zscore and how it's used to determine an outlier.ipynb

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        "name": "ipython",
        "version": 3
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      "display_name": "Python 3.7.7 64-bit ('base': conda)",
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          "hash": "6748257ddfb6c62cfaac10458a5970f1865cdfc8b829bd6d05d7729d55081232"
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      }
    },
    "colab": {
      "name": "zscore and how it's used to determine an outlier.ipynb",
      "provenance": [],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/idenw/statistics-with-python/blob/main/zscore%20and%20how%20it's%20used%20to%20determine%20an%20outlier.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s8FWu_RxcrKd"
      },
      "source": [
        "import matplotlib.pyplot as plt \n",
        "import numpy as np \n",
        "import pandas as pd \n",
        "import seaborn as sns\n",
        "from scipy import stats "
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_imj2gsbcrKw"
      },
      "source": [
        "https://statistics.laerd.com/statistical-guides/standard-score-4.php"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BJO0ri_XcrKz"
      },
      "source": [
        "https://medium.com/@gulcanogundur/normal-da%C4%9F%C4%B1l%C4%B1m-z-score-ve-standardizasyon-782963bc123e"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "36MuF9wJcrK0",
        "outputId": "dd0bec87-156b-41c2-f223-133ad138b4be"
      },
      "source": [
        "mu, sigma = 100, 5\n",
        "array = np.random.normal(mu, sigma, 200) # generate 200 samples, from a normal distubition,centered around the value 100, with a standart deviation of 10\n",
        "array"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([101.75450722,  96.96275494,  96.68231532,  95.10035341,\n",
              "       101.12508876,  97.67353916, 101.81861515,  93.09719832,\n",
              "       100.32647453,  92.27087004, 101.56634402, 102.36140045,\n",
              "        98.8490781 , 101.30561683, 112.04384   , 101.10504268,\n",
              "       103.22296064,  91.02678558, 106.24465285,  99.31347608,\n",
              "        94.16017958, 103.63895292, 103.56974573,  98.41506927,\n",
              "       102.62697759,  91.01980476,  97.72334041,  91.2235243 ,\n",
              "        92.71032738, 107.01294758,  89.9468579 ,  99.9567894 ,\n",
              "       101.62914473, 100.22742226, 100.06872227,  94.92073493,\n",
              "       103.57867175,  98.72684063, 104.01497106, 101.49554418,\n",
              "        90.67583675,  94.76194236,  91.26186682,  97.46803351,\n",
              "        91.59148842, 109.41757004,  96.54844858,  85.77123428,\n",
              "        96.11788662, 101.06990118,  94.33214421,  98.0479031 ,\n",
              "       108.47702136, 100.34725803, 108.79621609,  96.39040013,\n",
              "       106.4296348 ,  99.58235355,  92.52514185,  96.3816934 ,\n",
              "        96.83700832, 101.30634431, 112.00201548,  98.51667463,\n",
              "       105.45899259,  99.44869994,  95.37092355, 101.29340338,\n",
              "        86.57565005, 100.61339155, 102.09419472, 105.56614227,\n",
              "        98.43395539, 109.64578794,  98.66410399,  98.17020911,\n",
              "       110.8320989 , 103.63206037,  94.50815973, 104.24017987,\n",
              "       100.59331603, 100.7532284 ,  98.56507702, 101.09184867,\n",
              "        89.96521971,  96.72328851,  98.80266074, 104.94623252,\n",
              "        98.42262705, 106.80510776,  99.35486687,  90.41214712,\n",
              "        97.48491749,  98.52514525,  99.99856839, 107.08734292,\n",
              "       103.48424178,  89.60389833,  98.27241756, 103.03890144,\n",
              "       107.79608282,  97.51674854,  97.15190133, 104.61527672,\n",
              "        91.69408763, 104.48098062, 102.63228856, 100.72523992,\n",
              "        98.66166626, 100.04310694,  99.04689818,  94.42674329,\n",
              "       109.8668739 ,  95.46361317,  98.31872001, 103.66168632,\n",
              "        98.64943065, 100.65221564,  95.87110401, 104.80466408,\n",
              "       103.06502907, 108.83303186, 104.15533277,  96.32763765,\n",
              "        95.9123146 ,  99.24878326,  94.65547945, 101.12822333,\n",
              "       106.75040777, 100.29105268,  98.48329748,  97.75222689,\n",
              "        96.53141883,  99.7902052 ,  99.9167945 , 101.046692  ,\n",
              "       102.28356957, 104.86765464, 108.10689999, 105.00774755,\n",
              "        96.28260375, 104.97092098, 103.09077959, 100.38452683,\n",
              "        98.7997367 ,  97.21806754,  97.88810616,  95.0350015 ,\n",
              "        99.56525823, 107.32516596,  99.18132292, 102.61830337,\n",
              "       105.02246164,  99.71279331,  95.67612252, 102.3529252 ,\n",
              "       103.16069243, 106.30148912, 102.94195289,  94.05493667,\n",
              "        92.98308983,  99.59839298,  92.13130625, 110.99292307,\n",
              "       100.6153364 ,  99.61982831, 101.40466667,  97.26600862,\n",
              "        99.78247051,  93.11346061,  97.96554236,  98.54559437,\n",
              "        94.09362384, 106.29675155,  94.36270519, 105.51081305,\n",
              "        95.62369722,  98.93516237, 108.4246249 ,  98.16181064,\n",
              "       105.31170142,  95.55069436,  88.27434518,  96.10527178,\n",
              "       102.16636732, 103.50821865,  96.98503451,  98.95140718,\n",
              "       100.1176857 ,  95.43563761,  98.20693971, 108.88852416,\n",
              "        93.17331682,  96.26958254,  97.1850807 , 102.57503641,\n",
              "       100.2684986 ,  98.15507157, 100.32157443,  91.73765056])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "kUrhCWVScrK6",
        "outputId": "db933626-caae-4bc1-e71a-0cadf64bd1d8"
      },
      "source": [
        "sns.histplot(array) # as you see most of values are scattered between the values 40 and 60 as it is obvious that we have chosen a normal distrubition hving an average value of 50 and standart deviaton of 10\n",
        "plt.show()"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1fVFTvtpcrK8"
      },
      "source": [
        "array[90] = 180\n",
        "array[50] = -40"
      ],
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "XbzdHJD5crK9",
        "outputId": "e1fbb58d-bac0-43e7-e849-f1705d599cb3"
      },
      "source": [
        "sns.histplot(array)\r\n",
        "plt.show()"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAD4CAYAAADrRI2NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAASZklEQVR4nO3df4xl5X3f8ffHEzBoDQV2x8vu8mOpB21wI2UdjakTWxXGcUqgKnblurYiG1Wk46pQ2bLl2k7/CJFayanikLaibseBspEcO9QxhhjqhGAcy1KKMyQbfhhHTCesyrKws8HGZlsR7ey3f9yz6/HODDvAnntn5nm/pKs55znn7PnO0d3PnPucc5+TqkKS1I7XjLoASdJwGfyS1BiDX5IaY/BLUmMMfklqzE+MuoDV2LJlS+3cuXPUZUjSuvLQQw8dqqrxE9vXRfDv3LmTmZmZUZchSetKkn3LtdvVI0mNMfglqTEGvyQ1xuCXpMYY/JLUGINfkhpj8EtSYwx+SWrMuvgCl6SXZ2FhgdnZ2ePzExMTjI2NjbAirSUGv7QBzc7OMnXLPWzasp3Dh55m+oZr2LVr16jL0hph8Esb1KYt2zn7/ItHXYbWoN77+JOMJfmLJF/t5i9J8mCS2SS/l+T0vmuQJP3IMC7ufhh4fNH8rwM3V9UE8D3g+iHUIEnq9Br8SS4ArgF+u5sPcCXwpW6VPcC7+qxBkvTj+j7j/y3g3wBHu/nNwPer6kg3/xSwY7kNk0wlmUkyMz8/33OZktSO3oI/yT8CDlbVQ69k+6qarqrJqpocH1/yHAFJ0ivU5109bwX+cZKrgTOAs4H/CJyT5Ce6s/4LgP091iBJOkFvZ/xV9amquqCqdgLvA75eVb8EPAC8p1vtOuCuvmqQJC01iiEbPgF8NMksgz7/W0dQgyQ1ayhf4KqqbwDf6KbngMuHsV9J0lIO0iZJjTH4JakxBr8kNcbgl6TGGPyS1BiDX5IaY/BLUmMMfklqjMEvSY0x+CWpMQa/JDXG4Jekxhj8ktQYg1+SGmPwS1JjDH5JakyfD1s/I8m3k/xlkseS/FrXfnuSv06yt3vt7qsGSdJSfT6B60Xgyqp6IclpwLeS/M9u2cer6ks97luStILegr+qCnihmz2te1Vf+5MkrU6vffxJxpLsBQ4C91XVg92if5/k4SQ3J3ntCttOJZlJMjM/P99nmZLUlF6Dv6oWqmo3cAFweZKfAj4F/CTwZuA84BMrbDtdVZNVNTk+Pt5nmZLUlKHc1VNV3wceAK6qqgM18CLw34HLh1GDJGmgz7t6xpOc002fCbwT+G6SbV1bgHcBj/ZVgyRpqT7v6tkG7EkyxuAPzB1V9dUkX08yDgTYC/zLHmuQJJ2gz7t6HgbetEz7lX3tU5J0cn5zV5IaY/BLUmMMfklqTJ8XdyWtAXX0KHNzc8fnJyYmGBsbG2FFGjWDX9rgDj/3DDd9ZR+bdzzP4UNPM33DNezatWvUZWmEDH6pAZs2b+fs8y8edRlaI+zjl6TGGPyS1BiDX5IaY/BLUmMMfklqjMEvSY0x+CWpMQa/JDXG4Jekxhj8ktSYPh+9eEaSbyf5yySPJfm1rv2SJA8mmU3ye0lO76sGSdJSfZ7xvwhcWVU/DewGrkryFuDXgZuragL4HnB9jzVIkk7QW/DXwAvd7Gndq4ArgS917XsYPHBdkjQkvfbxJxlLshc4CNwH/G/g+1V1pFvlKWDHCttOJZlJMjM/P99nmZLUlF6Dv6oWqmo3cAFwOfCTL2Pb6aqarKrJ8fHx3mqUpNYM5a6eqvo+8ADws8A5SY49B+ACYP8wapAkDfR5V894knO66TOBdwKPM/gD8J5uteuAu/qqQZK0VJ9P4NoG7EkyxuAPzB1V9dUk3wG+mOTfAX8B3NpjDZKkE/QW/FX1MPCmZdrnGPT3S5JGwG/uSlJjDH5JaozBL0mN6fPirqQhWlhYYHZ2FoC5uTmqRlyQ1iyDX9ogZmdnmbrlHjZt2c78E3s568LLRl2S1ii7eqQNZNOW7Zx9/sWcee7rR12K1jCDX5IaY/BLUmMMfklqjMEvSY0x+CWpMQa/JDXG4Jekxhj8ktQYg1+SGmPwS1Jj+nz04oVJHkjynSSPJflw135Tkv1J9navq/uqQZK0VJ+DtB0BPlZVf57kLOChJPd1y26uqt/ocd+SpBX0+ejFA8CBbvqHSR4HdvS1P0nS6gyljz/JTgbP332wa7oxycNJbkty7jBqkCQN9B78SV4H/D7wkar6AfBZ4A3AbgafCD6zwnZTSWaSzMzPz/ddpiQ1o9fgT3Iag9D/fFV9GaCqnq2qhao6CnwOuHy5batquqomq2pyfHy8zzIlqSl93tUT4Fbg8ar6zUXt2xat9m7g0b5qkCQt1eddPW8FPgA8kmRv1/YrwPuT7AYKeBL4UI81SJJO0OddPd8Cssyie/vapyTp5FbV1ZPkratpkyStfavt4//Pq2yTJK1xL9nVk+RngZ8DxpN8dNGis4GxPguTJPXjZH38pwOv69Y7a1H7D4D39FWUJKk/Lxn8VfUnwJ8kub2q9g2pJkk9qaNHmZubOz4/MTHB2Jgf3luz2rt6XptkGti5eJuqurKPoiT14/Bzz3DTV/axecfzHD70NNM3XMOuXbtGXZaGbLXB/z+A/wr8NrDQXzmS+rZp83bOPv/iUZehEVpt8B+pqs/2WokkaShWezvnHyT5V0m2JTnv2KvXyiRJvVjtGf913c+PL2or4O+e2nIkSX1bVfBX1SV9FyJJGo5VBX+SDy7XXlW/c2rLkST1bbVdPW9eNH0G8A7gzwGDX5LWmdV29fzrxfNJzgG+2EtFkqRevdIHsRwG7PeXpHVotX38f8DgLh4YDM52GXBHX0VJkvqz2j7+31g0fQTYV1VP9VCPJKlnq+rq6QZr+y6DETrPBf72ZNskuTDJA0m+k+SxJB/u2s9Lcl+SJ7qf576aX0CS9PKs9glc7wW+DfxT4L3Ag0lONizzEeBjVfVG4C3ADUneCHwSuL+qLgXu7+YlSUOy2q6efwu8uaoOAiQZB/4Y+NJKG1TVAeBAN/3DJI8DO4BrgSu61fYA3wA+8QpqlyS9Aqu9q+c1x0K/8zcvY1uS7ATeBDwIbO3+KAA8A2xdYZupJDNJZubn51e7K0nSSaz2jP9rSf4Q+EI3/8+Ae1ezYZLXAb8PfKSqfpDk+LKqqiS13HZVNQ1MA0xOTi67jiTp5TvZM3cnGJyhfzzJPwHe1i36U+DzJ/vHk5zGIPQ/X1Vf7pqfTbKtqg4k2QYcXPlfkCSdaifrrvktBs/Xpaq+XFUfraqPAnd2y1aUwan9rcDjVfWbixbdzY9G+7wOuOuVFC5JemVO1tWztaoeObGxqh7p+u1fyluBDwCPJNnbtf0K8GngjiTXA/sY3CUkSRqSkwX/OS+x7MyX2rCqvgVkhcXvOMl+JUk9OVlXz0ySf3FiY5JfBh7qpyRJUp9Odsb/EeDOJL/Ej4J+EjgdeHefhUmS+vGSwV9VzwI/l+TtwE91zfdU1dd7r0yS1IvVjsf/APBAz7VIkobglY7HL0lapwx+SWqMwS9JjTH4JakxBr8kNcbgl6TGGPyS1BiDX5IaY/BLUmNW+wQuSRtMHT3K3Nzc8fmJiQnGxsZGWJGGxeCXGnX4uWe46Sv72LzjeQ4feprpG65h165doy5LQ2DwSw3btHk7Z59/8ajL0JD11sef5LYkB5M8uqjtpiT7k+ztXlf3tX9J0vL6vLh7O3DVMu03V9Xu7nVvj/uXJC2jt66eqvrmKp7LK+lVWFhYYHZ2FoC5uTmqRlyQ1oVR9PHfmOSDwAzwsar63nIrJZkCpgAuuuiiIZYnrR+zs7NM3XIPm7ZsZ/6JvZx14WWjLknrwLDv4/8s8AZgN3AA+MxKK1bVdFVNVtXk+Pj4sOqT1p1NWwYXaM889/WjLkXrxFCDv6qeraqFqjoKfA64fJj7lyQNOfiTbFs0+27g0ZXWlST1o7c+/iRfAK4AtiR5CvhV4Ioku4ECngQ+1Nf+JUnL6/Ounvcv03xrX/uTJK2Og7RJUmMMfklqjMEvSY1xkDZpnfHbunq1DH5pnfHbunq17OqR1iG/ratXw+CXpMYY/JLUGPv4Jfn83cYY/JJ8/m5jDH5JgM/fbYl9/JLUGINfkhpj8EtSYwx+SWqMwS9Jjekt+JPcluRgkkcXtZ2X5L4kT3Q/z+1r/5Kk5fV5xn87cNUJbZ8E7q+qS4H7u3lJ0hD1FvxV9U3guROarwX2dNN7gHf1tX9J0vKG3ce/taoOdNPPAFtXWjHJVJKZJDPz8/PDqU6SGjCyi7tVVcCKj5CoqumqmqyqyfHx8SFWJkkb27CD/9kk2wC6nweHvH9Jat6wg/9u4Lpu+jrgriHvX5Ka1+ftnF8A/hTYleSpJNcDnwbemeQJ4Oe7eUnSEPU2OmdVvX+FRe/oa5+SpJPzm7uS1BiDX5IaY/BLUmMMfklqjMEvSY0x+CWpMQa/JDXG4JekxvT2BS5Jp8bCwgKzs7PH5+fm5qgVhzeUTs7gl9a42dlZpm65h01btgMw/8RezrrwshFXpfXM4JfWgU1btnP2+RcD8MKhp0dcjdY7+/glqTEGvyQ1xuCXpMYY/JLUGINfkhozkrt6kjwJ/BBYAI5U1eQo6pCkFo3yds63V9WhEe5fkppkV48kNWZUZ/wF/FGSAv5bVU2PqA5JJ6ijR5mbmzs+PzExwdjY2Agr0qk2quB/W1XtT/J64L4k362qby5eIckUMAVw0UUXjaJGqUmHn3uGm76yj807nufwoaeZvuEadu3aNeqydAqNpKunqvZ3Pw8CdwKXL7POdFVNVtXk+Pj4sEuUmrZp82CIiGPjA2ljGXrwJ9mU5Kxj08AvAI8Ouw5JatUounq2AncmObb/362qr42gDklq0tCDv6rmgJ8e9n4lSQPezilJjTH4JakxBr8kNcbgl6TGGPyS1BiDX5IaY/BLUmMMfklqjMEvSY0Z5YNYJC2ysLDA7Ozs8fm1MByyQzRvTAa/tEbMzs4ydcs9bNqyfc0Mh+wQzRuTwS+tIZu2DIZDXkuODdGsjcM+fklqjMEvSY3Z0F09a/FimbQaiy+qzs3NUTXigjQUJ2YW9JNbGzr41+LFMmk1Fl9UnX9iL2ddeNmoS9IQLM4soLfc2tDBD2vzYpm0Gscuqr5w6OlRl6IhGkZmjaSPP8lVSf4qyWyST46iBklq1Sgetj4G3AL8IvBG4P1J3jjsOiSpVaPo6rkcmO2evUuSLwLXAt/pY2eHu4/Jhw89zdzc3+ljF9IpMTc3d/z9+v++d5DXvPgiPzjjtT82/VLL+p72/1D/Fr8H4Fh+vemU7yc15NsFkrwHuKqqfrmb/wDw96vqxhPWmwKmutldwN8Ah4ZZ6zqxBY/LiTwmS3lMlmrhmFxcVeMnNq7Zi7tVNQ1MH5tPMlNVkyMsaU3yuCzlMVnKY7JUy8dkFBd39wMXLpq/oGuTJA3BKIL/z4BLk1yS5HTgfcDdI6hDkpo09K6eqjqS5EbgD4Ex4LaqemwVm06ffJUmeVyW8pgs5TFZqtljMvSLu5Kk0XKQNklqjMEvSY1Z88Gf5KYk+5Ps7V5XL1r2qW7Yh79K8g9HWeewOezFQJInkzzSvTdmurbzktyX5Inu57mjrrNvSW5LcjDJo4valj0OGfhP3Xvn4SQ/M7rK+7PCMTFPWAfB37m5qnZ3r3sBumEe3gf8PeAq4L90w0FseA57scTbu/fGsXuyPwncX1WXAvd38xvd7Qz+Hyy20nH4ReDS7jUFfHZINQ7b7Sw9JmCerJvgX861wBer6sWq+mtglsFwEC04PuxFVf0tcGzYCw1cC+zppvcA7xphLUNRVd8EnjuheaXjcC3wOzXwv4BzkmwbTqXDs8IxWUlTebJegv/G7iPpbYs+tu8A/s+idZ7q2lrQ8u9+ogL+KMlD3TAfAFur6kA3/QywdTSljdxKx6H190/zebImgj/JHyd5dJnXtQw+hr4B2A0cAD4z0mK11rytqn6GQffFDUn+weKFNbhfufl7lj0Ox5knrJGxeqrq51ezXpLPAV/tZlse+qHl3/3HVNX+7ufBJHcy+Hj+bJJtVXWg68I4ONIiR2el49Ds+6eqnj023XKerIkz/pdyQt/ju4FjV+jvBt6X5LVJLmFwoerbw65vRBz2AkiyKclZx6aBX2Dw/rgbuK5b7TrgrtFUOHIrHYe7gQ92d/e8BXh+UZfQhmaeDKyJM/6T+A9JdjP4mPok8CGAqnosyR0MxvE/AtxQVQsjq3KIXsWwFxvNVuDOJDB4L/9uVX0tyZ8BdyS5HtgHvHeENQ5Fki8AVwBbkjwF/CrwaZY/DvcCVzO4gPl/gX8+9IKHYIVjcoV54pANktScNd/VI0k6tQx+SWqMwS9JjTH4JakxBr8kNcbgl6TGGPyS1Jj/D4Snt5M4KyEQAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "qyy4QZ1_crK-",
        "outputId": "56de427d-5c28-4baf-e467-bcfc85dbc6fd"
      },
      "source": [
        "df = pd.DataFrame(array, columns=[\"Data\"]) #create a dataframe from distrubution we have\n",
        "df.head()"
      ],
      "execution_count": 17,
      "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>Data</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>101.754507</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>96.962755</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>96.682315</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>95.100353</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>101.125089</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         Data\n",
              "0  101.754507\n",
              "1   96.962755\n",
              "2   96.682315\n",
              "3   95.100353\n",
              "4  101.125089"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d5fkKggocrK-"
      },
      "source": [
        "# Calculating the z_score"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "n7tTyytIcrK_",
        "outputId": "5ed3d644-bf87-4dbb-d3d8-e87f0296f007"
      },
      "source": [
        "for col in df.columns:\n",
        "    col_zscore = col + \"_zscore\"\n",
        "    df[col_zscore] = (df[col] - df[col].mean())/df[col].std(ddof=0)\n",
        "df.head()\n",
        "# creating a new column in my dataframe, which would be called \"data_zscore\" where I take the row value and I subtract that columns mean from that row value and divide by the standard deviation of that column "
      ],
      "execution_count": 18,
      "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>Data</th>\n",
              "      <th>Data_zscore</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>101.754507</td>\n",
              "      <td>0.190666</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>96.962755</td>\n",
              "      <td>-0.194420</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>96.682315</td>\n",
              "      <td>-0.216957</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>95.100353</td>\n",
              "      <td>-0.344091</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>101.125089</td>\n",
              "      <td>0.140083</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         Data  Data_zscore\n",
              "0  101.754507     0.190666\n",
              "1   96.962755    -0.194420\n",
              "2   96.682315    -0.216957\n",
              "3   95.100353    -0.344091\n",
              "4  101.125089     0.140083"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "Odbp-G_kfZiM",
        "outputId": "325488d8-1ce7-4f75-839a-efac40baae0e"
      },
      "source": [
        "df.head()"
      ],
      "execution_count": 19,
      "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>Data</th>\n",
              "      <th>Data_zscore</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>101.754507</td>\n",
              "      <td>0.190666</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>96.962755</td>\n",
              "      <td>-0.194420</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>96.682315</td>\n",
              "      <td>-0.216957</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>95.100353</td>\n",
              "      <td>-0.344091</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>101.125089</td>\n",
              "      <td>0.140083</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         Data  Data_zscore\n",
              "0  101.754507     0.190666\n",
              "1   96.962755    -0.194420\n",
              "2   96.682315    -0.216957\n",
              "3   95.100353    -0.344091\n",
              "4  101.125089     0.140083"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5h0smfBzcrLA"
      },
      "source": [
        ""
      ],
      "execution_count": 19,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YJyMNcR7crLA"
      },
      "source": [
        "pandas.DataFrame.std\n",
        "DataFrame.std(axis=None, skipna=None, level=None, ddof=1, numeric_only=None, **kwargs)[source]¶\n",
        "Return sample standard deviation over requested axis.\n",
        "\n",
        "Normalized by N-1 by default. This can be changed using the ddof argument\n",
        "\n",
        "Parameters\n",
        "axis{index (0), columns (1)}\n",
        "skipnabool, default True\n",
        "Exclude NA/null values. If an entire row/column is NA, the result will be NA.\n",
        "\n",
        "levelint or level name, default None\n",
        "If the axis is a MultiIndex (hierarchical), count along a particular level, collapsing into a Series.\n",
        "\n",
        "ddofint, default 1\n",
        "Delta Degrees of Freedom. The divisor used in calculations is N - ddof, where N represents the number of elements.\n",
        "\n",
        "numeric_onlybool, default None\n",
        "Include only float, int, boolean columns. If None, will attempt to use everything, then use only numeric data. Not implemented for Series.\n",
        "\n",
        "Returns\n",
        "Series or DataFrame (if level specified)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-1S0BXuecrLB"
      },
      "source": [
        "* Z-Score is essentially how many standart deviations away is my actual value from the mean value based on the business context, you can define the threshold value for the z score to classify a point as an outlier or not in the current scheme of things."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3YRT_Un3crLC"
      },
      "source": [
        "df[\"outlier\"] = (abs(df[\"Data_zscore\"])>3).astype(int)"
      ],
      "execution_count": 20,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BdCv899GcrLC"
      },
      "source": [
        "dataframe.abs() is one of the simplest pandas dataframe function. It returns an object with absolute value taken and it is only applicable to objects that are all numeric. It does not work with any Nan value either. abs() function can also be used with complex numbers to find their absolute value."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "ULOVF0vNcrLD",
        "outputId": "03dbaa27-a36d-4929-f2a5-9cec212fa8e8"
      },
      "source": [
        "df.tail() # actual data column,\tData_zscore,outlier"
      ],
      "execution_count": 21,
      "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>Data</th>\n",
              "      <th>Data_zscore</th>\n",
              "      <th>outlier</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>195</th>\n",
              "      <td>102.575036</td>\n",
              "      <td>0.256607</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>196</th>\n",
              "      <td>100.268499</td>\n",
              "      <td>0.071244</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>197</th>\n",
              "      <td>98.155072</td>\n",
              "      <td>-0.098600</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>198</th>\n",
              "      <td>100.321574</td>\n",
              "      <td>0.075509</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>199</th>\n",
              "      <td>91.737651</td>\n",
              "      <td>-0.614332</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "           Data  Data_zscore  outlier\n",
              "195  102.575036     0.256607        0\n",
              "196  100.268499     0.071244        0\n",
              "197   98.155072    -0.098600        0\n",
              "198  100.321574     0.075509        0\n",
              "199   91.737651    -0.614332        0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zyuYnLCkcrLE"
      },
      "source": [
        "* let's find out the rows at my z_score has classified as outliers"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 106
        },
        "id": "d2qZFJ-DcrLF",
        "outputId": "9a1e2105-ff99-4510-e265-81e59acb03e8"
      },
      "source": [
        "df.loc[df.outlier == 1]"
      ],
      "execution_count": 22,
      "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>Data</th>\n",
              "      <th>Data_zscore</th>\n",
              "      <th>outlier</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>50</th>\n",
              "      <td>-40.0</td>\n",
              "      <td>-11.201343</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>90</th>\n",
              "      <td>180.0</td>\n",
              "      <td>6.478814</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "     Data  Data_zscore  outlier\n",
              "50  -40.0   -11.201343        1\n",
              "90  180.0     6.478814        1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8ApaWftdcrLG",
        "outputId": "510aca76-2e8a-4512-fe4b-6a3e9d42968b"
      },
      "source": [
        "(df.outlier.value_counts())"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    198\n",
              "1      2\n",
              "Name: outlier, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "tags": [],
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6coDhMSrcrLG",
        "outputId": "1e736594-5c5a-4a5d-f6bb-95f504a43fc5"
      },
      "source": [
        "print(\"number of outliers = \" + str(df.outlier.value_counts()[1]))"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "number of outliers = 2\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Y7HojCF7crLH"
      },
      "source": [
        "def outlier_inspect(df, col, min_z=1, max_z = 5, step = 0.2, max_hist = None, bins = 50):\n",
        "    fig = plt.figure(figsize=(20, 6))\n",
        "    fig.suptitle(col, fontsize=16)\n",
        "    plt.subplot(1,3,1)\n",
        "    if max_hist == None:\n",
        "        sns.histplot(df[col], kde=False, bins = 50,color=\"r\")\n",
        "    else :\n",
        "        sns.distplot(df[df[col]<=max_hist][col], kde=False, bins = 50)\n",
        "    plt.subplot(1,3,2)\n",
        "    sns.boxplot(df[col])\n",
        "    plt.subplot(1,3,3)\n",
        "    z_score_inspect = outlier_zscore(df, col, min_z=min_z, max_z = max_z, step = step)\n",
        "    plt.show()"
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vrJ5XMhlcrLI"
      },
      "source": [
        "def outlier_zscore(df, col, min_z=1, max_z = 5, step = 0.1, print_list = False):\n",
        "    z_scores = df[\"Data_zscore\"]\n",
        "    threshold_list = []\n",
        "    for threshold in np.arange(min_z, max_z, step):\n",
        "        threshold_list.append((threshold, len(np.where(z_scores > threshold)[0])))\n",
        "        df_outlier = pd.DataFrame(threshold_list, columns = ['threshold', 'outlier_count'])\n",
        "        df_outlier['pct'] = (df_outlier.outlier_count - df_outlier.outlier_count.shift(-1))/df_outlier.outlier_count*100\n",
        "    plt.plot(df_outlier.threshold, df_outlier.outlier_count)\n",
        "    best_treshold = round(df_outlier.iloc[df_outlier.pct.argmax(), 0],2)\n",
        "    outlier_limit = int(df[col].dropna().mean() + (df[col].dropna().std()) * df_outlier.iloc[df_outlier.pct.argmax(), 0])\n",
        "    percentile_threshold = stats.percentileofscore(df[col].dropna(), outlier_limit)\n",
        "    plt.vlines(best_treshold, 0, df_outlier.outlier_count.max(), \n",
        "               colors=\"r\", ls = \":\"\n",
        "              )\n",
        "    plt.annotate(\"Zscore : {}\\nValue : {}\\nPercentile : {}\".format(best_treshold, outlier_limit, \n",
        "                                                                   (np.round(percentile_threshold, 3), \n",
        "                                                                    np.round(100-percentile_threshold, 3))), \n",
        "                 (best_treshold, df_outlier.outlier_count.max()/2))\n",
        "    #plt.show()\n",
        "    if print_list:\n",
        "        print(df_outlier)\n",
        "    return (plt, df_outlier, best_treshold, outlier_limit, percentile_threshold)"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 334
        },
        "id": "PtF-Upn6crLJ",
        "outputId": "1dd663fe-64ce-49ba-c1e3-49b1ce518420"
      },
      "source": [
        "outlier_inspect(df,\"Data\")"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/seaborn/_decorators.py:43: FutureWarning: Pass the following variable as a keyword arg: x. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.\n",
            "  FutureWarning\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 1440x432 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "y0ABASmWcrLJ",
        "outputId": "3a225700-e728-452e-f5c8-b7a2aef44f71"
      },
      "source": [
        "df[\"outlier\"] = (abs(df[\"Data_zscore\"])>1).astype(int)\r\n",
        "df.head()"
      ],
      "execution_count": 28,
      "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>Data</th>\n",
              "      <th>Data_zscore</th>\n",
              "      <th>outlier</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>101.754507</td>\n",
              "      <td>0.190666</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>96.962755</td>\n",
              "      <td>-0.194420</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>96.682315</td>\n",
              "      <td>-0.216957</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>95.100353</td>\n",
              "      <td>-0.344091</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>101.125089</td>\n",
              "      <td>0.140083</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         Data  Data_zscore  outlier\n",
              "0  101.754507     0.190666        0\n",
              "1   96.962755    -0.194420        0\n",
              "2   96.682315    -0.216957        0\n",
              "3   95.100353    -0.344091        0\n",
              "4  101.125089     0.140083        0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 225
        },
        "id": "G9GhpdQwhZvw",
        "outputId": "9b28f1a8-2fbb-4470-85d0-78caccb72696"
      },
      "source": [
        "df.loc[df.outlier == 1]"
      ],
      "execution_count": 29,
      "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>Data</th>\n",
              "      <th>Data_zscore</th>\n",
              "      <th>outlier</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>112.043840</td>\n",
              "      <td>1.017562</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>47</th>\n",
              "      <td>85.771234</td>\n",
              "      <td>-1.093819</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50</th>\n",
              "      <td>-40.000000</td>\n",
              "      <td>-11.201343</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>62</th>\n",
              "      <td>112.002015</td>\n",
              "      <td>1.014200</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>68</th>\n",
              "      <td>86.575650</td>\n",
              "      <td>-1.029173</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>90</th>\n",
              "      <td>180.000000</td>\n",
              "      <td>6.478814</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "          Data  Data_zscore  outlier\n",
              "14  112.043840     1.017562        1\n",
              "47   85.771234    -1.093819        1\n",
              "50  -40.000000   -11.201343        1\n",
              "62  112.002015     1.014200        1\n",
              "68   86.575650    -1.029173        1\n",
              "90  180.000000     6.478814        1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Qhpm5okVhpNU",
        "outputId": "f3ed8697-d902-47b8-a1e6-914fe8901504"
      },
      "source": [
        "print(\"number of outliers = \" + str(df.outlier.value_counts()[1]))"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "number of outliers = 6\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_BX0RgfKjFRG"
      },
      "source": [
        "df=df.loc[df.outlier == 0]"
      ],
      "execution_count": 31,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        },
        "id": "8zV7-wjSjnfy",
        "outputId": "9034ef29-47b8-4456-cb41-7cd5e5ba5d06"
      },
      "source": [
        "df.head()"
      ],
      "execution_count": 32,
      "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>Data</th>\n",
              "      <th>Data_zscore</th>\n",
              "      <th>outlier</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>101.754507</td>\n",
              "      <td>0.190666</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>96.962755</td>\n",
              "      <td>-0.194420</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>96.682315</td>\n",
              "      <td>-0.216957</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>95.100353</td>\n",
              "      <td>-0.344091</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>101.125089</td>\n",
              "      <td>0.140083</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         Data  Data_zscore  outlier\n",
              "0  101.754507     0.190666        0\n",
              "1   96.962755    -0.194420        0\n",
              "2   96.682315    -0.216957        0\n",
              "3   95.100353    -0.344091        0\n",
              "4  101.125089     0.140083        0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 47
        },
        "id": "ckj0Aes4jXtE",
        "outputId": "d71c811a-78e8-4cc1-b282-c534288c66c6"
      },
      "source": [
        "df.loc[df.outlier == 1]"
      ],
      "execution_count": 33,
      "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>Data</th>\n",
              "      <th>Data_zscore</th>\n",
              "      <th>outlier</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "Empty DataFrame\n",
              "Columns: [Data, Data_zscore, outlier]\n",
              "Index: []"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Gsy68C-pjyfs",
        "outputId": "d3eef5cc-817a-4d46-9d69-fd4cee82f5ee"
      },
      "source": [
        "(df.outlier.value_counts())"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    194\n",
              "Name: outlier, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "mgB1Q6pakDyK",
        "outputId": "101775a2-fb96-406d-d988-e48fa4db2892"
      },
      "source": [
        "sns.histplot(df[\"Data\"])\r\n",
        "plt.show()"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6TCfSN69km18"
      },
      "source": [
        ""
      ],
      "execution_count": 35,
      "outputs": []
    }
  ]
}