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   "source": [
    "# Calculating Weighted Mean, Standard Deviation, $\\chi^2$ and $\\chi^2$-probability.\n",
    "\n",
    "### Authors: \n",
    "- Christian Michelsen (Niels Bohr Institute)\n",
    "- Troels C. Petersen (Niels Bohr Institute)\n",
    "\n",
    "### Date:    \n",
    "- 11-11-2020 (latest update)\n",
    "\n",
    "***\n",
    "\n",
    "Very small notebook testing if your calculation of the weighted mean, the standard deviation, the $\\chi^2$-value and the $\\chi^2$-probability are correct. We use as example five measurements of a distance (too a hook!) with uncertainty. You should insert your own code in the cells below. If you can run the entire notebook without any (Assertion)errors, your code has passed!\n",
    "\n",
    "***\n",
    "\n",
    "First, we import the modules we want to use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we define the data for the measurements of the heights of the hook (in mm, though that is irrelavant here) and their estimated uncertainties:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "dhook = np.array([17.8, 18.1, 17.7, 17.7 ])\n",
    "err_dhook = np.array([0.5, 0.3, 0.5, 0.2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing the weighted mean calculation. This is where you should start pasting your code! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "# Insert own code here to calculate the weighted mean, mean_weighted\n",
    "\n",
    "# mean_weighted = ...\n",
    "\n",
    "\n",
    "\n",
    "print(mean_weighted)\n",
    "assert np.isclose(mean_weighted, 17.80982367758186)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing the weighted error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "# Insert own code here to calculate the weighted error, err_weighted\n",
    "\n",
    "\n",
    "# err_weighted = ...\n",
    "\n",
    "\n",
    "\n",
    "print(err_weighted)\n",
    "assert np.isclose(err_weighted, 0.15056568396854866)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing the $\\chi^2$-value:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "# Insert own code here to calculate the chi2 value, chi2\n",
    "\n",
    "\n",
    "#chi2 = ...\n",
    "\n",
    "\n",
    "\n",
    "print(chi2)\n",
    "assert np.isclose(chi2, 1.2857430730478727)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing the $\\chi^2$-probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "lines_to_next_cell": 2
   },
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "# Insert own code here to calculate the chi2 probability, chi2_prob\n",
    "\n",
    "\n",
    "#chi2_prob = ...\n",
    "\n",
    "\n",
    "\n",
    "print(chi2_prob)\n",
    "assert np.isclose(chi2_prob, 0.7325212770446814)"
   ]
  }
 ],
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