diff --git a/Charting Notebook (Coin Flips).ipynb b/Charting Notebook (Coin Flips).ipynb
new file mode 100644
index 0000000..1f1c590
--- /dev/null
+++ b/Charting Notebook (Coin Flips).ipynb	
@@ -0,0 +1,481 @@
+{
+ "metadata": {
+  "name": "",
+  "signature": "sha256:daade9b050b437a97c51f1fa25c972b96c52f69cd46b3fb809c5aa2f869691d7"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "import random\n",
+      "import math\n",
+      "import statistics as st\n",
+      "import matplotlib.pyplot as plt\n",
+      "import seaborn\n",
+      "%matplotlib inline"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 3
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def flip_coin():\n",
+      "    heads_or_tails = ['H', 'T']\n",
+      "    return random.choice(heads_or_tails)"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 4
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "heads = []\n",
+      "tails = []\n",
+      "interval_difference_counts = []\n",
+      "heads_count = []\n",
+      "tails_count = []\n",
+      "\n",
+      "def trial_flip_n_times(n=100000):\n",
+      "    count = 0\n",
+      "    i = 0\n",
+      "    results = [flip_coin() for _ in range(n)]\n",
+      "    for result in results:\n",
+      "        count += 1\n",
+      "        if result == 'H':\n",
+      "            heads.append(result)\n",
+      "        else:\n",
+      "            tails.append(result)\n",
+      "        if count == 2 ** (i):\n",
+      "            heads_count.append(len(heads))\n",
+      "            tails_count.append(len(tails))\n",
+      "            interval_difference_counts.append(abs(len(heads) - len(tails)))\n",
+      "            i += 1\n",
+      "            \n",
+      "            \n",
+      "\n",
+      "trial_flip_n_times()\n",
+      "print(\"Heads: {}\".format(len(heads)))\n",
+      "print(\"Tails: {}\".format(len(tails)))\n",
+      "print(\"Heads at 2**n: {}\".format(heads_count))\n",
+      "print(\"Tails at 2**n: {}\".format(tails_count))\n",
+      "print(\"Difference at 2 ** n: {}\".format(interval_difference_counts))\n",
+      "\n",
+      "        \n",
+      "    "
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "Heads: 50434\n",
+        "Tails: 49566\n",
+        "Heads at 2**n: [0, 0, 2, 5, 8, 16, 30, 64, 126, 246, 499, 1023, 2047, 4141, 8273, 16640, 33212]\n",
+        "Tails at 2**n: [1, 2, 2, 3, 8, 16, 34, 64, 130, 266, 525, 1025, 2049, 4051, 8111, 16128, 32324]\n",
+        "Difference at 2 ** n: [1, 2, 0, 2, 0, 0, 4, 0, 4, 20, 26, 2, 2, 90, 162, 512, 888]\n"
+       ]
+      }
+     ],
+     "prompt_number": 5
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "x1 = [\"n0\", \"n1\", \"n2\", \"n3\", \"n4\", \"n5\", \"n6\", \"n7\", \n",
+      "      \"n8\", \"n9\", \"n10\", \"n11\", \"n12\", \"n13\", \"n14\", \"n15\", \"n16\"]\n",
+      "y1 = interval_difference_counts\n",
+      "plt.plot(y1)\n",
+      "plt.xticks(range(17), x1)\n",
+      "plt.xlabel(\"# of Flips\")\n",
+      "plt.ylabel(\"Difference\")\n",
+      "plt.title(\"Difference between Heads and Tails\")\n",
+      "plt.show()\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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TUlK44xWgm/JERGKzblu4bqeQL5lNU7EQEYlJevLAQlzsqDsVCxGRmPjWBsrG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\ngA8MNSbwGcIJ9/lABfCSHMR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+       "text": [
+        "<matplotlib.figure.Figure at 0x109a226d8>"
+       ]
+      }
+     ],
+     "prompt_number": 6
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "def ratio_of_heads_to_tails():\n",
+      "    heads_count = [1, 1, 2, 4, 10, 17, 36, 73, 138, 270, 536, 1049, 2050, 4128, 8247, 16425, 32845]\n",
+      "    tails_count = [1, 1, 2, 4, 6, 15, 28, 55, 118, 242, 488, 999, 2046, 4064, 8137, 16343, 32691]\n",
+      "    ratios = [round(x/y, 2) for x, y in zip(heads_count, tails_count)]\n",
+      "    return ratios\n",
+      "       \n",
+      "\n",
+      "heads_to_tails_ratios = ratio_of_heads_to_tails()\n",
+      "print(heads_to_tails_ratios)            "
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "[1.0, 1.0, 1.0, 1.0, 1.67, 1.13, 1.29, 1.33, 1.17, 1.12, 1.1, 1.05, 1.0, 1.02, 1.01, 1.01, 1.0]\n"
+       ]
+      }
+     ],
+     "prompt_number": 7
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "x2 = [\"n0\", \"n1\", \"n2\", \"n3\", \"n4\", \"n5\", \"n6\", \"n7\", \n",
+      "      \"n8\", \"n9\", \"n10\", \"n11\", \"n12\", \"n13\", \"n14\", \"n15\", \"n16\"]\n",
+      "y2 = heads_to_tails_ratios\n",
+      "plt.plot(y2)\n",
+      "plt.xticks(range(17), x2)\n",
+      "plt.xlabel(\"# of Flips\")\n",
+      "plt.ylabel(\"Ratio\")\n",
+      "plt.title(\"Ratio of Heads and Tails\")\n",
+      "plt.show()\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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5uLOmIvFE9UGCJOYY0FitWFhBeXEez247TFdPX6LTMcZzXrYcaoDLgcGtgi7g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\nRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x109a68eb8>"
+       ]
+      }
+     ],
+     "prompt_number": 8
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "x3 = [2**0, 2**1, 2**2, 2**3, 2**4, 2**5, 2**6, 2**7, 2**8, 2**9, 2**10, 2**11, 2**12, 2**13, 2**14, 2**15, 2**16]\n",
+      "y3 = interval_difference_counts\n",
+      "plt.scatter(x3, y3, c='blue')\n",
+      "plt.xscale('log')\n",
+      "plt.xlabel(\"# of Flips\")\n",
+      "plt.ylabel(\"Difference\")\n",
+      "plt.title(\"Difference between Heads and Tails\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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aS2r39kF7t7Gd2wbt3b52bhvUrn0t+4KUWMvWZ/sdJWlzo4qpgXZvH7R3G9u5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\niJmZ5eYQMTOz3BwiZmaWm0PEzMxy+x9MBnKAa0ZhEgAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x109bc4860>"
+       ]
+      }
+     ],
+     "prompt_number": 10
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "x4 = [2**0, 2**1, 2**2, 2**3, 2**4, 2**5, 2**6, 2**7, 2**8, 2**9, 2**10, 2**11, 2**12, 2**13, 2**14, 2**15, 2**16]\n",
+      "y4 = heads_to_tails_ratios\n",
+      "plt.scatter(x4, y4, c='red')\n",
+      "plt.xscale('log')\n",
+      "plt.xlabel(\"# of Flips\")\n",
+      "plt.ylabel(\"Ratio\")\n",
+      "plt.title(\"Ratio of Heads:Tails\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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+       "text": [
+        "<matplotlib.figure.Figure at 0x109b386a0>"
+       ]
+      }
+     ],
+     "prompt_number": 11
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "# Other than the outlier I'm observing a normal distribution"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 9
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "heads = []\n",
+      "tails = []\n",
+      "heads_count = []\n",
+      "tails_count = []\n",
+      "means = []\n",
+      "stdevs = []\n",
+      "\n",
+      "def ratio_of_lists(list1, list2):\n",
+      "    ratios = [round(x/y, 2) for x, y in zip(list1,list2)]\n",
+      "    return ratios\n",
+      "\n",
+      "for _ in range(20):\n",
+      "    trial_flip_n_times()\n",
+      "    means.append(st.mean(ratio_of_lists(heads_count, tails_count)))\n",
+      "    stdevs.append(st.pstdev(ratio_of_lists(heads_count, tails_count)))\n",
+      "    heads_count = []\n",
+      "    tails_count = []\n",
+      "    \n",
+      "print(means)\n",
+      "print(stdevs)    \n",
+      "   \n",
+      "    \n",
+      "    "
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "output_type": "stream",
+       "stream": "stdout",
+       "text": [
+        "[0.72, 1.0094117647058825, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0]\n",
+        "[0.4268075747715274, 0.00235294117647059, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]\n"
+       ]
+      }
+     ],
+     "prompt_number": 13
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "x5 =([2**0, 2**1, 2**2, 2**3, 2**4, 2**5, 2**6, 2**7, 2**8, 2**9, \n",
+      "      2**10, 2**11, 2**12, 2**13, 2**14, 2**15, 2**16, 2**17, 2**18, 2**19])\n",
+      "y5 = means\n",
+      "plt.xscale('log')\n",
+      "plt.scatter(x5, y5, c='blue')\n",
+      "plt.xlabel(\"Trial\")\n",
+      "plt.ylabel(\"Ratio Mean\")\n",
+      "plt.title(\"Mean of the Ratio\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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5uE6HqtSTHKqStky7XsPItg8AP4iIXwPfB34K7Fdut9ehnuODnCRJlThUJUmq\nxOCQJFVicEiSKjE4JEmVGBySpEoMDklSJQaHJKkSg0OSVMn/B7QOy9G6sBX4AAAAAElFTkSuQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x109a99d30>"
+       ]
+      }
+     ],
+     "prompt_number": 14
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "x6 =([2**0, 2**1, 2**2, 2**3, 2**4, 2**5, 2**6, 2**7, 2**8, 2**9, \n",
+      "      2**10, 2**11, 2**12, 2**13, 2**14, 2**15, 2**16, 2**17, 2**18, 2**19])\n",
+      "y6 = stdevs\n",
+      "plt.xscale('log')\n",
+      "plt.scatter(x6, y6, c='blue')\n",
+      "plt.xlabel(\"Trial\")\n",
+      "plt.ylabel(\"Ratio Standard Deviation\")\n",
+      "plt.title(\"Standard Deviation of Ratios\")\n",
+      "plt.show()"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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DDmXDF+kTqK+Um5lXRcTciV6UmUf1Jt6kivJn5jXAwr4kbG9K+79B+31M6f5/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\nnQAAAABJRU5ErkJggg==\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x109f1a0b8>"
+       ]
+      }
+     ],
+     "prompt_number": 16
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "heads = []\n",
+      "tails = []\n",
+      "heads_count = []\n",
+      "tails_count = []\n",
+      "means = []\n",
+      "stdevs = []\n",
+      "head_ratios = []\n",
+      "\n",
+      "\n",
+      "for _ in range(100000):\n",
+      "    trial_flip_n_times(100)\n",
+      "    head_ratios.append(len(heads)/100)\n",
+      "    heads = []\n",
+      "\n",
+      "   "
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 18
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.hist(head_ratios, bins=20, color='pink')\n",
+      "plt.xlabel('Ratio per 100 Flips')\n",
+      "plt.ylabel('Count')\n",
+      "plt.title('Ratio of Heads: Total Flips')\n",
+      "ymin, ymax = plt.ylim()\n",
+      "plt.show()\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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zaz+cNC3GNsD/l3ReH9t7kvRF19K53S4gfTltpqRTIuJ24H2S/lpIp2yL4UCx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\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x109bf6860>"
+       ]
+      }
+     ],
+     "prompt_number": 19
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "heads = []\n",
+      "tails = []\n",
+      "heads_count = []\n",
+      "tails_count = []\n",
+      "means = []\n",
+      "stdevs = []\n",
+      "head_ratios2 = []\n",
+      "\n",
+      "\n",
+      "for _ in range(100000):\n",
+      "    trial_flip_n_times(1000)\n",
+      "    head_ratios2.append(len(heads)/1000)\n",
+      "    heads = []"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [],
+     "prompt_number": 20
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.hist(head_ratios2, bins=20, color='red')\n",
+      "plt.xlabel('Ratio per 1000 Flips')\n",
+      "plt.ylabel('Count')\n",
+      "plt.title('Ratio of Heads: Total Flips')\n",
+      "ymin, ymax = plt.ylim()\n",
+      "plt.show()\n",
+      "\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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bLPexmJlZoXzEYmYNrXsomHHjyusD7Gn8+P1obm4uPrAdmBOLmTW07qFgoLw+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\nVignFjMzK5QTi5mZFer/AzmZiRQg1WGEAAAAAElFTkSuQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x10a007550>"
+       ]
+      }
+     ],
+     "prompt_number": 21
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "plt.boxplot([head_ratios, head_ratios2])\n",
+      "ymin, ymax = plt.ylim()\n",
+      "plt.ylim(ymin, ymax)\n",
+      "plt.title(\"100 Flips vs. 1000 Flips\")\n",
+      "plt.ylabel(\"Ratio of Heads: Flips\")\n",
+      "plt.xticks(range(1,3), [\"100 Flips\", \"1000 Flips\"])\n",
+      "plt.show()\n"
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": [
+      {
+       "metadata": {},
+       "output_type": "display_data",
+       "png": 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7w2Z2PfA3ZvZz4BOEXlc7AP/fzH7s7htTnysDV7n7jVXfAVB29x/l+FNkFNjW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\nAElFTkSuQmCC\n",
+       "text": [
+        "<matplotlib.figure.Figure at 0x109dc4860>"
+       ]
+      }
+     ],
+     "prompt_number": 22
+    },
+    {
+     "cell_type": "code",
+     "collapsed": false,
+     "input": [
+      "# Seems to be narrowing in on a more accurate ratio the more trials we run. "
+     ],
+     "language": "python",
+     "metadata": {},
+     "outputs": []
+    }
+   ],
+   "metadata": {}
+  }
+ ]
+}
\ No newline at end of file