The Normal Distribution, Clearly Explained!!! — Transcript

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1. 0:00static which makes me crazy when it's
2. 0:02upside-down stack which makes me bonkers
3. 0:06when it's upside-down
4. 0:08stack West hello and welcome to stack
5. 0:13quest stack quest is brought to you by
6. 0:16the friendly folks in the genetics
7. 0:18department at the University of North
8. 0:20Carolina at Chapel Hill
9. 0:22today we're going to be talking about
10. 0:24the normal distribution this is part one
11. 0:26of a handful of stack quests on this
12. 0:28distribution because it's so darn
13. 0:30important today let's just start with
14. 0:32the basics chances are you've seen a
15. 0:35normal or Gaussian distribution before
16. 0:38it's also called
17. 0:40a bell-shaped curve because it's a
18. 0:42symmetrical curve that wait for it looks
19. 0:46like a bell in this example the curve
20. 0:50represents human height measurements
21. 0:52people can be short average or tall or
22. 0:56anywhere in between the y-axis
23. 1:00represents the relative probability of
24. 1:02observing someone who is really short or
25. 1:05really tall or who has an average height
26. 1:08for example it's relatively rare to see
27. 1:11someone who is super short
28. 1:13so the bell-shaped curve is relatively
29. 1:16low in this part of the graph but it's
30. 1:19quite common to see someone who is close
31. 1:22to the average height so the bell-shaped
32. 1:24curve is very tall in this region and
33. 1:26it's relatively rare to see someone who
34. 1:29is really tall so again the bell-shaped
35. 1:32curve is relatively low in this region
36. 1:35here are two normal distributions of the
37. 1:39height of male humans when born and as
38. 1:42adults this is the distribution for the
39. 1:45babies and this is the distribution for
40. 1:48the adults the average baby height is 20
41. 1:52inches the average adult height is 70
42. 1:56inches normal distributions are always
43. 2:00centered on the average value just by
44. 2:04looking at the graph we can tell there
45. 2:06is a high probability that a newborn
46. 2:08baby will be between 19 and 21 inches
47. 2:12tall
48. 2:13in contrast adults are between 60 and 80
49. 2:17inches tall you may have noticed that
50. 2:20the curve for babies is way tall
51. 2:22compared to the curve for adults this is
52. 2:25because there are many more
53. 2:26possibilities for adult height than for
54. 2:29babies the more options there are for
55. 2:32height the less likely any specific
56. 2:35measurement will be one of them
57. 2:38the width of the curve is defined by the
58. 2:41standard deviation we can tell just by
59. 2:44looking at the curves that babies have a
60. 2:46relatively small standard deviation
61. 2:48compared to adults the standard
62. 2:51deviation for babies is 0.6 the standard
63. 2:56deviation for adults is 4 knowing the
64. 3:00standard deviation is helpful because
65. 3:02normal curves are drawn such that 95% of
66. 3:05the measurements fall between plus or
67. 3:08minus two standard deviations around the
68. 3:10mean
69. 3:11this means that 95% of the baby
70. 3:14measurements fall between 20 plus or
71. 3:17minus 1.2 inches and 95% of the adult
72. 3:22measurements fall between 70 plus or
73. 3:25minus 8 inches to draw a normal
74. 3:29distribution you need to know one
75. 3:32the average measurement this tells you
76. 3:35where the center of the curve goes to
77. 3:39the standard deviation of the
78. 3:41measurements this tells you how wide the
79. 3:43curve should be and the width of the
80. 3:46curve determines how tall it is the
81. 3:49wider the curve the shorter the narrower
82. 3:52the curve the taller the curves then
83. 3:56tell us that there is a high probability
84. 3:58of measuring a newborn baby boy within
85. 4:01plus or minus 1.2 inches of the mean
86. 4:06and there's a low probability of
87. 4:08measuring a man within plus or minus 1.2
88. 4:11inches of the mean
89. 4:14lots of things are normally distributed
90. 4:16we've been talking about height but
91. 4:19there's also weight commuting times and
92. 4:24many many many many many many many more
93. 4:27things the normal distribution is kind
94. 4:31of magical in that we see it a lot in
95. 4:34nature but there's a reason for that and
96. 4:37that reason makes it super useful for
97. 4:40statistics as well spoiler alert it's
98. 4:44called the central limit theorem I'm
99. 4:47already working on a whole stack quest
100. 4:49on the central limit theorem so that's
101. 4:51something we can all look forward to
102. 4:53hooray
103. 4:55we've made it to the end of another
104. 4:56exciting stat quest if you like this
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109. 5:08below until next time quest on