good grading rubric.ipynb

good-grading-rubric.ipynb

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      "name": "good grading rubric.ipynb",
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
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        "<a href=\"https://colab.research.google.com/gist/benrosenberg/282c830d2a87a7b199526df6cfd67520/good-grading-rubric.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0b7b127f"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt"
      ],
      "id": "0b7b127f",
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
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        "id": "2d5e74ba"
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      "source": [
        "n = 200 #number of students"
      ],
      "id": "2d5e74ba",
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "952a9ac1"
      },
      "source": [
        "def voting(q1, q2, q2_min = 65):\n",
        "    if q2 > q2_min:\n",
        "        return 2\n",
        "    if np.random.uniform() > 0.5:\n",
        "        return 1\n",
        "    return 0"
      ],
      "id": "952a9ac1",
      "execution_count": 4,
      "outputs": []
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    {
      "cell_type": "code",
      "metadata": {
        "id": "1c6ad8ed"
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      "source": [
        ""
      ],
      "id": "1c6ad8ed",
      "execution_count": 4,
      "outputs": []
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    {
      "cell_type": "code",
      "metadata": {
        "id": "7b9e5191"
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      "source": [
        ""
      ],
      "id": "7b9e5191",
      "execution_count": 4,
      "outputs": []
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    {
      "cell_type": "code",
      "metadata": {
        "id": "deb1e769"
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      "source": [
        "##scores and p are expressed as percents, not decimals \n",
        "\n",
        "def student_scores(df, winner, p):\n",
        "    #everyone omits, so grade easy and no points lost\n",
        "    df['score'] = 0 #create score column\n",
        "\n",
        "    if winner == 0:\n",
        "        df['score'] = df.q1\n",
        "        return df\n",
        "    \n",
        "    #winner is q1\n",
        "    if winner == 1:\n",
        "        df.loc[df.vote == 0 , ['score']] = df.q1 - 5*p/8 #voted omit \n",
        "        df.loc[df.vote == 1 , ['score']] = df.q1  #voted 1\n",
        "        df.loc[df.vote == 2 , ['score']] = df.q1 - p/4  #voted 2\n",
        "\n",
        "    #winner is q2\n",
        "    if winner == 2:\n",
        "        df.loc[df.vote == 0 , ['score']] = df.q2 #voted omit \n",
        "        df.loc[df.vote == 1 , ['score']] = df.q2 - p #voted 1\n",
        "        df.loc[df.vote == 2 , ['score']] = df.q2 + p/7  #voted 2\n",
        "    \n",
        "    return df\n",
        "    \n",
        "    \n",
        "        \n"
      ],
      "id": "deb1e769",
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xwUNaALqnvyb"
      },
      "source": [
        ""
      ],
      "id": "xwUNaALqnvyb",
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "38e29129"
      },
      "source": [
        "# p = % of people who chose q2\n",
        "\n",
        "\n",
        "#n is number of students in class\n",
        "#votes should be a one-column dataframe of votes indexed by student number (same as q1 and q2 that are creatd in here)\n",
        "\n",
        "def exam_sim(n, means= (90, 50), sigmas = (5, 15), cor = 0.3):\n",
        "    #both out of 100\n",
        "    #q1 = np.random.normal(90, 5, size = n)\n",
        "    #q2 = np.random.normal(50, 15, size = n)\n",
        "    \n",
        "    \n",
        "    \n",
        "    \n",
        "    \n",
        "    cov = [[sigmas[0]**2, sigmas[0]*sigmas[1]*cor], \n",
        "           [sigmas[0]*sigmas[1]*cor, sigmas[1]**2]]\n",
        "\n",
        "    scores = np.random.multivariate_normal(means, cov, size = n)\n",
        "    q1 = pd.Series(scores[:,0]).map(lambda x: 0 if x < 0 else x).map(lambda x : 100 if x>100 else x)\n",
        "    q2 = pd.Series(scores[:,1]).map(lambda x: 0 if x < 0 else x).map(lambda x : 100 if x>100 else x)\n",
        "    \n",
        "    \n",
        "    ##gather voting data using voting function\n",
        "    score_df = pd.DataFrame(scores, columns = ['q1', 'q2'])\n",
        "    score_df['vote'] = score_df.apply(lambda row: voting(row[0], row[1], q2_min = means[1] + 0.5*sigmas[1]), axis = 1)\n",
        "\n",
        "    counts = score_df.groupby(\"vote\")[\"vote\"].count()\n",
        "\n",
        "\n",
        "    #fill in lack of votes (bad students colluding xd)\n",
        "    try:\n",
        "      counts.loc[0]\n",
        "    except KeyError:\n",
        "      counts.loc[0] = 0\n",
        "\n",
        "    try:\n",
        "      counts.loc[1]\n",
        "    except KeyError:\n",
        "      counts.loc[1] = 0\n",
        "\n",
        "    try:\n",
        "      counts.loc[2]\n",
        "    except KeyError:\n",
        "      counts.loc[2] = 0\n",
        "\n",
        "\n",
        "\n",
        "    #now calculate winners \n",
        "\n",
        "    #everyone omits (dumb)\n",
        "    if counts.loc[0] == n:\n",
        "        winner = 0\n",
        "\n",
        "    #ommission wins, but other people voted for other things\n",
        "    elif counts.idxmax() == 0:\n",
        "        counts_temp = counts[counts.index!=0]\n",
        "        winner = counts_temp.idxmax()\n",
        "\n",
        "    #a real question wins\n",
        "    else:\n",
        "        winner = counts.idxmax()\n",
        "    \n",
        "    p = 100*counts.loc[2]/n\n",
        "    \n",
        "    concatenated = pd.DataFrame([q1, q2, score_df.vote.values.flatten()]).T\n",
        "    concatenated.columns= ['q1', 'q2', 'vote']\n",
        "    scores = student_scores(concatenated, winner, p)\n",
        "    \n",
        "    return scores, winner"
      ],
      "id": "38e29129",
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UWer8qFJnMej"
      },
      "source": [
        ""
      ],
      "id": "UWer8qFJnMej",
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "32e6a48e"
      },
      "source": [
        "results = []\n",
        "\n",
        "for i in range(1000):\n",
        "    results.append(exam_sim(n, means= (90, 70), sigmas = (5, 15), cor = 0.5))"
      ],
      "id": "32e6a48e",
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "41acafe3"
      },
      "source": [
        "results_1_mean = [result[0].score for result in results if result[1] == 1]\n",
        "results_2_mean = [result[0].score for result in results if result[1] == 2]\n",
        "results_0_mean = [result[0].score for result in results if result[1] == 0]\n",
        "\n",
        "results_1_vote = [result[0].vote for result in results if result[1] == 1]\n",
        "results_2_vote = [result[0].vote for result in results if result[1] == 2]\n",
        "results_0_vote = [result[0].vote for result in results if result[1] == 0]\n",
        "\n",
        "results_1_df = [result[0] for result in results if result[1] == 1]\n",
        "results_2_df = [result[0] for result in results if result[1] == 2]\n",
        "results_0_df = [result[0] for result in results if result[1] == 0]\n",
        "\n",
        "#we expect results_0 lists to be blank\n"
      ],
      "id": "41acafe3",
      "execution_count": 8,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a91bd77e"
      },
      "source": [
        "means1 = [res.mean() for res in results_1_mean]\n",
        "means2 = [res.mean() for res in results_2_mean]\n",
        "means0 = [res.mean() for res in results_0_mean]"
      ],
      "id": "a91bd77e",
      "execution_count": 9,
      "outputs": []
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    {
      "cell_type": "code",
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        "id": "9e73b992",
        "outputId": "5e228a55-50df-47ef-8af3-0090d7155b98"
      },
      "source": [
        "np.mean(means1), np.std(means1)\n"
      ],
      "id": "9e73b992",
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(81.29162626086344, 0.736270127423834)"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3f25a7a7",
        "outputId": "4e74fcd9-4468-41c9-9abc-00110dbd6ae3"
      },
      "source": [
        "np.mean(means2), np.std(means2)"
      ],
      "id": "3f25a7a7",
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(61.72214782976048, 0.9733428715359489)"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "pZQ-kgCnv920",
        "outputId": "23ad5c21-5b83-4576-8cee-8fbbfd709354"
      },
      "source": [
        "np.mean(means0), np.std(means0)"
      ],
      "id": "pZQ-kgCnv920",
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/numpy/core/fromnumeric.py:3373: RuntimeWarning: Mean of empty slice.\n",
            "  out=out, **kwargs)\n",
            "/usr/local/lib/python3.7/dist-packages/numpy/core/_methods.py:170: RuntimeWarning: invalid value encountered in double_scalars\n",
            "  ret = ret.dtype.type(ret / rcount)\n",
            "/usr/local/lib/python3.7/dist-packages/numpy/core/_methods.py:234: RuntimeWarning: Degrees of freedom <= 0 for slice\n",
            "  keepdims=keepdims)\n",
            "/usr/local/lib/python3.7/dist-packages/numpy/core/_methods.py:195: RuntimeWarning: invalid value encountered in true_divide\n",
            "  arrmean, rcount, out=arrmean, casting='unsafe', subok=False)\n",
            "/usr/local/lib/python3.7/dist-packages/numpy/core/_methods.py:226: RuntimeWarning: invalid value encountered in double_scalars\n",
            "  ret = ret.dtype.type(ret / rcount)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(nan, nan)"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 402
        },
        "id": "851d5c09",
        "outputId": "0dee35d1-5fff-4e5b-8762-03f21dfda9ab"
      },
      "source": [
        "plt.hist(means1, bins = 20)"
      ],
      "id": "851d5c09",
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([  3.,  10.,  26.,  47.,  91.,  72., 101.,  89.,  85.,  76.,  43.,\n",
              "         49.,  33.,  17.,  10.,   4.,   4.,   2.,   0.,   1.]),\n",
              " array([79.5103356 , 79.74463434, 79.97893308, 80.21323182, 80.44753056,\n",
              "        80.6818293 , 80.91612804, 81.15042678, 81.38472552, 81.61902426,\n",
              "        81.853323  , 82.08762174, 82.32192048, 82.55621922, 82.79051796,\n",
              "        83.02481669, 83.25911543, 83.49341417, 83.72771291, 83.96201165,\n",
              "        84.19631039]),\n",
              " <a list of 20 Patch objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 13
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 402
        },
        "id": "745e8a88",
        "outputId": "7f611b34-40d5-4705-d6a8-f672e23c86d3"
      },
      "source": [
        "plt.hist(means2, bins = 20)"
      ],
      "id": "745e8a88",
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([ 1.,  0.,  1.,  1.,  4.,  9., 17., 20., 21., 28., 25., 32., 23.,\n",
              "        19., 10., 13.,  3.,  2.,  4.,  4.]),\n",
              " array([58.62405377, 58.91395797, 59.20386217, 59.49376638, 59.78367058,\n",
              "        60.07357478, 60.36347899, 60.65338319, 60.9432874 , 61.2331916 ,\n",
              "        61.5230958 , 61.81300001, 62.10290421, 62.39280841, 62.68271262,\n",
              "        62.97261682, 63.26252102, 63.55242523, 63.84232943, 64.13223363,\n",
              "        64.42213784]),\n",
              " <a list of 20 Patch objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAAD4CAYAAAD1jb0+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAOGUlEQVR4nO3df6zdd13H8eeLMdTAdCO91DpW78QJWZR182ZCRgg/ZA5q3FAhLgSrkhTilkBCNAWMYpSkBGExxmDKBvSPARLYsskQ1zQkhAQm7SjQruBgKdKmW4uwbGgi6fb2j/Ntdr2c03POPefc08/t85HcnHM+53vu9/1Oe1/3c7/n8/2eVBWSpPY8bd4FSJJWxwCXpEYZ4JLUKANckhplgEtSo56+ljvbsGFDLS4uruUuJal5+/fv/35VLawcX9MAX1xcZN++fWu5S0lqXpLv9hv3EIokNcoAl6RGGeCS1CgDXJIaZYBLUqMMcElqlAEuSY0ywCWpUQa4JDVqTc/ElNarxR33rPq1R3ZunWIlOpc4A5ekRhngktQoA1ySGmWAS1KjDHBJapQBLkmNMsAlqVEGuCQ1amiAJ/npJP+e5GtJDiX562780iT3Jfl2kn9O8ozZlytJOm2UGfj/Aq+oqiuALcB1SV4EvBe4pap+Gfgh8KbZlSlJWmlogFfPj7qH53dfBbwC+FQ3vhu4YSYVSpL6GukYeJLzkhwATgB7gO8Aj1bVqW6To8DFsylRktTPSAFeVU9U1RbgucDVwAtG3UGS7Un2Jdl38uTJVZYpSVpprFUoVfUo8HngxcCFSU5fzfC5wLEBr9lVVUtVtbSwsDBRsZKkp4yyCmUhyYXd/Z8BXgUcphfkv99ttg24a1ZFSpJ+0ijXA98E7E5yHr3A/2RVfSbJA8Ankvwt8FXgthnWKUlaYWiAV9XXgSv7jD9E73i4JGkOPBNTkhplgEtSowxwSWqUAS5JjTLAJalRBrgkNcoAl6RGGeCS1KhRzsSUmrC4455Vv/bIzq1TrERaG87AJalRBrgkNcoAl6RGGeCS1CgDXJIaZYBLUqMMcElqlAEuSY0ywCWpUQa4JDXKAJekRhngktQoA1ySGmWAS1KjDHBJatTQAE9ySZLPJ3kgyaEkb+3G353kWJID3ddrZl+uJOm0UT7Q4RTw9qq6P8kFwP4ke7rnbqmqv5tdeZKkQYYGeFUdB4539x9Pchi4eNaFSZLObKyPVEuyCFwJ3AdcA9yc5A+BffRm6T/s85rtwHaAzZs3T1iuNBuTfBybNC8jv4mZ5FnAp4G3VdVjwAeB5wFb6M3Q39/vdVW1q6qWqmppYWFhCiVLkmDEAE9yPr3wvr2q7gCoqkeq6omqehL4EHD17MqUJK00yiqUALcBh6vqA8vGNy3b7LXAwemXJ0kaZJRj4NcAbwS+keRAN/ZO4MYkW4ACjgBvnkmFkqS+RlmF8kUgfZ767PTLkSSNyjMxJalRBrgkNcoAl6RGGeCS1CgDXJIaZYBLUqMMcElq1FgXs5I0fZNcSOvIzq1TrEStcQYuSY0ywCWpUQa4JDXKAJekRhngktQoA1ySGmWAS1KjDHBJapQBLkmNMsAlqVEGuCQ1ygCXpEZ5MSudVSa5sJN0rnEGLkmNMsAlqVFDAzzJJUk+n+SBJIeSvLUbf3aSPUke7G4vmn25kqTTRpmBnwLeXlWXAy8CbkpyObAD2FtVlwF7u8eSpDUyNMCr6nhV3d/dfxw4DFwMXA/s7jbbDdwwqyIlST9prFUoSRaBK4H7gI1Vdbx76mFg44DXbAe2A2zevHm1daohriSR1sbIb2ImeRbwaeBtVfXY8ueqqoDq97qq2lVVS1W1tLCwMFGxkqSnjBTgSc6nF963V9Ud3fAjSTZ1z28CTsymRElSP6OsQglwG3C4qj6w7Km7gW3d/W3AXdMvT5I0yCjHwK8B3gh8I8mBbuydwE7gk0neBHwXeP1sSpQk9TM0wKvqi0AGPP3K6ZYjSRqVZ2JKUqO8mJXUsEmWbB7ZuXWKlWgenIFLUqMMcElqlAEuSY0ywCWpUQa4JDXKAJekRhngktQoA1ySGmWAS1KjDHBJapQBLkmNMsAlqVFezEo/wc+0lNrgDFySGmWAS1KjDHBJapQBLkmNMsAlqVEGuCQ1ygCXpEYZ4JLUKANckho1NMCTfDjJiSQHl429O8mxJAe6r9fMtkxJ0kqjzMA/ClzXZ/yWqtrSfX12umVJkoYZGuBV9QXgB2tQiyRpDJMcA785yde7QywXDdooyfYk+5LsO3ny5AS7kyQtt9oA/yDwPGALcBx4/6ANq2pXVS1V1dLCwsIqdydJWmlVAV5Vj1TVE1X1JPAh4OrpliVJGmZVAZ5k07KHrwUODtpWkjQbQz/QIcnHgZcBG5IcBf4KeFmSLUABR4A3z7BGSVIfQwO8qm7sM3zbDGqRJI3BMzElqVEGuCQ1ygCXpEYZ4JLUKANckhplgEtSowxwSWrU0HXgkrTS4o57Jnr9kZ1bp1TJuc0ZuCQ1ygCXpEYZ4JLUKANckhplgEtSowxwSWqUAS5JjTLAJalRBrgkNcoAl6RGGeCS1CgDXJIaZYBLUqMMcElqlAEuSY0aGuBJPpzkRJKDy8aenWRPkge724tmW6YkaaVRZuAfBa5bMbYD2FtVlwF7u8eSpDU0NMCr6gvAD1YMXw/s7u7vBm6Ycl2SpCFW+5FqG6vqeHf/YWDjoA2TbAe2A2zevHmVu5M0bZN+LJrmb+I3MauqgDrD87uqaqmqlhYWFibdnSSps9oAfyTJJoDu9sT0SpIkjWK1AX43sK27vw24azrlSJJGNcoywo8DXwKen+RokjcBO4FXJXkQ+M3usSRpDQ19E7Oqbhzw1CunXIskaQyeiSlJjVrtMkKd5VwiJq1/zsAlqVEGuCQ1ygCXpEYZ4JLUKANckhplgEtSowxwSWqUAS5JjTLAJalRBrgkNcoAl6RGGeCS1CgDXJIaZYBLUqMMcElqlAEuSY0ywCWpUQa4JDXKAJekRhngktQoA1ySGjXRp9InOQI8DjwBnKqqpWkUJUkabqIA77y8qr4/he8jSRqDh1AkqVGTBngB9ybZn2R7vw2SbE+yL8m+kydPTrg7SdJpkwb4S6rqKuDVwE1JXrpyg6raVVVLVbW0sLAw4e4kSadNFOBVday7PQHcCVw9jaIkScOtOsCTPDPJBafvA9cCB6dVmCTpzCZZhbIRuDPJ6e/zsar63FSqkiQNteoAr6qHgCumWIskaQwuI5SkRk3jRB7NyOKOe+ZdgrSuzPNn6sjOrVP/ns7AJalRBrgkNcoAl6RGGeCS1CgDXJIa5SoUSWtuktUgs1jN0Spn4JLUKANckhplgEtSowxwSWqUAS5JjTLAJalRLiOU1BQv8vYUZ+CS1CgDXJIaZYBLUqMMcElqlAEuSY1qZhXKPC9+47veks5GzsAlqVEGuCQ1ygCXpEZNFOBJrkvyrSTfTrJjWkVJkoZbdYAnOQ/4R+DVwOXAjUkun1ZhkqQzm2QGfjXw7ap6qKp+DHwCuH46ZUmShplkGeHFwPeWPT4K/MbKjZJsB7Z3D3+U5FsT7HNV8t6+wxuA769tJTO13vqB9dfTeusH1l9PM+tnQA6N6hf7Dc58HXhV7QJ2zXo/40qyr6qW5l3HtKy3fmD99bTe+oH111Nr/UxyCOUYcMmyx8/txiRJa2CSAP8KcFmSS5M8A/gD4O7plCVJGmbVh1Cq6lSSm4F/A84DPlxVh6ZW2eyddYd1JrTe+oH119N66wfWX09N9ZOqmncNkqRV8ExMSWqUAS5JjTonAjzJkSTfSHIgyb5u7IokX+rG/yXJz867znEkuTDJp5J8M8nhJC9O8uwke5I82N1eNO86RzWgn9clOZTkySTNLO06bUBP7+sefz3JnUkunHedoxrQz990vRxIcm+SX5h3nePo19Oy596epJJsmGeNZ3JOBHjn5VW1Zdkaz1uBHVX1a8CdwJ/Nr7RV+Xvgc1X1AuAK4DCwA9hbVZcBe7vHrejXz0Hgd4EvzLOwCfTraQ/wq1X1QuA/gHfMsb5x9evnfVX1wqraAnwG+Mt5FrgK/XoiySXAtcB/zrG2oc6lAF/pV3gqGPYAvzfHWsaS5OeAlwK3AVTVj6vqUXqXMtjdbbYbuGE+FY5nUD9Vdbiq1vzM3Wk4Q0/3VtWpbrMv0zt/4qx3hn4eW7bZM4FmVkWc4ecI4BbgzznL+zlXAryAe5Ps707tBzjEU9dueR3//6Sks92lwEngI0m+muTWJM8ENlbV8W6bh4GNc6twPIP6adkoPf0J8K9rX9qqDOwnyXuSfA94A23NwPv2lOR64FhVfW3O9Q11rgT4S6rqKnpXTrwpyUvp/fD8aZL9wAXAj+dZ4JieDlwFfLCqrgT+mxWHS6q3PvSsnj0sM7SfBp2xpyTvAk4Bt8+nvLEN7Keq3lVVl9Dr5eb5lTi2fj29G3gnjfwiOicCvKqOdbcn6B3vvrqqvllV11bVrwMfB74zzxrHdBQ4WlX3dY8/Re8/4iNJNgF0tyfmVN+4BvXTsoE9Jfkj4LeBN1Q7J2KM8m90Ow0dimRwT5cCX0tyhN4hrvuT/Px8SjyzdR/g3Z9EF5y+T++NiYNJntONPQ34C+Cf5lfleKrqYeB7SZ7fDb0SeIDepQy2dWPbgLvmUN7YztBPswb1lOQ6esdWf6eq/mduBY7pDP1ctmyz64FvrnlxqzSgp/ur6jlVtVhVi/RC/qpu27POuj8TM8kv0Zt1Q+9Ppo9V1XuSvBW4qRu/A3hHQ7Mhkmyht5LmGcBDwB/T+4X8SWAz8F3g9VX1g7kVOYYB/bwM+AdgAXgUOFBVvzWvGsc1oKevAD8F/Fe32Zer6i3zqXA8A/q5FXg+8CS9/3NvOf0Xbwv69VRVP1z2/BFgqarOykvmrvsAl6T1at0fQpGk9coAl6RGGeCS1CgDXJIaZYBLUqMMcElqlAEuSY36P7ZM0q7XIckhAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 351
        },
        "id": "iGBs0oiJwEMT",
        "outputId": "0d684503-38af-44ff-9a1b-63664d23d2da"
      },
      "source": [
        "plt.hist(means0, bins = 20)"
      ],
      "id": "iGBs0oiJwEMT",
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "        0., 0., 0.]),\n",
              " array([0.  , 0.05, 0.1 , 0.15, 0.2 , 0.25, 0.3 , 0.35, 0.4 , 0.45, 0.5 ,\n",
              "        0.55, 0.6 , 0.65, 0.7 , 0.75, 0.8 , 0.85, 0.9 , 0.95, 1.  ]),\n",
              " <a list of 20 Patch objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "01df6727",
        "outputId": "cc3a1fb6-5cf8-4300-ba11-57d733e9c4f7"
      },
      "source": [
        "results_1_mean[0].hist(bins = 20)\n",
        "#results_1_vote[0].hist(bins = 20)"
      ],
      "id": "01df6727",
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fa0638cbbd0>"
            ]
          },
          "metadata": {},
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e0ad19d6"
      },
      "source": [
        "#results_2_mean[0].hist(bins = 20)"
      ],
      "id": "e0ad19d6",
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "L6_ACo63wHlL"
      },
      "source": [
        "# results_0_mean[0].hist(bins = 20)"
      ],
      "id": "L6_ACo63wHlL",
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "68k0G75lmDjL"
      },
      "source": [
        ""
      ],
      "id": "68k0G75lmDjL",
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nnz5rC8fm8Sk",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 205
        },
        "outputId": "598f688c-c2af-4184-bb39-9f8fe302cb53"
      },
      "source": [
        "df_0 = results_2_df[0]\n",
        "df_0[df_0.vote == 0].head()"
      ],
      "id": "nnz5rC8fm8Sk",
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "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>q1</th>\n",
              "      <th>q2</th>\n",
              "      <th>vote</th>\n",
              "      <th>score</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>94.267431</td>\n",
              "      <td>69.088655</td>\n",
              "      <td>0.0</td>\n",
              "      <td>69.088655</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>86.459075</td>\n",
              "      <td>68.201978</td>\n",
              "      <td>0.0</td>\n",
              "      <td>68.201978</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>95.421476</td>\n",
              "      <td>75.102574</td>\n",
              "      <td>0.0</td>\n",
              "      <td>75.102574</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>94.940139</td>\n",
              "      <td>72.701886</td>\n",
              "      <td>0.0</td>\n",
              "      <td>72.701886</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>94.604543</td>\n",
              "      <td>77.297937</td>\n",
              "      <td>0.0</td>\n",
              "      <td>77.297937</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "           q1         q2  vote      score\n",
              "9   94.267431  69.088655   0.0  69.088655\n",
              "11  86.459075  68.201978   0.0  68.201978\n",
              "13  95.421476  75.102574   0.0  75.102574\n",
              "16  94.940139  72.701886   0.0  72.701886\n",
              "21  94.604543  77.297937   0.0  77.297937"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "UXDfbfcSl7as",
        "outputId": "2a6b9d61-7819-48c3-f9c2-7929c0d7b92e"
      },
      "source": [
        "#histogram of the first sample's results\n",
        "plt.hist([df_0[df_0.vote == 1].score, df_0[df_0.vote == 2].score, df_0[df_0.vote == 0].score], bins = 50, stacked=True, label = [\"1\", \"2\", \"omit\"])\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "id": "UXDfbfcSl7as",
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
            "  return array(a, dtype, copy=False, order=order)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vX2-i9n4sCRk",
        "outputId": "dfc5a995-21ed-4e77-db33-7917f05a1912"
      },
      "source": [
        "results[0]"
      ],
      "id": "vX2-i9n4sCRk",
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(            q1         q2  vote      score\n",
              " 0    98.098980  89.344124   2.0  91.723980\n",
              " 1    80.966572  62.261346   0.0  65.029072\n",
              " 2    89.578718  56.668733   1.0  89.578718\n",
              " 3    90.912488  71.572587   0.0  74.974988\n",
              " 4    84.161308  75.151597   0.0  68.223808\n",
              " ..         ...        ...   ...        ...\n",
              " 195  86.880582  53.282016   1.0  86.880582\n",
              " 196  97.703398  87.604168   2.0  91.328398\n",
              " 197  88.586517  43.739715   1.0  88.586517\n",
              " 198  86.966433  40.683585   0.0  71.028933\n",
              " 199  89.326367  56.201768   1.0  89.326367\n",
              " \n",
              " [200 rows x 4 columns], 1)"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "y4nyISIssGPz"
      },
      "source": [
        "results_1 = [result for result in results if result[1] == 1]\n",
        "results_2 = [result for result in results if result[1] == 2]\n",
        "results_0 = [result for result in results if result[1] == 0]"
      ],
      "id": "y4nyISIssGPz",
      "execution_count": 23,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "be9e7853"
      },
      "source": [
        "##get the results across all trials (\"average\" histograms for when q1 won and when q2 won)\n",
        "\n",
        "results_1_total = []\n",
        "\n",
        "for ser in results_1: \n",
        "  results_1_total += list(ser)\n",
        "\n",
        "results_2_total = []\n",
        "for ser in results_2:\n",
        "  results_2_total += list(ser)\n",
        "\n",
        "results_0_total = []\n",
        "for ser in results_0:\n",
        "  results_0_total += list(ser)"
      ],
      "id": "be9e7853",
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hlT2b3UWtCy3",
        "outputId": "841aa044-f217-4f09-bf92-130abe7cdc37"
      },
      "source": [
        "results_1[0][0].score"
      ],
      "id": "hlT2b3UWtCy3",
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0      91.723980\n",
              "1      65.029072\n",
              "2      89.578718\n",
              "3      74.974988\n",
              "4      68.223808\n",
              "         ...    \n",
              "195    86.880582\n",
              "196    91.328398\n",
              "197    88.586517\n",
              "198    71.028933\n",
              "199    89.326367\n",
              "Name: score, Length: 200, dtype: float64"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jKz0UM8qsdpd"
      },
      "source": [
        "results_1_total = []\n",
        "\n",
        "for ser in results_1: \n",
        "  results_1_total.append(ser[0].score.mean())\n",
        "\n",
        "results_2_total = []\n",
        "for ser in results_2:\n",
        "  results_2_total.append(ser[0].score.mean())\n",
        "\n",
        "results_0_total = []\n",
        "for ser in results_0:\n",
        "  results_0_total.append(ser[0].score.mean())"
      ],
      "id": "jKz0UM8qsdpd",
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 539
        },
        "id": "BIkeYwowuqSy",
        "outputId": "df644cd5-5336-4a4f-c7ed-733a270f2aec"
      },
      "source": [
        "plt.hist(results_1_total, bins=50)"
      ],
      "id": "BIkeYwowuqSy",
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([ 2.,  0.,  3.,  4.,  4.,  7., 13., 12., 22., 19., 28., 44., 36.,\n",
              "        27., 28., 49., 38., 27., 41., 35., 40., 27., 34., 35., 25., 12.,\n",
              "        23., 19., 17., 21., 16.,  9., 11., 11.,  3.,  4.,  5.,  2.,  2.,\n",
              "         1.,  1.,  2.,  2.,  0.,  1.,  0.,  0.,  0.,  0.,  1.]),\n",
              " array([79.5103356 , 79.6040551 , 79.69777459, 79.79149409, 79.88521359,\n",
              "        79.97893308, 80.07265258, 80.16637207, 80.26009157, 80.35381106,\n",
              "        80.44753056, 80.54125006, 80.63496955, 80.72868905, 80.82240854,\n",
              "        80.91612804, 81.00984754, 81.10356703, 81.19728653, 81.29100602,\n",
              "        81.38472552, 81.47844501, 81.57216451, 81.66588401, 81.7596035 ,\n",
              "        81.853323  , 81.94704249, 82.04076199, 82.13448148, 82.22820098,\n",
              "        82.32192048, 82.41563997, 82.50935947, 82.60307896, 82.69679846,\n",
              "        82.79051796, 82.88423745, 82.97795695, 83.07167644, 83.16539594,\n",
              "        83.25911543, 83.35283493, 83.44655443, 83.54027392, 83.63399342,\n",
              "        83.72771291, 83.82143241, 83.9151519 , 84.0088714 , 84.1025909 ,\n",
              "        84.19631039]),\n",
              " <a list of 50 Patch objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 27
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 539
        },
        "id": "_FNTTx17urdy",
        "outputId": "f39ffb3c-46ce-4254-fabb-13d9075d2d7c"
      },
      "source": [
        "plt.hist(results_2_total, bins = 50)"
      ],
      "id": "_FNTTx17urdy",
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  1.,  0.,  0.,  3.,  3.,\n",
              "         2.,  5.,  5.,  9.,  6.,  9.,  8.,  5.,  8., 13., 13., 10., 10.,\n",
              "        10., 13., 15.,  9., 14.,  4., 10.,  8.,  6.,  3.,  5.,  4.,  7.,\n",
              "         4.,  2.,  0.,  1.,  1.,  1.,  4.,  0.,  0.,  1.,  3.]),\n",
              " array([58.62405377, 58.74001545, 58.85597713, 58.97193881, 59.08790049,\n",
              "        59.20386217, 59.31982386, 59.43578554, 59.55174722, 59.6677089 ,\n",
              "        59.78367058, 59.89963226, 60.01559394, 60.13155563, 60.24751731,\n",
              "        60.36347899, 60.47944067, 60.59540235, 60.71136403, 60.82732571,\n",
              "        60.9432874 , 61.05924908, 61.17521076, 61.29117244, 61.40713412,\n",
              "        61.5230958 , 61.63905748, 61.75501917, 61.87098085, 61.98694253,\n",
              "        62.10290421, 62.21886589, 62.33482757, 62.45078925, 62.56675093,\n",
              "        62.68271262, 62.7986743 , 62.91463598, 63.03059766, 63.14655934,\n",
              "        63.26252102, 63.3784827 , 63.49444439, 63.61040607, 63.72636775,\n",
              "        63.84232943, 63.95829111, 64.07425279, 64.19021447, 64.30617616,\n",
              "        64.42213784]),\n",
              " <a list of 50 Patch objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 28
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 419
        },
        "id": "MKnvK98bu1dj",
        "outputId": "7def236f-95ea-434a-898a-b979840cef19"
      },
      "source": [
        "plt.hist(results_0_total, bins = 50)"
      ],
      "id": "MKnvK98bu1dj",
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(array([0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
              "        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]),\n",
              " array([0.  , 0.02, 0.04, 0.06, 0.08, 0.1 , 0.12, 0.14, 0.16, 0.18, 0.2 ,\n",
              "        0.22, 0.24, 0.26, 0.28, 0.3 , 0.32, 0.34, 0.36, 0.38, 0.4 , 0.42,\n",
              "        0.44, 0.46, 0.48, 0.5 , 0.52, 0.54, 0.56, 0.58, 0.6 , 0.62, 0.64,\n",
              "        0.66, 0.68, 0.7 , 0.72, 0.74, 0.76, 0.78, 0.8 , 0.82, 0.84, 0.86,\n",
              "        0.88, 0.9 , 0.92, 0.94, 0.96, 0.98, 1.  ]),\n",
              " <a list of 50 Patch objects>)"
            ]
          },
          "metadata": {},
          "execution_count": 29
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fF_s0djovv0I"
      },
      "source": [
        "##row-concatenated df of results across all trials\n",
        "total_df = pd.DataFrame()\n",
        "for tup in results:\n",
        "  total_df = pd.concat([total_df, tup[0]], axis = 0)\n"
      ],
      "id": "fF_s0djovv0I",
      "execution_count": 30,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "Zo7xL-Gmts5T",
        "outputId": "fe26718d-5547-4cd3-d987-cd78c1db9b69"
      },
      "source": [
        "## histogram of results across all trials:\n",
        "#histogram of the first sample's results\n",
        "plt.hist(total_df[total_df.vote == 1].score, bins = 1000, stacked=True, label = \"1\", alpha=0.75)\n",
        "plt.hist(total_df[total_df.vote == 2].score, bins = 1000, stacked=True, label = \"2\", alpha=0.75)\n",
        "plt.hist(total_df[total_df.vote == 0].score, bins = 1000, stacked=True, label = \"omit\", alpha=0.75)\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "id": "Zo7xL-Gmts5T",
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 319
        },
        "id": "BruCG6dpUtwu",
        "outputId": "aa150390-fea7-4c65-8d9d-7a7e7fb67118"
      },
      "source": [
        "## histogram of results across all trials:\n",
        "#histogram of the first sample's results\n",
        "plt.hist([total_df[total_df.vote == 1].score, total_df[total_df.vote == 2].score, \n",
        "          total_df[total_df.vote == 0].score], bins = 1000, stacked=True, label = [\"1\", \"2\", \"omit\"])\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "id": "BruCG6dpUtwu",
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
            "  return array(a, dtype, copy=False, order=order)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_Zex5ga1UwKf"
      },
      "source": [
        ""
      ],
      "id": "_Zex5ga1UwKf",
      "execution_count": 31,
      "outputs": []
    }
  ]
}