "2026-05-21T16:38:57.515982Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2021-12  minmaxrange    8131.000000\n",
       "2022-01  minmaxrange    8543.000000\n",
       "2022-02  minmaxrange    4490.666667\n",
       "dtype: float64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grouped.agg([minmaxrange]).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d515ab5",
   "metadata": {},
   "source": [
    "Durch die Verwendung der Methode `as_index=False` werden einige unnötige Berechnungen vermieden. Natürlich ist es jederzeit möglich, das Ergebnis wieder mit Index zu erhalten, indem `reset_index` für das Ergebnis aufgerufen wird. "
   ]
  }
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