Introductory Statistics. Lecture 1 Sinan Hanay
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1 Introductory Statistics Lecture 1 Sinan Hanay
2 Image: wikipedia.org
3 There are three kinds of lies: Image: wikipedia.org
4 There are three kinds of lies: lies, Image: wikipedia.org
5 There are three kinds of lies: lies, damned lies, Image: wikipedia.org
6 There are three kinds of lies: lies, damned lies, and statistics. Image: wikipedia.org
7 There are three kinds of lies: lies, damned lies, and statistics. Mark Twain Image: wikipedia.org
8 Statistics Does Not Lie
9 but, what is Statistics?
10 Before that, what can Statistics do?
11 Statistics The heart of Data Science, Machine Learning Machine Learning The process of learning patterns by computer Some examples: Google Translate Google Driverless Car
12 Google driverless car completed 500,000 km accident-free
13
14
15
16 Watch movies online (or rent DVDs, like Tsutaya, Hulu)
17 Why Netflix Is #1?
18 Alternatives Why Netflix Is #1?
19 Why Netflix Is #1? Alternatives Amazon Prime, itunes, Hulu, Vudu, PSN,
20 Why Netflix Is #1? Alternatives Amazon Prime, itunes, Hulu, Vudu, PSN, May have many answers: price, amount of movies
21 Why Netflix Is #1? Alternatives Amazon Prime, itunes, Hulu, Vudu, PSN, May have many answers: price, amount of movies One cool feature of Netflix
22 Why Netflix Is #1? Alternatives Amazon Prime, itunes, Hulu, Vudu, PSN, May have many answers: price, amount of movies One cool feature of Netflix Movie recommendation system
23 Netflix Competition
24 movies watched Netflix Competition
25 Netflix Competition movies watched Develop a suggestion system that improves 10%
26 Netflix Competition movies watched the movies suggested Develop a suggestion system that improves 10%
27 Netflix Competition movies watched the movies suggested e z i r P r a l l o D n o i l l i M 1 Develop a suggestion system that improves 10%
28 How Does It Work? Machine Learning Based on Statistical Inference Other applications Credit score Amazon recommendation Travel sites: price predictors
29 Photo: wikipedia.org
30 Flight from Brasil to France on 31 May 2009 Photo: wikipedia.org
31 Flight from Brasil to France on 31 May 2009 Lost contact after a few hours Photo: wikipedia.org
32 Flight from Brasil to France on 31 May 2009 Lost contact after a few hours Five days later, the first wreckage was discovered Photo: wikipedia.org
33 Flight from Brasil to France on 31 May 2009 Lost contact after a few hours Five days later, the first wreckage was discovered What was the cause of the accident? Photo: wikipedia.org
34 The Cause Photo: wikipedia.org
35 The Cause They had to find the voice recorder (i.e. black box) Photo: wikipedia.org
36 Image: wikipedia.org
37 Image: wikipedia.org
38 Image: wikipedia.org 6,300 square km search area
39 Search for the Black Box By April 2011, it was still not found (22 months after the crash) Metron started to search using a statistical method In one week, a huge part of wreckage In May 2011, the black box was found
40 Probability What is the probability of at least two people having the same birthday in this class?(i.e. same month and day) Guess?
41 For 23 people, it is 50% For 30 people, it is 70% For 66 people, it is 99%
42 Statistics for Experiments Uncertainties in experiments and populations Image: freerangestock.com
43 Expressing Values
44 Expressing Values Is this 6.80 or 6.89 grams?
45 Expressing Values Is this 6.80 or 6.89 grams? Display shows only one digit
46 Expressing Values Is this 6.80 or 6.89 grams? Display shows only one digit Furthermore, the device rounds up or rounds down?
47 Expressing Values Is this 6.80 or 6.89 grams? Display shows only one digit Furthermore, the device rounds up or rounds down? Both are possible
48 Expressing Values Is this 6.80 or 6.89 grams? Display shows only one digit Furthermore, the device rounds up or rounds down? Both are possible It can be even 6.71 grams
49 Expressing Values Is this 6.80 or 6.89 grams? Display shows only one digit Furthermore, the device rounds up or rounds down? Both are possible It can be even 6.71 grams Express as 6.8 ± 0.1 g
50 Measure Length Image: flicker.com
51 Image: ebay.com
52 Image: ebay.com
53 Image: ebay.com
54 Thermal Expansion Image: ebay.com
55 Systematic Error Thermal Expansion Image: ebay.com
56 Statistics cannot fix systematic errors.
57 Systematic Error Statistics cannot eliminate systematic errors You need to calibrate the measurement devices Accurate measurements
58 Are we done, after fixing devices?
59 Photo: rolex.com
60 could be perfectly accurate but not precise enough Photo: rolex.com
61 Random Errors could be perfectly accurate but not precise enough Photo: rolex.com
62 Random Errors Maybe you have the perfect device. Photo: riverviews.net Photo: timex.com
63 Random Errors Maybe you have the perfect device. Photo: riverviews.net Photo: timex.com
64 Random Errors But you are not Maybe you have the perfect device. punctual enough Photo: riverviews.net Photo: timex.com
65 Random Errors Depends on the measurement Fortunately, Statistics can reduce the uncertainty
66 What Is Statistics? Statistics emerged as a communication tool Censuses as early as 3000 BC in Egypt
67 Data Name Height Acker Alex NBA players How do we summarize? Adams Hassan 1.93 Afflalo Arron 1.96 Young Nick 1.98 Young Thaddeus 2.03
68 Centrality - Mean Name Height mean = sum of heights players Acker Alex 1.96 Adams Hassan 1.93 Afflalo Arron NBA players Young Nick 1.98 Young Thaddeus 2.03
69 Centrality - Mean Name Height mean = sum of heights players Acker Alex 1.96 Adams Hassan 1.93 Afflalo Arron NBA players ( ) / 436 = 2.01 meters Young Nick 1.98 Young Thaddeus 2.03
70 Centrality - Median Name Height Sort heights Mode: value in the middle Acker Alex 1.96 Adams Hassan 1.93 Afflalo Arron NBA players Young Nick 1.98 Young Thaddeus 2.03
71 Centrality - Median Name Height Sort heights Mode: value in the middle Acker Alex 1.96 Adams Hassan 1.93 Afflalo Arron NBA players Young Nick 1.98 Median= 2.03 meters Young Thaddeus 2.03
72 Centrality - Mode Name Height Acker Alex 1.96 Mode: Most frequent value Adams Hassan 1.93 Afflalo Arron NBA players Young Nick 1.98 Young Thaddeus 2.03
73 Centrality - Mode Name Height Acker Alex 1.96 Mode: Most frequent value Adams Hassan 1.93 Afflalo Arron NBA players Mode= 2.06 meters Young Nick 1.98 Young Thaddeus 2.03
74 Example 1 Shoe Size Mean 27 Median 28 Mode 29
75 Example 1 You own a shoe store Shoe Size Mean 27 Median 28 Mode 29
76 Example 1 You own a shoe store Shoe Size Can only manufacture one size Mean 27 Median 28 Mode 29
77 Example 1 You own a shoe store Shoe Size Can only manufacture one size Fitting should be exact Mean 27 Median 28 Mode 29
78 Example 1 You own a shoe store Shoe Size Can only manufacture one size Fitting should be exact Mean 27 Median 28 Which size would you set? Mode 29
79 Example 1 You own a shoe store Shoe Size Can only manufacture one size Fitting should be exact Mean 27 Median 28 Which size would you set? You should choose mode, 29. Mode 29
80 Example 2 Salary (M yen) Mean 5 Median 4.5 Mode 3.5
81 Example 2 Salary (M yen) You are a governor of 1,000 people Mean 5 Median 4.5 Mode 3.5
82 Example 2 Salary (M yen) You are a governor of 1,000 people You need to collect a tax of 1 billion yen Mean 5 Median 4.5 Mode 3.5
83 Example 2 Salary (M yen) You are a governor of 1,000 people You need to collect a tax of 1 billion yen Only fixed percentage Mean 5 Median 4.5 Mode 3.5
84 Example 2 Salary (M yen) You are a governor of 1,000 people You need to collect a tax of 1 billion yen Only fixed percentage Mean 5 Median 4.5 Not high, not low Mode 3.5
85 Example 2 Salary (M yen) You are a governor of 1,000 people You need to collect a tax of 1 billion yen Only fixed percentage Mean 5 Median 4.5 Not high, not low You should consider mean, and set tax as 20%. Mode 3.5
86 Is Centrality Enough? Yearly Salaries (million yen) Mean, mode and median are same Country A Country B Mean: 4.20 Median: 4 Mode: 4 Are they equal?
87 Is Centrality Enough? Yearly Salaries (million yen) Mean, mode and median are same Country A Country B Mean: 4.20 Median: 4 Mode: No, we need another measure Are they equal?
88 Measure of Dispersion Salary A Difference from Mean Salary B Difference from Mean Mean: sum of differences, A: = 3.6 sum of differences, B: = 11.6
89 Variance It is rather subjective However, Statisticians use something different Instead of differences, take squares of differences sum of differences, A: = 3.2 use squares, = 4.8 Finally, divide by number of elements, 4.8/5= 0.96 Var(A) = 0.96, Var(B) = 9.76 or σ 2 (A) = 0.96, σ 2 (B) = 9.76
90 Mean: 4.20 Median: 4 Mode: 4 σ 2 (A) = 0.96 σ 2 (B) = 9.76 What is σ? Yearly Salaries (million yen) Country A Country B
91 Mean: 4.20 Median: 4 Mode: 4 σ 2 (A) = 0.96 σ 2 (B) = 9.76 What is σ? Yearly Salaries (million yen) Country A Country B
92 Standard Deviation Denoted by σ Square root of variance (σ 2 ) A measure of dispersion
93 Overview Why we need Statistics? What is Statistics? Reading Assignment: Sections from the book Download and install R and Rstudio
94 The End
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