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       "      <td>8.0</td>\n",
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       "     a    b     c     d     e     f\n",
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     "execution_count": 61,
     "metadata": {},
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    }
   ],
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   "source": [
    "df1.add(df2, fill_value=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another important point here is although the normal arithmetic operations work here, there also exist dedicated methods like `DataFrame.add()` which achieve the same functionality + a bit extra.\n",
    "\n",
    "Here's a list of all arithmetic operations within pandas:\n",
    "\n",
    "| Operator | Method | Description |\n",
    "| -- | -- | -- |\n",
    "| + | add, radd | Addition |\n",
    "| - | sub, rsub | Subtraction |\n",
    "| / | div, rdiv | Division |\n",
    "| // | floordiv, rfloordiv | Floor division |\n",
    "| * | mul, rmul | Multiplication |\n",
    "| ** | pow, rpow | Exponentiation |\n",
    "\n",
    "Notice how some of the methods have `r` in front of them? That stands for reversed and effectively reverses the operands. For example\n",
    "\n",
    "```python\n",
    "df1.div(df2)\n",
    "```\n",
    "would be the same as\n",
    "```python\n",
    "df2/df1\n",
    "```"
   ]
  },
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 3\n",
    "Create a (3,3) DataFrame and square all elements in it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Broadcasting\n",
    "Similar to numpy, in pandas you can also broadcast data structures. Let's consider a simple example:"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 62,
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   "source": [
    "df1 = pd.DataFrame(np.arange(16).reshape((4,4)))\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 63,
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       "dtype: int64"
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     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
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   "source": [
    "df2 = pd.Series(np.arange(4))\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 64,
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     "execution_count": 64,
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   "source": [
    "df1 - df2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the Series of [0, 1, 2, 3] got removed from each row? That is called broadcasting.\n",
    "\n",
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    "It can also be used for columns, but for that, you have to use the method arithmetic operations."
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 65,
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   "source": [
    "df1.sub(df2, axis=\"index\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sorting\n",
    "Sorting is an important built-in operation of pandas. Let's have a look at how you can do it:"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "df1 = pd.DataFrame(np.arange(16).reshape((4,4)), index=[\"b\", \"a\", \"d\", \"c\"])\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
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     "metadata": {},
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   "source": [
    "df2 = df1.sort_index()\n",
    "df2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "Easy as that. Furthermore, you can also sort along the column axis with\n",
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    "```python\n",
    "df1.sort_index(axis=1)\n",
    "```\n",
    "\n",
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    "You can also sort by the actual values inside, but you have to give the column by which you want to sort."
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 68,
   "metadata": {},
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      "text/plain": [
       "   a\n",
       "0  4\n",
       "1  3\n",
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       "3  1\n",
       "4  3\n",
       "5  5"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
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   "source": [
    "df1 = pd.DataFrame([4, 3, 6, 1, 3, 5], columns=[\"a\"])\n",
    "df1"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 69,
   "metadata": {},
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   "source": [
    "df1.sort_values(by=\"a\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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    "## Summarizing and computing descriptive stats <a name=\"sums\"></a>\n",
    "`pandas` is equipped with common mathematical and statistical methods. Most of which fall into the category of reductions or summary statistics. These are methods that extract a single value from a list of values. For example, you can extract the mean of a `Series` object like this:"
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   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 70,
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   "source": [
    "df = pd.DataFrame(np.arange(20).reshape(5,4),\n",
    "                 columns=[\"a\", \"b\", \"c\", \"d\"])\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a    40\n",
       "b    45\n",
       "c    50\n",
       "d    55\n",
       "dtype: int64"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
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   "source": [
    "df.sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how that created the sum of each column?\n",
    "\n",
    "Well you can actually make that the other way around by adding an extra option to `sum()`"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     6\n",
       "1    22\n",
       "2    38\n",
       "3    54\n",
       "4    70\n",
       "dtype: int64"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
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   "source": [
    "df.sum(axis=\"columns\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A similar method also exists for obtaining the mean of data:"
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "a     8.0\n",
       "b     9.0\n",
       "c    10.0\n",
       "d    11.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
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   "source": [
    "df.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, the mother of the methods we discussed here is `describe()` "
   ]
  },
  {
   "cell_type": "code",
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   "execution_count": 74,
   "metadata": {},
   "outputs": [
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