{ "cells": [ { "cell_type": "code", "execution_count": 305, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Math + `pandas` = 😍\n", "\n", "Since y'all love math, we're going to do plenty of both today.\n", "\n", "## Flavors of statistics\n", "\n", "One of the most basic ways to split statistics is to break it into two categories: **descriptive** and **inferential**.\n", "\n", "* **Inferential statistics** takes part of a population and attempts to *infer* something about the entire population. **For example,** I interview 100 likely voters about who they're going to vote for, and *infer* who is going to win an election.\n", "* **Descriptive statistics** describes only the numbers you have right in front of you. **For example,** I have a list of all the planes that took off from the airport yesterday, and they were on average ten minutes late.\n", "\n", "We're going to be doing some **basic descriptive statistics**, because we sure aren't going to release our entire dataset to our readers. Summing it all up into a few numbers works much more nicely.\n", "\n", "## Types of data\n", "\n", "The two major categories of data are **qualitative/categorical** and **quantitative/numerical**. I'll use both words to describe each because I'm incapcable of picking a term and stick to it.\n", "\n", "* **Qualitative** or **categorical** data is... well, categories. Things that aren't numbers. Whether you're married or single, live in Arkansas or Alabama, or have blue eyes or brown eyes.\n", "* **Quantitative** or **numerical** data is, obviously, based on numbers. \n", "\n", "### Kinds of numeric data\n", "\n", "And, lucky us, there are kinds of numeric data!\n", "\n", "* **Continuous** data can be broken down into smaller and smaller numerical pieces. **For example,** is the temperature in your apartment 69°F, or 69.4°F, or 69.123°F?\n", "* **Discrete** data are still numbers, but they can only have certain values. **For example,** Yelp ratings are 1, 2, 3, 4 or 5 stars.\n", "\n", "# Your good friend descriptive statistics\n", "\n", "You use descriptive statistics all the time! Averages! Maximums! Minimums! These old friends are your new friends, too.\n", "\n", "We can break down descriptive statistics into a few major concepts, we'll talk about **central tendency** and **variability**. Let's take a look at those with a really dumb sample data set." ] }, { "cell_type": "code", "execution_count": 306, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
namesalary
0Smushface1200
1Jen25000
2James55000
3John35000
4Josephine25000
5Jacques15000
6Bill Gates100000
\n", "
" ], "text/plain": [ " name salary\n", "0 Smushface 1200\n", "1 Jen 25000\n", "2 James 55000\n", "3 John 35000\n", "4 Josephine 25000\n", "5 Jacques 15000\n", "6 Bill Gates 100000" ] }, "execution_count": 306, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Let's build a data set\n", "df = pd.DataFrame([\n", " { 'name': 'Smushface', 'salary': 1200 } ,\n", " { 'name': 'Jen', 'salary': 25000 },\n", " { 'name': 'James', 'salary': 55000 },\n", " { 'name': 'John', 'salary': 35000 },\n", " { 'name': 'Josephine', 'salary': 25000 },\n", " { 'name': 'Jacques', 'salary': 15000 },\n", " { 'name': 'Bill Gates', 'salary': 100000 } \n", "])\n", "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Central Tendency\n", "\n", "If someone hears we have this data set about salaries, they're probably going to ask, \"how much do people make?\" They don't want a long list of numbers, they want a single, solitary number. We can get most of the way there by describing **the central tendency**.\n", "\n", "Data in the world tends to clump around certain numbers - the average height of a man, or the average score on a test. This is called the **central tendency**, and is usually just called the **average**. Luckily for us average has like *two hundred different meanings*: **mean**, **median**, and **mode**.\n", "\n", "Double-luckily for us, `pandas` can compute all of those for us with appropriately-named functions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The MEAN\n", "\n", "The **mean** is what we've always thought of as the average. You add up all the data points and divide by the number of data points." ] }, { "cell_type": "code", "execution_count": 307, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2888571.4285714286" ] }, "execution_count": 307, "metadata": {}, "output_type": "execute_result" } ], "source": [ "(0 + 25000 + 55000 + 35000 + 25000 + 80000 + 20000000) / 7" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But like I said, `pandas` can help us out here with the `.mean()` method." ] }, { "cell_type": "code", "execution_count": 308, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "36600.0" ] }, "execution_count": 308, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['salary'].mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That looks ugly, let's convert it to an integer!" ] }, { "cell_type": "code", "execution_count": 309, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "36600" ] }, "execution_count": 309, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['salary'].mean().astype(int)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we want to get real crazy, we can add commas to it using our old friend `.format()`" ] }, { "cell_type": "code", "execution_count": 310, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "'36,600'" ] }, "execution_count": 310, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# format trick stolen from http://stackoverflow.com/a/10742904\n", "mean_salary = df['salary'].mean().astype(int)\n", "\"{:,}\".format(mean_salary)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But **back to the mean:** apparently the average of all of these salaries is **over two million dollars**. Does that look right to you?" ] }, { "cell_type": "code", "execution_count": 311, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
namesalary
0Smushface1200
1Jen25000
2James55000
3John35000
4Josephine25000
5Jacques15000
6Bill Gates100000
\n", "
" ], "text/plain": [ " name salary\n", "0 Smushface 1200\n", "1 Jen 25000\n", "2 James 55000\n", "3 John 35000\n", "4 Josephine 25000\n", "5 Jacques 15000\n", "6 Bill Gates 100000" ] }, "execution_count": 311, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The problem with adding everything together is **Bill Gates is exerting undue influence**. His salary is an **outlier** - a number that's either way too high or way too low and kind of screws up our data. He might actually be making that much money, sure, but by taking the mean we aren't doing a good job describing what we'd think of as the \"average.\"\n", "\n", "Because of how it's calculated, **the mean is suseptible to outliers.** Because you need to be so careful with it, the mean is definitely not my favorite way of getting the average." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The MEDIAN\n", "\n", "The **median** is like a new, improved mean, in that it describes the central tendency **without being suseptible to outliers**. To compute the median you do two things:\n", "\n", "1. Order the numbers largest to smallest\n", "2. Pick the middle number" ] }, { "cell_type": "code", "execution_count": 312, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0 1200\n", "5 15000\n", "1 25000\n", "4 25000\n", "3 35000\n", "2 55000\n", "6 100000\n", "Name: salary, dtype: int64" ] }, "execution_count": 312, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['salary'].sort_values()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have seven values, so it will be number four. Count up the list to discover it: **35,000** is the median. I'll prove it, too, using the power of `pandas`." ] }, { "cell_type": "code", "execution_count": 313, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "25000.0" ] }, "execution_count": 313, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df['salary'].median()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See? Told you!\n", "\n", "If you happen to have an **even number of data points** you won't have a middle number, you'll take the **mean of the middle two numbers**.\n", "\n", "My favorite description of the median comes from [Statistics for the Terrified](http://www.conceptstew.co.uk/pages/mean_or_median.html)\n", "\n", "> We are all much more familiar with the mean - why? People like using the mean because it is a much easier thing to deal with than the median, mathematically, particularly in more complex situations...\n", "> ...\n", "> Always use the median when the distribution is skewed. You can use either the mean or the median when the population is symmetrical, because then they will give almost identical results.\n", "\n", "Which to me reads like \"if you have a computer, **use the median.**\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The MODE\n", "\n", "The **mode** is the least-used measurement of central tendency: it's the **most popular value**. Even though our salary dataset has a most popular value, the mode actually shouldn't be used with *continuous* data, you should only use it with discrete data.\n", "\n", "Let's say our buddies are reviewing a restaurant" ] }, { "cell_type": "code", "execution_count": 314, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
restaurantrevieweryelp_stars
0Burger KingSmushface2
1Burger KingJen2
2Burger KingJames5
3Burger KingJohn4
4Burger KingJosephine4
5Burger KingJacques3
6Burger KingBill Gates2
\n", "
" ], "text/plain": [ " restaurant reviewer yelp_stars\n", "0 Burger King Smushface 2\n", "1 Burger King Jen 2\n", "2 Burger King James 5\n", "3 Burger King John 4\n", "4 Burger King Josephine 4\n", "5 Burger King Jacques 3\n", "6 Burger King Bill Gates 2" ] }, "execution_count": 314, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import pandas as pd\n", "\n", "# Let's build a data set\n", "reviews_df = pd.DataFrame([\n", " { 'restaurant': 'Burger King', 'reviewer': 'Smushface', 'yelp_stars': 2 } ,\n", " { 'restaurant': 'Burger King', 'reviewer': 'Jen', 'yelp_stars': 2 },\n", " { 'restaurant': 'Burger King', 'reviewer': 'James', 'yelp_stars': 5 },\n", " { 'restaurant': 'Burger King', 'reviewer': 'John', 'yelp_stars': 4 },\n", " { 'restaurant': 'Burger King', 'reviewer': 'Josephine', 'yelp_stars': 4 },\n", " { 'restaurant': 'Burger King', 'reviewer': 'Jacques', 'yelp_stars': 3 },\n", " { 'restaurant': 'Burger King', 'reviewer': 'Bill Gates', 'yelp_stars': 2 } \n", "])\n", "reviews_df" ] }, { "cell_type": "code", "execution_count": 315, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0 2\n", "dtype: int64" ] }, "execution_count": 315, "metadata": {}, "output_type": "execute_result" } ], "source": [ "reviews_df['yelp_stars'].mode()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Despite the fact that most people gave Burger King a `3` or above, the fact that **the most popular score is `2`** might mean something.\n", "\n", "My favorite example of the mode being useful (and possibly only example of the mode being useful) is **Amazon reviews.** For example, [this charger for a MacBook](https://www.amazon.com/Apple-Magsafe-Adapter-Charger-MacBook/dp/B014Z9P2VI/ref=sr_1_3?ie=UTF8&qid=1467768369&sr=8-3&keywords=macbook+charger) has some... interesting reviews." ] }, { "cell_type": "code", "execution_count": 316, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Import this because it won't let us display images otherwise\n", "from IPython.display import display, HTML" ] }, { "cell_type": "code", "execution_count": 317, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(HTML(''''''))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Look at that adapter!**\n", "\n", "2.5 stars, not too shabby. And so cheap! The real ones are like 80 bucks, I think.\n", "\n", "Let's take a look at the actual distribution of the scores..." ] }, { "cell_type": "code", "execution_count": 318, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(HTML(''''''))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Oh wait, *the mode of the data is 1*. **The adapters are probably terrible**, cancel that order." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measures of central tendency, a review\n", "\n", "There are three measures of central tendency.\n", "\n", "* The **mean** is the sum of all the numbers divided by the count of the numbers, and is pulled towards outliers.\n", "* The **median** is the middle number, and is not affected by outliers.\n", "* The **mode** is the most frequent number, is only used with nominal data, and isn't terribly useful.\n", "\n", "The median should probably be favorite." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Slight detour: Making sense of `.describe()`\n", "\n", "One of our old pandas friends is `.describe()`, which... describes some math-y stuff about a data set." ] }, { "cell_type": "code", "execution_count": 319, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
namesalary
0Smushface1200
1Jen25000
2James55000
3John35000
4Josephine25000
\n", "
" ], "text/plain": [ " name salary\n", "0 Smushface 1200\n", "1 Jen 25000\n", "2 James 55000\n", "3 John 35000\n", "4 Josephine 25000" ] }, "execution_count": 319, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df.head()" ] }, { "cell_type": "code", "execution_count": 320, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
salary
count7.000
mean36600.000
std32530.806
min1200.000
25%20000.000
50%25000.000
75%45000.000
max100000.000
\n", "
" ], "text/plain": [ " salary\n", "count 7.000\n", "mean 36600.000\n", "std 32530.806\n", "min 1200.000\n", "25% 20000.000\n", "50% 25000.000\n", "75% 45000.000\n", "max 100000.000" ] }, "execution_count": 320, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Make it so we only have three decimal places\n", "pd.set_option('display.float_format', lambda x: '%.3f' % x)\n", "df.describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And you see the mean displayed in all its glory, and so you scream, **it doesn't include the median what garbage!!!**\n", "\n", "But it does! Really! Give it a look around and see if you can find it.\n", "\n", "---\n", "\n", "waiting!\n", "\n", "---\n", "\n", "waiting!\n", "\n", "---\n", "\n", "waiting!\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Yes, that's right - **50% is the median**. Half of the values are above, half are below. The 25% and 75% are similar meaures:\n", "\n", "* 25%, a.k.a. **Q1**, a.k.a. **the first quartile**, has 25% of the values below it and 75% above it.\n", "* 75%, a.k.a. **Q3**, a.k.a. **the third quartile**, has 75% of the values below it and 25% below it.\n", "* and, of course, 50% i also known as **Q2**.\n", "\n", "25% can be thought of as the median of the bottom half of the data, and 75% can describe the median of the top half of the data. They give you a sense of **the range of data**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Box-and-whisker plots\n", "\n", "If we get tired of looking at lists of numbers, there's always [box-and-whisker plots](http://www.regentsprep.org/regents/math/algebra/ad3/boxwhisk.htm). They're the visual version of `.describe()` - they describe the minimum, Q1, median, Q3, and maximum.\n", "\n", "Well, **usually.**" ] }, { "cell_type": "code", "execution_count": 321, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 321, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df.boxplot(column='salary', sym='o', return_type='axes')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The box part is 25%-75%, with the red line being the median. The **whiskers** are usually the maximum and minimum, but `matplotlib`/`pandas` likes to display it as \"oh this is where nice values live\" (a.k.a. IQR 1.5). We can make it do max and min by passing `whis='range'` when we make the box plot." ] }, { "cell_type": "code", "execution_count": 322, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 322, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df.boxplot(column='salary', sym='o', whis='range', return_type='axes')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It might look a little bit better if we pull in an actual data set. Let's use those billionaires we worked on before." ] }, { "cell_type": "code", "execution_count": 323, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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52014Abdulla Al Futtaim687United Arab EmiratesARE2.500inheritedinheritedmalenan...relation1930.000nanauto dealers, investmentscompany split between him and cousin in 2000NaNhttp://en.wikipedia.org/wiki/Al-Futtaim_Grouphttp://www.al-futtaim.ae/content/groupProfile.aspNaNNaN
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" ], "text/plain": [ " year name rank citizenship countrycode \\\n", "1 2014 A. Jerrold Perenchio 663 United States USA \n", "5 2014 Abdulla Al Futtaim 687 United Arab Emirates ARE \n", "\n", " networthusbillion selfmade typeofwealth gender age ... \\\n", "1 2.600 self-made executive male 83.000 ... \n", "5 2.500 inherited inherited male nan ... \n", "\n", " relationshiptocompany foundingdate gdpcurrentus \\\n", "1 former chairman and CEO 1955.000 nan \n", "5 relation 1930.000 nan \n", "\n", " sourceofwealth notes \\\n", "1 television, Univision represented Marlon Brando and Elizabeth Taylor \n", "5 auto dealers, investments company split between him and cousin in 2000 \n", "\n", " notes2 source \\\n", "1 NaN http://en.wikipedia.org/wiki/Jerry_Perenchio \n", "5 NaN http://en.wikipedia.org/wiki/Al-Futtaim_Group \n", "\n", " source_2 \\\n", "1 http://www.forbes.com/profile/a-jerrold-perenc... \n", "5 http://www.al-futtaim.ae/content/groupProfile.asp \n", "\n", " source_3 source_4 \n", "1 COLUMN ONE; A Hollywood Player Who Owns the Ga... NaN \n", "5 NaN NaN \n", "\n", "[2 rows x 30 columns]" ] }, "execution_count": 323, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rich_df = pd.read_excel(\"rich_people.xlsx\")\n", "rich_df = rich_df[rich_df['year'] == 2014]\n", "rich_df.head(2)" ] }, { "cell_type": "code", "execution_count": 324, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Library/Frameworks/Python.framework/Versions/3.4/lib/python3.4/site-packages/numpy/lib/function_base.py:3823: RuntimeWarning: Invalid value encountered in percentile\n", " RuntimeWarning)\n" ] }, { "data": { "text/html": [ "
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count1578.0001578.0001578.0001578.0001578.00054.0001578.0001578.0000.000
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min2014.0001.0001.00024.0000.0001.0000.0001615.000nan
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" ], "text/plain": [ " year rank networthusbillion age north \\\n", "count 1578.000 1578.000 1578.000 1578.000 1578.000 \n", "mean 2014.000 805.160 3.958 63.393 0.577 \n", "std 0.000 463.300 5.857 13.154 0.494 \n", "min 2014.000 1.000 1.000 24.000 0.000 \n", "25% 2014.000 408.000 1.400 53.000 0.000 \n", "50% 2014.000 796.000 2.200 63.000 1.000 \n", "75% 2014.000 1210.000 3.700 73.000 1.000 \n", "max 2014.000 1565.000 76.000 98.000 1.000 \n", "\n", " politicalconnection founder foundingdate gdpcurrentus \n", "count 54.000 1578.000 1578.000 0.000 \n", "mean 1.000 0.519 1963.465 nan \n", "std 0.000 0.500 38.329 nan \n", "min 1.000 0.000 1615.000 nan \n", "25% nan 0.000 1948.000 nan \n", "50% nan 1.000 1973.000 nan \n", "75% nan 1.000 1991.000 nan \n", "max 1.000 1.000 2012.000 nan " ] }, "execution_count": 324, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rich_df = rich_df.dropna(subset=['age', 'networthusbillion', 'foundingdate'])\n", "rich_df.describe()" ] }, { "cell_type": "code", "execution_count": 325, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 325, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rich_df.boxplot(column='networthusbillion', whis='range', return_type='axes')" ] }, { "cell_type": "code", "execution_count": 326, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 326, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rich_df.boxplot(column='age', whis='range', return_type='axes')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Officializing the spread\n", "\n", "I'm going to steal a set of numbers from [Khan Academy](https://www.khanacademy.org/math/probability/descriptive-statistics/variance-std-deviation/v/range-variance-and-standard-deviation-as-measures-of-dispersion). Let's say we have two very boring sets of numbers." ] }, { "cell_type": "code", "execution_count": 327, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "list one is\n", "0 -10\n", "1 0\n", "2 10\n", "3 20\n", "4 30\n", "dtype: int64\n", "list two is\n", "0 8\n", "1 9\n", "2 10\n", "3 11\n", "4 12\n", "dtype: int64\n" ] } ], "source": [ "list_one = pd.Series([-10, 0, 10, 20, 30])\n", "list_two = pd.Series([8, 9, 10, 11, 12])\n", "print(\"list one is\")\n", "print(list_one)\n", "print(\"list two is\")\n", "print(list_two)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use their central tendencies to describe them." ] }, { "cell_type": "code", "execution_count": 328, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The mean of list_one is 10.0\n", "The mean of list_two is 10.0\n", "The median of list_one is 10.0\n", "The median of list_two is 10.0\n" ] } ], "source": [ "print(\"The mean of list_one is\", list_one.mean())\n", "print(\"The mean of list_two is\", list_one.mean())\n", "print(\"The median of list_one is\", list_one.median())\n", "print(\"The median of list_two is\", list_one.median())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Huh! But I mean, let's be honest: THESE LISTS OF NUMBERS ARE VERY DIFFERENT. If their central tendencies are the same, the way to describe them, then, is to talk about the *spread*, or how the actual numbers themselves are distributed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we learned about the **range** before, it's the difference between the smallest and largest number.\n", "\n", "* For `[-10, 0, 10, 20, 30]`, the range is `40`. It's much more dispersed.\n", "* For `[8, 9, 10, 11, 12]`, the range is `4`. It's much tighter.\n", "\n", "That's helpful! But there are more ways to measure the spread than just range.\n", "\n", "## Measures of spread\n", "\n", "Along with range, there are two other things we need to learn about how these numbers are distributed: **variance** and **standard deviation**.\n", "\n", "* **Range** is the difference between the largest and smallest number\n", "* **Variance** is difference between each data point and the mean, squared. And then you take the mean of that. *What* Yeah, I know, we'll break it down in a second.\n", "* **Standard deviation** is the square root of the variance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Variance\n", "\n", "Each data point, subtracted from the mean, squared, and then you add all that together. It looks like this:" ] }, { "cell_type": "code", "execution_count": 329, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "200.0" ] }, "execution_count": 329, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Data points [-10, 0, 10, 20, 30]\n", "# Mean: 10\n", "((-10 - 10)**2 + (0 - 10)**2 + (10 - 10)**2 + (20 - 10)**2 + (30 - 10)**2) / 5" ] }, { "cell_type": "code", "execution_count": 330, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "2.0" ] }, "execution_count": 330, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Data points [8, 9, 10, 11, 12]\n", "# Mean: 10\n", "((8 - 10)**2 + (9 - 10)**2 + (10 - 10)**2 + (11 - 10)**2 + (12 - 10)**2) / 5" ] }, { "cell_type": "code", "execution_count": 331, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "200.0\n", "2.0\n" ] } ], "source": [ "# And pandas agrees\n", "# Please don't ask why ddof=0 it has to do with sample variance\n", "print(list_one.var(ddof=0))\n", "print(list_two.var(ddof=0))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So first, the first data set has a much higher variance than the first variance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Standard deviation" ] }, { "cell_type": "code", "execution_count": 332, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import math" ] }, { "cell_type": "code", "execution_count": 333, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "14.142135623730951" ] }, "execution_count": 333, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Data points [-10, 0, 10, 20, 30]\n", "# Variance: 200\n", "math.sqrt(200)" ] }, { "cell_type": "code", "execution_count": 334, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "1.4142135623730951" ] }, "execution_count": 334, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Data points [8, 9, 10, 11, 12]\n", "# Variance: 2.0\n", "math.sqrt(2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The guy on Khan Academy is like \"Yeah! The first data set has ten times the standard deviation than the second data set!\" which he is really excited about. Since the standard deviation is 10x larger, think about it as \"generally, a data point in the first data set is 10x further from the mean than in the second data set.\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Measures of spread recap\n", "\n", "Range is easy. Variance and standard deviation are a little tougher - think of them as **measurements of how far away from the mean your data generally is**. High variance/standard deviation = numbers are generally spread out. Small variance/standard deviation = numbers are generally closer to the mean." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Finding outliers\n", "\n", "Standard deviation is helpful because it describes how far away from the mean your data generally is. We can use this to **find data points that are usually far from the mean.** These are outliers!" ] }, { "cell_type": "code", "execution_count": 335, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " year name rank citizenship countrycode \\\n", "516 2014 David Rockefeller, Sr. 580 United States USA \n", "1277 2014 Karl Wlaschek 305 Austria AUT \n", "1328 2014 Kirk Kerkorian 328 United States USA \n", "\n", " networthusbillion selfmade typeofwealth gender age \\\n", "516 2.900 inherited inherited male 98.000 \n", "1277 4.800 self-made founder non-finance male 96.000 \n", "1328 4.500 self-made self-made finance male 96.000 \n", "\n", " ... relationshiptocompany foundingdate gdpcurrentus \\\n", "516 ... relation 1870.000 nan \n", "1277 ... founder 1953.000 nan \n", "1328 ... investor 1924.000 nan \n", "\n", " sourceofwealth notes \\\n", "516 oil, banking family made most of fortune in the late 19th a... \n", "1277 retail NaN \n", "1328 casinos, investments purchased in 1969 \n", "\n", " notes2 source \\\n", "516 NaN http://en.wikipedia.org/wiki/David_Rockefeller \n", "1277 NaN http://en.wikipedia.org/wiki/BILLA \n", "1328 NaN http://en.wikipedia.org/wiki/Kirk_Kerkorian \n", "\n", " source_2 \\\n", "516 http://en.wikipedia.org/wiki/Standard_Oil \n", "1277 http://en.wikipedia.org/wiki/Karl_Wlaschek \n", "1328 http://www.forbes.com/profile/kirk-kerkorian/ \n", "\n", " source_3 source_4 \n", "516 http://en.wikipedia.org/wiki/Rockefeller_family NaN \n", "1277 https://www.billa.at/Footer_Nav_Seiten/Geschic... NaN \n", "1328 PROFILE: Las Vegas billionaire amassed his wea... NaN \n", "\n", "[3 rows x 30 columns]" ] }, "execution_count": 335, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rich_df.sort_values(by='age', ascending=False).head(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How strange is it that those old rich people are *so old*? We can see how many standard deviations they are away from the mean." ] }, { "cell_type": "code", "execution_count": 336, "metadata": { "collapsed": false }, "outputs": [], "source": [ "rich_df['age_std'] = ((rich_df['age'] - rich_df['age'].mean()).apply(abs) / rich_df['age'].std())" ] }, { "cell_type": "code", "execution_count": 337, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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12772014Karl Wlaschek305AustriaAUT4.800self-madefounder non-financemale96.000...1953.000nanretailNaNNaNhttp://en.wikipedia.org/wiki/BILLAhttp://en.wikipedia.org/wiki/Karl_Wlaschekhttps://www.billa.at/Footer_Nav_Seiten/Geschic...NaN2.479
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" ], "text/plain": [ " year name rank citizenship countrycode \\\n", "516 2014 David Rockefeller, Sr. 580 United States USA \n", "1277 2014 Karl Wlaschek 305 Austria AUT \n", "1328 2014 Kirk Kerkorian 328 United States USA \n", "\n", " networthusbillion selfmade typeofwealth gender age ... \\\n", "516 2.900 inherited inherited male 98.000 ... \n", "1277 4.800 self-made founder non-finance male 96.000 ... \n", "1328 4.500 self-made self-made finance male 96.000 ... \n", "\n", " foundingdate gdpcurrentus sourceofwealth \\\n", "516 1870.000 nan oil, banking \n", "1277 1953.000 nan retail \n", "1328 1924.000 nan casinos, investments \n", "\n", " notes notes2 \\\n", "516 family made most of fortune in the late 19th a... NaN \n", "1277 NaN NaN \n", "1328 purchased in 1969 NaN \n", "\n", " source \\\n", "516 http://en.wikipedia.org/wiki/David_Rockefeller \n", "1277 http://en.wikipedia.org/wiki/BILLA \n", "1328 http://en.wikipedia.org/wiki/Kirk_Kerkorian \n", "\n", " source_2 \\\n", "516 http://en.wikipedia.org/wiki/Standard_Oil \n", "1277 http://en.wikipedia.org/wiki/Karl_Wlaschek \n", "1328 http://www.forbes.com/profile/kirk-kerkorian/ \n", "\n", " source_3 source_4 age_std \n", "516 http://en.wikipedia.org/wiki/Rockefeller_family NaN 2.631 \n", "1277 https://www.billa.at/Footer_Nav_Seiten/Geschic... NaN 2.479 \n", "1328 PROFILE: Las Vegas billionaire amassed his wea... NaN 2.479 \n", "\n", "[3 rows x 31 columns]" ] }, "execution_count": 337, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rich_df.sort_values(by='age', ascending=False).head(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "They are **thirteen standard deviations away from the mean.** Generally, 3.0 is considered a crazy outlier. 1.5 is considered *maybe* an outlier, but probably not really. So no one's looking *crazy old* here.\n", "\n", "What about in terms of wealth?" ] }, { "cell_type": "code", "execution_count": 338, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 338, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rich_df['age'].plot(kind='box')" ] }, { "cell_type": "code", "execution_count": 339, "metadata": { "collapsed": true }, "outputs": [], "source": [ "rich_df['wealth_std'] = ((rich_df['networthusbillion'] - rich_df['networthusbillion'].mean()).apply(abs) / rich_df['networthusbillion'].std())" ] }, { "cell_type": "code", "execution_count": 340, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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yearnamerankcitizenshipcountrycodenetworthusbillionselfmadetypeofwealthgenderage...gdpcurrentussourceofwealthnotesnotes2sourcesource_2source_3source_4age_stdwealth_std
2842014Bill Gates1United StatesUSA76.000self-madefounder non-financemale58.000...nanMicrosoftNaNNaNhttp://www.forbes.com/profile/bill-gates/NaNNaNNaN0.41012.301
3482014Carlos Slim Helu2MexicoMEX72.000self-madeprivatized and resourcesmale74.000...nantelecomNaNNaNhttp://www.ozy.com/provocateurs/carlos-slims-w...NaNNaNNaN0.80611.618
1242014Amancio Ortega3SpainESP64.000self-madefounder non-financemale77.000...nanretailNaNNaNhttp://www.forbes.com/profile/amancio-ortega/NaNNaNNaN1.03410.252
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" ], "text/plain": [ " year name rank citizenship countrycode \\\n", "284 2014 Bill Gates 1 United States USA \n", "348 2014 Carlos Slim Helu 2 Mexico MEX \n", "124 2014 Amancio Ortega 3 Spain ESP \n", "\n", " networthusbillion selfmade typeofwealth gender age \\\n", "284 76.000 self-made founder non-finance male 58.000 \n", "348 72.000 self-made privatized and resources male 74.000 \n", "124 64.000 self-made founder non-finance male 77.000 \n", "\n", " ... gdpcurrentus sourceofwealth notes notes2 \\\n", "284 ... nan Microsoft NaN NaN \n", "348 ... nan telecom NaN NaN \n", "124 ... nan retail NaN NaN \n", "\n", " source source_2 source_3 \\\n", "284 http://www.forbes.com/profile/bill-gates/ NaN NaN \n", "348 http://www.ozy.com/provocateurs/carlos-slims-w... NaN NaN \n", "124 http://www.forbes.com/profile/amancio-ortega/ NaN NaN \n", "\n", " source_4 age_std wealth_std \n", "284 NaN 0.410 12.301 \n", "348 NaN 0.806 11.618 \n", "124 NaN 1.034 10.252 \n", "\n", "[3 rows x 32 columns]" ] }, "execution_count": 340, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rich_df.sort_values(by='wealth_std', ascending=False).head(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hey, look at that! They're crazy wealthy! It's OUT OF CONTROL! **THEY ARE SO WEALTHY**. **UNBELIEVABLE!!!!**\n", "\n", "We could also know that by looking at a simple histogram, of course." ] }, { "cell_type": "code", "execution_count": 341, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 341, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rich_df['networthusbillion'].hist()" ] }, { "cell_type": "code", "execution_count": 342, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 342, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rich_df['networthusbillion'].hist(bins=25)" ] }, { "cell_type": "code", "execution_count": 343, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 343, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rich_df['networthusbillion'].hist(bins=50)" ] }, { "cell_type": "code", "execution_count": 344, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "count 1578.000\n", "mean 3.958\n", "std 5.857\n", "min 1.000\n", "25% 1.400\n", "50% 2.200\n", "75% 3.700\n", "max 76.000\n", "Name: networthusbillion, dtype: float64" ] }, "execution_count": 344, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rich_df['networthusbillion'].describe()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Even though we have a ton of billionaires, basically everyone is a **baby billionaire** with barely billions of dollars. This is **skewed data**. Compare it with a histograph of age." ] }, { "cell_type": "code", "execution_count": 345, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 345, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rich_df['networthusbillion'].hist(bins=25)" ] }, { "cell_type": "code", "execution_count": 346, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 346, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "rich_df['age'].hist(bins=25)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Mostly billionaires are around 60, but sometimes they're younger or older. **This is something you can use simple summary statistics on**. The net worth data is **skewed**, and attempting to use your normal boring statistics on it is a [terrible mistake](https://www.ma.utexas.edu/users/mks/statmistakes/skeweddistributions.html).\n", "\n", "The age data is called a **normal distribution**. It's nice, it's pleasant, it's **normal.** You can do normal things with it, like look for outliers. Let's read in some NBA data and look for outliers." ] }, { "cell_type": "code", "execution_count": 347, "metadata": { "collapsed": false }, "outputs": [], "source": [ "nba_df = pd.read_csv(\"nba.csv\")" ] }, { "cell_type": "code", "execution_count": 348, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "count 528.000\n", "mean 221.206\n", "std 27.943\n", "min 20.000\n", "25% 200.000\n", "50% 220.000\n", "75% 240.000\n", "max 290.000\n", "Name: WT, dtype: float64" ] }, "execution_count": 348, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nba_df['WT'].describe()" ] }, { "cell_type": "code", "execution_count": 349, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 349, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "nba_df['WT'].hist()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That mostly looks clustered around one value. But what's that weird one? Let's grab a standard deviation for every point." ] }, { "cell_type": "code", "execution_count": 350, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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NameAgeTeamPOS#2013 $Ht (In.)WTEXP1st YearDOBSchoolCityState (Province, Territory, Etc..)CountryRaceHS Onlywt_std
40Taylor, Jermaine26CavaliersG8$780,87177204200912/8/1986Central FloridaTavares, FLFloridaUSBlackNo7.201
136Brown, Kwame3176ersC54$2,945,901832901220013/10/1982Glynn Adademy (GA)Charleston, SCSouth CarolinaUSBlackYes2.462
315Pekovi?, Nikola27TimberwolvesC14$12,000,00083290320101/3/1986n/aBijelo Poljen/aYugoslaviaWhiteNo2.462
374Jefferson, Al28BobcatsF/C25$13,500,00082289920041/4/1985Prentiss HS (MS)Monticello, MSMississippiUSBlackYes2.426
207Davis, Glen27MagicF/C11$6,400,00081289620071/1/1986LSUBaton Rouge, LALouisianaUSBlackNo2.426
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" ], "text/plain": [ " Name Age Team POS # 2013 $ Ht (In.) WT \\\n", "40 Taylor, Jermaine 26 Cavaliers G 8 $780,871 77 20 \n", "136 Brown, Kwame 31 76ers C 54 $2,945,901 83 290 \n", "315 Pekovi?, Nikola 27 Timberwolves C 14 $12,000,000 83 290 \n", "374 Jefferson, Al 28 Bobcats F/C 25 $13,500,000 82 289 \n", "207 Davis, Glen 27 Magic F/C 11 $6,400,000 81 289 \n", "\n", " EXP 1st Year DOB School City \\\n", "40 4 2009 12/8/1986 Central Florida Tavares, FL \n", "136 12 2001 3/10/1982 Glynn Adademy (GA) Charleston, SC \n", "315 3 2010 1/3/1986 n/a Bijelo Polje \n", "374 9 2004 1/4/1985 Prentiss HS (MS) Monticello, MS \n", "207 6 2007 1/1/1986 LSU Baton Rouge, LA \n", "\n", " State (Province, Territory, Etc..) Country Race HS Only wt_std \n", "40 Florida US Black No 7.201 \n", "136 South Carolina US Black Yes 2.462 \n", "315 n/a Yugoslavia White No 2.462 \n", "374 Mississippi US Black Yes 2.426 \n", "207 Louisiana US Black No 2.426 " ] }, "execution_count": 350, "metadata": {}, "output_type": "execute_result" } ], "source": [ "nba_df['wt_std'] = ((nba_df['WT'] - nba_df['WT'].mean()).apply(abs) / nba_df['WT'].std())\n", "nba_df.sort_values(by='wt_std', ascending=False).head(5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Jermaine Taylor has a weight that's **7 standard deviations away**, which means we should probably look at it.\n", "\n", "Oh look, he weighs 20 pounds. Does he actually weigh 20 pounds? We could do some research, but **I'm thinking he doesn't**. \n", "\n", "How about we get rid of everyone that's a bad outlier? We only have one guy so far, but we might as well." ] }, { "cell_type": "code", "execution_count": 351, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Only keep people with a standard deviation of less than three\n", "cleaned_nba_df = nba_df[nba_df['wt_std'] < 3]" ] }, { "cell_type": "code", "execution_count": 352, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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NameAgeTeamPOS#2013 $Ht (In.)WTEXP1st YearDOBSchoolCityState (Province, Territory, Etc..)CountryRaceHS Onlywt_std
315Pekovi?, Nikola27TimberwolvesC14$12,000,00083290320101/3/1986n/aBijelo Poljen/aYugoslaviaWhiteNo2.462
136Brown, Kwame3176ersC54$2,945,901832901220013/10/1982Glynn Adademy (GA)Charleston, SCSouth CarolinaUSBlackYes2.462
374Jefferson, Al28BobcatsF/C25$13,500,00082289920041/4/1985Prentiss HS (MS)Monticello, MSMississippiUSBlackYes2.426
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" ], "text/plain": [ " Name Age Team POS # 2013 $ Ht (In.) WT \\\n", "315 Pekovi?, Nikola 27 Timberwolves C 14 $12,000,000 83 290 \n", "136 Brown, Kwame 31 76ers C 54 $2,945,901 83 290 \n", "374 Jefferson, Al 28 Bobcats F/C 25 $13,500,000 82 289 \n", "\n", " EXP 1st Year DOB School City \\\n", "315 3 2010 1/3/1986 n/a Bijelo Polje \n", "136 12 2001 3/10/1982 Glynn Adademy (GA) Charleston, SC \n", "374 9 2004 1/4/1985 Prentiss HS (MS) Monticello, MS \n", "\n", " State (Province, Territory, Etc..) Country Race HS Only wt_std \n", "315 n/a Yugoslavia White No 2.462 \n", "136 South Carolina US Black Yes 2.462 \n", "374 Mississippi US Black Yes 2.426 " ] }, "execution_count": 352, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cleaned_nba_df.sort_values(by='wt_std', ascending=False).head(3)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we got rid of some people, we can also recalculate the standard deviation! Remember, standard deviation is a relationship to the **mean**, and **outliers move the mean**." ] }, { "cell_type": "code", "execution_count": 353, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Library/Frameworks/Python.framework/Versions/3.4/lib/python3.4/site-packages/ipykernel/__main__.py:1: SettingWithCopyWarning: \n", "A value is trying to be set on a copy of a slice from a DataFrame.\n", "Try using .loc[row_indexer,col_indexer] = value instead\n", "\n", "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy\n", " if __name__ == '__main__':\n" ] }, { "data": { "text/html": [ "
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NameAgeTeamPOS#2013 $Ht (In.)WTEXP1st YearDOBSchoolCityState (Province, Territory, Etc..)CountryRaceHS Onlywt_stdnew_wt_std
315Pekovi?, Nikola27TimberwolvesC14$12,000,00083290320101/3/1986n/aBijelo Poljen/aYugoslaviaWhiteNo2.4622.576
136Brown, Kwame3176ersC54$2,945,901832901220013/10/1982Glynn Adademy (GA)Charleston, SCSouth CarolinaUSBlackYes2.4622.576
207Davis, Glen27MagicF/C11$6,400,00081289620071/1/1986LSUBaton Rouge, LALouisianaUSBlackNo2.4262.539
374Jefferson, Al28BobcatsF/C25$13,500,00082289920041/4/1985Prentiss HS (MS)Monticello, MSMississippiUSBlackYes2.4262.539
205Hamilton, Justin23HeatC7$490,18084155020134/1/1990LSUNewport Beach, CACaliforniaUSBlackNo2.3692.508
\n", "
" ], "text/plain": [ " Name Age Team POS # 2013 $ Ht (In.) WT \\\n", "315 Pekovi?, Nikola 27 Timberwolves C 14 $12,000,000 83 290 \n", "136 Brown, Kwame 31 76ers C 54 $2,945,901 83 290 \n", "207 Davis, Glen 27 Magic F/C 11 $6,400,000 81 289 \n", "374 Jefferson, Al 28 Bobcats F/C 25 $13,500,000 82 289 \n", "205 Hamilton, Justin 23 Heat C 7 $490,180 84 155 \n", "\n", " EXP 1st Year DOB School City \\\n", "315 3 2010 1/3/1986 n/a Bijelo Polje \n", "136 12 2001 3/10/1982 Glynn Adademy (GA) Charleston, SC \n", "207 6 2007 1/1/1986 LSU Baton Rouge, LA \n", "374 9 2004 1/4/1985 Prentiss HS (MS) Monticello, MS \n", "205 0 2013 4/1/1990 LSU Newport Beach, CA \n", "\n", " State (Province, Territory, Etc..) Country Race HS Only wt_std \\\n", "315 n/a Yugoslavia White No 2.462 \n", "136 South Carolina US Black Yes 2.462 \n", "207 Louisiana US Black No 2.426 \n", "374 Mississippi US Black Yes 2.426 \n", "205 California US Black No 2.369 \n", "\n", " new_wt_std \n", "315 2.576 \n", "136 2.576 \n", "207 2.539 \n", "374 2.539 \n", "205 2.508 " ] }, "execution_count": 353, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cleaned_nba_df['new_wt_std'] = ((cleaned_nba_df['WT'] - cleaned_nba_df['WT'].mean()).apply(abs) / cleaned_nba_df['WT'].std())\n", "cleaned_nba_df.sort_values(by='new_wt_std', ascending=False).head(5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So now it's a little bit crazier to be so far from the mean, but generally things are all legitimate and pleasant." ] }, { "cell_type": "code", "execution_count": 354, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 354, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Histogram of weights with uncleaned data\n", "nba_df['WT'].hist()" ] }, { "cell_type": "code", "execution_count": 355, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 355, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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sTBN+T19ERDKhpl8ilzlfLjlzme8qZ51C6gBR8tlD1ajpi4i0iGb6Y0ozfdVrfr1uTfWB\nldFMX0REoqnpl8hlzpdLzlzmu8pZp5A6QJR89lA1avoiIi2imf6Y0kxf9Zpfr1tTfWBlNNMXEZFo\navolcpnz5ZIzl/muctYppA4QJZ89VI2avohIi2imP6Y001e95tfr1lQfWBnN9EVEJJqafolc5ny5\n5MxlvqucdQqpA0TJZw9Vo6YvItIimumPKc30Va/59bo11QdWRjN9ERGJpqZfIpc5Xy45c5nvKmed\nQuoAUfLZQ9VMpA7QFlNT0ywu7k8dQ0RaTjP9ERn/Gbtm+qq3uppt6gN10ExfRESiqemXyGfOF1IH\niBRSB4gUUgeIFFIHiBBSB4iSz16vRk1fRKRFNNMfEc30x6Gm6g2jZpv6QB000xcRkWhq+iXymfOF\n1AEihdQBIoXUASKF1AEihNQBouSz16tR0xcRaRHN9EdEM/1xqKl6w6jZpj5Qh2QzfTNbZ2Y7zOwh\nM9ttZlcXx9eY2TYz22dmd5nZSautISIi9aoy3jkMfNTdzwfeAnzIzM4BNgLb3f1sYAewqXrMdPKZ\n84XUASKF1AEihdQBIoXUASKE1AGi5LPXq1l103f3Q+4+X1z/FbAXWAdcAWwt7rYVuLJqSBERqUct\nM30zm6b77fy3gAPuvqbntsfc/eQBj9FMf7gVx7xeipqqV7+XAk+NrNratWdy6NDCyOoNQ9WZfuV3\n2TSzlwNfA65x91+ZWf9XTXs6u4is0FOMskUsLq66V46NSk3fzCboNvwvufudxeFFM1vr7otmNgX8\nbLnHz87OMj09DcDk5CQzMzN0Oh3gyHwt9XrpWNWP1xWATs91alzfBMz0rIddr38dW2/pWF31Kbl9\ntev+8znsesuty+otHRtVvdWsez/2KOodbV2sBuzX+fl5rr322mVvT7UOITA3NwfwfL+sotJ4x8y+\nCPzc3T/ac2wL8Ji7bzGzDcAad9844LFZjHdCCH2Ne3WGP94JvLABN3U0EHhhzlHUXI3Ai3M28ZwG\nmn8+A8tnHP05Xa7v1LXXh63qeGfVTd/M3gp8B9hN97PmwPXAfcDtwOnAfmC9u/9ywOOzaPp10Ux/\nHGqqXv418/+7gGRNvyo1/aFXHPN6KWqqXv411fT1Ngwl8vnd3ZA6QKSQOkCkkDpApJA6QISQOkCU\nfPZ6NWr6IiItovHOiGi8Mw41VS//mhrv6Jm+iEiLqOmXyGfOF1IHiBRSB4gUUgeIFFIHiBBSB4iS\nz16vRk1fRKRFNNMfEc30x6Gm6uVfUzN9PdMXEWkRNf0S+cz5QuoAkULqAJFC6gCRQuoAEULqAFHy\n2evVqOmLiLSIZvojopn+ONRUvfxraqavZ/oiIi2ipl8inzlfSB0gUkgdIFJIHSBSSB0gQkgdIEo+\ne70aNX0RkRbRTH9ENNMfh5qql39NzfT1TF9EpEXU9EvkM+cLqQNECqkDRAqpA0QKqQNECKkDRMln\nr1ejpi8i0iKa6Y+IZvrjUFP18q/5UuCpkVVbu/ZMDh1aqPVj6t/IzYSa/jjUVL38a+b/wrFeyB2y\nfOZ8IXWASCF1gEghdYBIIXWACCF1gEghdYCRUNMXEWkRjXdGROOdcaipevnX1HhHz/RFRFpkInWA\nFJ588kkWFxej7nvvvfdy0UUXDTlRHQLQSZwhRkA56xRofs5A8zNCPjmraWXTv+SSP+KBB/Zw7LEv\nLb3v4cP/x8TECZXqPf30zys9XkSkLq2c6Z999oX88IefAy4cSb2JiY9x+PCnGPfZpebBqtf8mprp\na6YvItIiQ2v6ZnapmT1sZj80sw3DqjN8IXWASCF1gEghdYBIIXWASCF1gAghdYBIIXWAkRhK0zez\nY4DPAe8Czgfea2bnDKPW8M2nDhBJOeulnPXJISPkk7OaYT3TvxB4xN33u/szwG3AFUOqNWS/TB0g\nknLWSznrk0NGyCdnNcNq+qcBB3rWPymOiYhIQq38lc3jj38JL3vZRzn22DWl9/31r3dx4ok/qFTv\n6af3cPhwpQ8RYWHYBWqykDpApIXUASItpA4QYSF1gEgLqQOMxFB+ZdPM3gz8rbtfWqw3Au7uW3ru\n0573YBARqVHj3lrZzI4F9gEXAz8F7gPe6+57ay8mIiLRhjLecfdnzeyvgG10Xze4WQ1fRCS9ZH+R\nKyIiozfMP8662cwWzezBAbf9tZk9Z2Yn9xzbZGaPmNleM7tkWLlic5rZh4ssu81scxNzmtkFZnaf\nme0q/vumlDnNbJ2Z7TCzh4rzdnVxfI2ZbTOzfWZ2l5md1LCcHy6O31jkmDezr5vZKxuW8+q+2xux\nj46Wsyn76Chfmxc2bA8db2b3FnkeMrNPFMfr20PuPpQL8DZgBniw7/g64D+AHwMnF8fOBXbRHTdN\nAz+i+Clk2JdBOem+1d42YKJYv6qhOXcClxTXLwN2FtfPS5ETmAJmiusvp/u6zjnAFuBjxfENwOaG\n5nwHcExxfDPwySbmLNaN2UdHOZ+N2UcDMj5c5GjUHipqn1j891jgHuCtde6hoT3Td/fvAo8PuOmz\nwHV9x64AbnP3w+6+ADzCiN4NbZmcf0n3pB4u7rP0NplNy/lTYOk7/iRwsLh+eYqc7n7I3eeL678C\n9tJtTlcAW4u7bQWubGDO09x9u7s/V9ztniJ743IWNzdmHx0lZ2P20YCMDwO/QXcPTRZ3S76Hiny/\nLq4eT3ca8zg17qGRvuGamV0OHHD33X039f8x10HS/jHXa4HfM7N7zGynmb2xON60nBuBz5jZo8CN\nwKbiePKcZjZN9yeTe4C17r4I3c0HnFrcrUk57+276Srg28X1RuVs8j7qO5+N3Ed9GTcCn27SHjKz\nY8xsF3AICO6+hxr30MiavpmdAFwP3DCqmhVMAGvc/c3Ax4A7EudZzs3Ah939DOAjwL8kzgOAmb0c\n+BpwTfGsqv+3BRrx2wMDci4d/zjwjLt/JVm4Hr05gWdp6D4acD4bt48GZGzcHnL359z9DXR/0vxd\nM+tQ4x4a5TP919CdOT1gZj+m+z90v5mdSve70xk9913HkR+zUjgAfAPA3b8HPGtmp9C8nBe5+78D\nuPvXgAuK4weB03vuN7KcZjZBd1N9yd3vLA4vmtna4vYp4GcNzYmZzQLvBt7Xc/cm5WzkPlrmfDZq\nHy2TsXF7aIm7/y/dnzbfRJ17aMgvSEwDu5e57cd0nwXAkRcjjgPOYoQvmgzKCfwF8HfF9dcC+xua\n8wfA24vrFwPfS50T+CLwmb5jW4ANvvyLUE3JeSnwEHBK3/FG5ey7vRH7aJnz2ah9tEzGRu0h4FXA\nScX1E4DvFLlq20PDDH8r8D/AU8CjwJ/23f7fFL91UKw3FYH3UryaPqIv1hflpPtj6ZeA3cD3l74o\nGpjzjXTnkruAu4E3pMxJ97cMnqX7HrW7gPuLRnoysJ3ub3VsAyYbmPMyui+C7S/W9wOfb2DOS/vu\nk3wfHeXz/pKm7KOjZGzaHvrtItsu4AHgb4rjte0h/XGWiEiL6J9LFBFpETV9EZEWUdMXEWkRNX0R\nkRZR0xcRaRE1fRGRFlHTFxFpETV9EZEW+X8lwmdnfrOlpAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Histogram of weights with cleaned data\n", "cleaned_nba_df['WT'].hist()" ] }, { "cell_type": "code", "execution_count": 356, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 356, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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iyUWr7Kmyy68yKbl8jckZ+hu616RBMdC1yu4CfhM4WxOPAr+Aga6BMtC1yu4HXgD863lj\nP6yqs1Nj3qyhQfDGIklqhGfoktQIA12SGmGgS1IjDHRJaoSBLkmNMNAlqREGuiQ1wkCXpEb8L1O1\nXjmX3cJ9AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Box-and-whisker plot of weights with uncleaned data\n", "nba_df['WT'].plot(kind='box', whis='range')" ] }, { "cell_type": "code", "execution_count": 357, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 357, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Box-and-whisker plot of weights with cleaned data\n", "cleaned_nba_df['WT'].plot(kind='box', whis='range')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See how pleasant that is? So pleasant." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.4.2" } }, "nbformat": 4, "nbformat_minor": 0 }