{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Introduction to statistics for Geoscientists (with Python)\n", "### Lecturer: Gerard Gorman\n", "### Lecture 5: Statistics and graphs - an introduction\n", "### URL: [http://ggorman.github.io/Introduction-to-stats-for-geoscientists/](http://ggorman.github.io/Introduction-to-stats-for-geoscientists/)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Aims and objectives of these lectures\n", "\n", "Most of you will have done stats before - most probably not in detail. This section of course will be concerned with:\n", "\n", "* Teaching you practical applications of stats.\n", "* Teaching you how to use Python to undertake statistical analyses of data.\n", "* Practise with graphing data in Python.\n", "\n", "This course will **NOT** be concerned with mathematical theory underlying statistics. Goal is for you to pick up practical statistical skills and knowledge." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is statistics?\n", "Statistics is the study of the collection, organisation, analysis and interpretation of data. It is comprised of methods for describing and analysing non-deterministic phenomena.\n", "\n", "### What do we mean by this?\n", "\n", "Deterministic phenomena - can be precisely predicted:\n", "\n", "* Orbits of planets.\n", "* Chemical reactions.\n", "\n", "Non-deterministic phenomena - include randomness:\n", "\n", "* Heights of people in the UK.\n", "* Measurements of mineral ages in rock sample.\n", "* Lengths of a certain fossil from a certain locality.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Populations and distributions\n", "\n", "Population - whole underlying universe of possible values. This is normally unattainable!\n", "\n", "* Height measurements of all people in the UK.\n", "* Lengths of EVERY fossil specimen from locality.\n", "\n", "Distribution - shape of population histogram.\n", "\n", "Lets have a look at a few examples:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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BXwK+BXwoM29reP864G1Nt/1/mfk/d9I/DQ4XPUr9yh0VWqx20BAR5wJXAe8C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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Here we import the standard plotting library from matplotlib, and give it the\n", "# moniker 'plt'. If you are used to using pylab, don't worry! The two modules\n", "# can be used almost interchangeably.\n", "from scipy import stats\n", "import matplotlib.pyplot as plt\n", "\n", "# This command simply ensures that all matplotlib windows are opened in the \n", "# notebook and not as pop-ups\n", "%matplotlib inline\n", "\n", "# Generate normal distribution.\n", "x = stats.norm.rvs(size=100000)\n", "\n", "# Plot a histogram\n", "plt.hist(x, 100, normed=1)\n", "\n", "# The histogram uses the input data of 'x', separates it into '100' bins and\n", "# normalises it ('normed')\n", "# axis: x0,x1,y0, y1\n", "plt.axis([-4, 4, 0, 0.45])\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Generate Wald distribution.\n", "x = stats.wald.rvs(size=200000)\n", "\n", "# Plot a histogram\n", "plt.hist(x, 300, normed=1)\n", "plt.axis([0, 5, 0, 1.2])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Generate exponential distribution.\n", "x = stats.expon.rvs(size=100000)\n", "\n", "# Plot a histogram\n", "plt.hist(x, 200, normed=1)\n", "plt.axis([0, 5, 0, 1.0])\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sample\n", "A sample is a subset of the population that we have actually measured.\n", "\n", "* Heights of all people in this room.\n", "* Lengths of fossils in a collection.\n", "\n", "Statistics involves using samples to represent populations.\n", "\n", "Samples must be unbiased for statistics to be of any use!\n", "\n", "## Biased sampling\n", "Popular example: In the [1936 US Presidential Election](http://en.wikipedia.org/wiki/United_States_presidential_election,_1936), Literary Digest undertook a massive pre-election poll. They sent out 10 million questionnaires to list of names obtained from phone books and car-registration lists. The survey predicted a Republican landslide...actual result was biggest Democratic landslide in 20th centry - Roosevelt received 98.49% of the electoral vote, the highest percentage since the uncontested election of 1820. [Two key errors were made](http://en.wikipedia.org/wiki/United_States_presidential_election,_1936#Campaign): \n", "(1) only the better off owned cars and phones and were statistically more likely to vote Republican; (2) as the survey was voluntary typically only the really passionate voters who were unhappy with the status quo (i.e. Democrat) replied to the survey.\n", "\n", "Are our first set of samples also likely to be biased?\n", "\n", "* Heights of all people in this room.\n", "* Lengths of fossils in a collection.\n", "\n", "Are there better ways to sample these populations?\n", "\n", "Not going to talk any more in this course about need for non-biased (random) samples. However, sample bias can get you into serious trouble so keep it in mind (consider these other fun examples: sampling bias in the fossil record; or the Caveman Effect)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Branches of statistics\n", "\n", "Two branches/classes of statistics:\n", "\n", "**Descriptive statistics**: Numbers used to summarise samples (and hence hopefully populations) e.g. averages.\n", "\n", "**Inferential statistics**: Methods for drawing conclusions from samples or combinations of samples, e.g. 'On basis of my samples, how likely is it that height and shoe size are related?'\n", "\n", "In this lecture we will stick to descriptive statistics." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Averages\n", "\n", "Averages are *measures of central tendency*. Several types of average exist. The most commonly used are:\n", "\n", "* **Mean** (technically arithmetic mean)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean = 3.92307692308\n" ] } ], "source": [ "import numpy as np \n", "\n", "values = np.array([1, 3, 5, 2, 4, 7, 2, 6, 8, 3, 2, 3, 5])\n", "\n", "# Here we use conditional formatting. We add curly braces in the string, and whatever \n", "# is in '.format()' will be inserted in their place.\n", "print \"Mean = {}\".format(np.mean(values))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* **Median**: middle value when numbers ordered." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sorted array = [1 2 2 2 3 3 3 4 5 5 6 7 8], Median = 3.0\n" ] } ], "source": [ "# Here there are two sets of braces, and format has two arguments. This way you can\n", "# insert multiple strings, lists, and floats into a string!\n", "print \"Sorted array = {}, Median = {}\".format(np.sort(values), np.median(values))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this example there are 13 numbers so the median is the $7^{th}$ number in the sorted array. If there were 14 numbers (e.g. the number 10 was appended to the array) then the median would be the mean of $7^{th}$ and $8^{th}$ values, i.e. 3.5 in this case.\n", "* **Mode**: most common value." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mode = [2]\n" ] } ], "source": [ "# Although we have not gone far we quickly find that we have to look for\n", "# python's stats module to provide a method for the the mode.\n", "from scipy import stats\n", "\n", "mode, count = stats.mode(values)\n", "\n", "print \"Mode = {}\".format(mode)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that for when there are multiple modes, only the first is returned.\n", "\n", "The mean and the median are the two most common averages. The advantages of median over the mean are:\n", "\n", "* May be better for skewed distributions.\n", "* Reduces effect of outliers.\n", "* Don’t need to know values of end-values.\n", "\n", "In practice the mode much more rarely used." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measures of spread\n", "\n", "There is much more to a distribution than average. These samples have the same mean and median:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "values1 mean = 0.0, median = 0.0\n", "values2 mean = 0.0, median = 0.0\n" ] } ], "source": [ "values1 = np.array([-0.2, -0.1, -0.1, 0.0, 0.0, 0.0 , 0.1 , 0.1 , 0.2])\n", "print \"values1 mean = {}, median = {}\".format(np.mean(values1), np.median(values1))\n", "\n", "values2 = np.array([-1000, -500, 0, 500, 1000])\n", "print \"values2 mean = {}, median = {}\".format(np.mean(values2), np.median(values2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "...but they have very different spread:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "values1 spread = 0.4\n", "values1 spread = 2000\n" ] } ], "source": [ "print \"values1 spread = \", np.ptp(values1)\n", "print \"values1 spread = \", np.ptp(values2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Percentile\n", "This is best explained with distributions - lets first define a normal distribution:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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lpaXRqlUrzjzzTN9RpIjExMTw22+/sWCBHpcj4U2lQaQI7dmzh3fffVdLE2Hu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\n6dKF7t27s2TJEt+RpJCpNEihOXjwILf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RUarsVP0kfR74ct6i6wiVuz5BqI1R04rdzwJS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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mu, std = 0, 1\n", "xmin, xmax = [-4, 4]\n", "x = np.linspace(xmin, xmax, 100)\n", "p = stats.norm.pdf(x, mu, std)\n", "plt.plot(x, p, 'k')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The 20th percentile indicates that 20% of all values are lower than this value - the shaded region below:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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SGDp0KOeddx41atTwHSXutG/fnp9//pnp06f7jiKS8FQ0iCS4rVu3MmbMGNq1a6fjoA/g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\nSUEqGiTl/PDDD0ydOhXnHNo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(x, p, 'k')\n", "plt.fill_between(x, 0, p, interpolate=True,\n", " where=(x<=stats.norm.ppf(0.2)))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are four percentiles that get their own name:\n", "* 25th percentile is also known as the first quartile (Q1)\n", "* 50th percentile as the median or second quartile (Q2)\n", "* 75th percentile as the third quartile (Q3) \n", "* Interquartile (IQ) range range from Q1 to Q3." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Gjx4NgHPaBTJZZWRksGvXrsi5IiLJS0WDSBHaunUrs2fPjry7wWsWKTpnnnkm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\n8h1JCpmKBik0e/bsoWPHjrz66quRWdT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# First quartile (Q1)\n", "plt.plot(x, p, 'k')\n", "plt.fill_between(x, 0, p, interpolate=True,\n", " where=(x<=stats.norm.ppf(0.25)))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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CggJee+216H0mrvOQwM/mTqW1bt2a/fffXydEiiSYSoNIGhk5ciS//PILweDhwKkeEvjb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\nOWAq0KyclzWLPl/S5DKOP8fMVpnZEjN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Median or second quartile (Q2)\n", "plt.plot(x, p, 'k')\n", "plt.fill_between(x, 0, p, interpolate=True,\n", " where=(x<=stats.norm.ppf(0.5)))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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PHhxbNaEbVPmT/CsNAO3atcPMGD16dNLHFkk1KhpEqtmyZcuYO3cuZjlAG99x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\nt24npgw65+J6ADOBf5V5bsDXwF0VnP8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Third quartile (Q3)\n", "plt.plot(x, p, 'k')\n", "plt.fill_between(x, 0, p, interpolate=True,\n", " where=(x<=stats.norm.ppf(0.75)))\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-0.674489750196\n", "0.674489750196\n" ] }, { "data": { "image/png": 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3GPBYJY+dVe73o6oZ60cgOuedicS5vLw8fvOb39C6deuojqt4onpmGVGbaQBv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\nLruMO++8ky1btvhdjsQpvRNLXNq4cSO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# * Interquartile (IQ) range range from Q2 to Q3.\n", "plt.plot(x, p, 'k')\n", "\n", "plt.fill_between(x, 0, p, interpolate=True,\n", " where=((x>=stats.norm.ppf(0.25)) & (x<=stats.norm.ppf(0.75))))\n", "print stats.norm.ppf(0.25)\n", "print stats.norm.ppf(0.75)\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Variance and standard deviation\n", "\n", "These are the most commonly used measures of spread. The sample variance is:\n", "\n", "$$ v = \\frac{1}{N-1} \\sum_{i=1}^{N} \\left( x_i - \\bar{x}\\right)^2 ,$$\n", "\n", "where $N$ is the number of measurements, $x_i$ is the individual measurement and $\\bar{x}$ is the sample mean. We can interpret this expression (almost) as the average of squared distances from the sample mean. Indeed, this intuitively gives us the spread. However, rather than the expected $\\frac{1}{N}$ we have $\\frac{1}{N-1}$. This is known as Bessel’s correction and it corrects the bias in the estimation of the population variance.\n", "\n", "The sample standard deviation is the square root of the sample variance: $s = \\sqrt{v}$. It gives a measure of spread in the same units as the measurements themselves." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise 5.1\n", "\n", "If you need remind yourself of how to get started using iPython see the [introduction to programming lecture](http://ggorman.github.io/Introduction-to-programming-for-geoscientists/) from the first term.\n", "\n", "1. Inspect the file [qzpercentages.csv](https://raw.githubusercontent.com/ggorman/Introduction-to-stats-for-geoscientists/gh-pages/data/qzpercentages.csv) (use !cat or %cat qzpercentages.csv for example).\n", "2. Write a program to read in the data. **Before launching into writing your own read function from first principles for reading .csv files consider if there is already a *right way* of doing this.** The same sage advice applies to all tasks given here.\n", "3. Calculate the mean, median, range, interquartile range, standard deviation, variance, and mode." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Develop your solution here...\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Plotting graphs\n", "\n", "In this course we will be using matplotlib for plotting. \n", "\n", "Within iPython remember to start your programs with the command:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bar charts\n", "\n", "Bar charts are a common chart type. They are used for plotting discrete data, e.g.:\n", "\n", "* Shoe-size.\n", "* Countries.\n", "\n", "Bar charts should not be confused with histograms. In the example here we have fossil species from a certain locality." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kGZOBT6amkm2Iq54CDAFm1CswERERaW19nowLuAC4Avgvca2Sm9LyjYEn6xSX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\n/j44/2s1bORVibQ5x4wlklaJiJvL3xOVOftM4NWIGC7p+zi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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sample program for bar chart of relative abundances of 5 species of fossil from a locality\n", "\n", "# Finds of each fossil\n", "bardata = np.array([121, 59, 16, 20, 81]) \n", "species=[\"Apatobolus micula\", \"Lingulella davisii\", \"Divobolus quadratus\",\n", " \"Tarphyteina taylori\", \"Bathmoleca addisoni\"]\n", "\n", "# Colours to be used in bar chart\n", "colours=[\"red\", \"green\", \"blue\", \"orange\", \"purple\"] \n", "\n", "# Set up chart with 5 bars using my values and colours\n", "plt.bar([1, 2, 3, 4, 5], bardata, 1, 0, color=colours)\n", "\n", "# Add datalabels to x-axis\n", "plt.xticks([1, 2, 3, 4, 5],species, rotation=45, style='italic')\n", "\n", "# Title for y axis.\n", "plt.ylabel(\"Number of specimens found\")\n", "\n", "# Title for chart.\n", "plt.title(\"Brachiopod fossils from locality #23\", weight='bold', color=(.5, .1, .1))\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Histograms\n", "\n", "Histograms are a way to summarize distributions. The distribution is split into categories or *bins* - usually of equal size. The size of the bins is arbitrary - whatever works best for the task at hand.\n", "\n", "The number of samples falling into each bin are counted - this is the frequency. They are then plotted as adjacent rectangles akin to a bar-chart. The profile of a histogram approximates probability distribution of the population." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise 5.2\n", "\n", "Generate a histogram from [qzpercentages.csv](https://raw.githubusercontent.com/ggorman/Introduction-to-stats-for-geoscientists/gh-pages/data/qzpercentages.csv).\n", "\n", "Your histogram should include the following features:\n", "\n", "1. Label the x and y axis.\n", "2. Need to fix x-axis labels to make sure all bins are labelled.\n", "3. Need to fix y-axis ticks to avoid ‘0’ crashing into ’20’.\n", "4. Specify the number of bins.\n", "5. Increas the line thickness in your plot.\n", "6. Specify the colour.\n", "7. Add a title." ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Solutions here..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Exercise 5.3\n", "\n", "Now that you have made a bar chart and a histogram, let's try making another simple statistical plot.\n", "A pie chart! As you are aware, pie charts are a simple way of showing the relative sizes of data in a\n", "given set. Pie charts are easy to make in matplotlib, and only require one function. Most functions in matplotlib use similar, if not identical, arguments to do certain things, like 'color' in the bar chart example. This can be used to decipher which arguments a function might take!\n", "\n", "Although there are no examples of pie charts in this page, it is relatively simple and can be found in the matplotlib docs [here](http://matplotlib.org/api/pyplot_api.html). The function is matplotlib.pylot.pie(...)\n", "\n", "Use the data below and:\n", "\n", "1. Make a pie chart\n", "2. Make the pie chart circular and not an ellipse\n", "3. Make the pie chart use the correct colours for the joke to work\n", "4. Rotate the chart such that the joke is clear\n", "5. Add labels to each section, such that anyone will get it\n", "6. Add a title as the icing on the cake\n", "\n", "**BONUS**\n", "7. 'explode' the small wedge, and give it shadow.\n", "\n", "**HINT**\n", "\n", "Start simple, and build up. REMEMBER: The online docs will give the function with ALL \n", "its possible arguments. However only those without an equals sign (e.g. plt.xxx(X,label=...)) are mandatory (X in this case). Those with an equals sign (label) are not required for the function to work, but allow for more\n", "customisation should you wish it.\n", "\n", "Most of the tricks you will use here are applicable on other plots and figures throughout this course, do not forget them as they can make your life easier later." ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", " \n", "# This is your data to plot\n", "data = np.array([['Pacman','not Pacman'],[270, 90]])\n" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "celltoolbar": "Raw Cell Format", "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }