Standard deviation (simply explained) — Transcript

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1. 0:00Today is about standard deviation. After
2. 0:03this video, you will know what standard
3. 0:05deviation is, how you can calculate it,
4. 0:08and why there are two different
5. 0:10formulas. And finally, what is the
6. 0:13difference to the variance? At the end
7. 0:15of this video, I have a tip for you. So,
8. 0:18let's get started. So, what is the
9. 0:20standard deviation? The standard
10. 0:22deviation is a measure of how much your
11. 0:25data scatters around the mean. So the
12. 0:28standard deviation has something to do
13. 0:31with the scatter of your data. For
14. 0:33example, how different the answers of
15. 0:36your respondents are. Here's an example.
16. 0:40Let's say you measure the hate of a
17. 0:43small group of people.
18. 0:45The standard deviation tells us how much
19. 0:48your data scatters around the mean. So
20. 0:51we first need to calculate the mean. You
21. 0:54can get a mean simply by summing the
22. 0:57hats of all individuals and dividing it
23. 1:01by the number of individuals.
24. 1:04Let's say we get a mean value of 155 cm.
25. 1:09Now we want to know how much each person
26. 1:12deviates from the mean. So we look at
27. 1:15the first person who deviates 18 cm from
28. 1:19the mean value. The second person
29. 1:22deviates 8 cm from the mean value and so
30. 1:27on. Finally, person number six deviates
31. 1:316 cm from the mean value. So simply
32. 1:35said, people that are very small or very
33. 1:38tall deviate more from the mean value.
34. 1:42Now, of course, you're not interested in
35. 1:44the deviation of each individual person
36. 1:47from the mean value, but you want to
37. 1:50know how much the persons deviate from
38. 1:52the mean value on average.
39. 1:55So, how much do these persons on average
40. 1:59deviate from the mean value? This is
41. 2:01what the standard deviation tells us. In
42. 2:04our example, the average deviation from
43. 2:07the mean value is 12.06 06 cm. And now
44. 2:12of course the next question is how can
45. 2:14we calculate the standard deviation? You
46. 2:17can calculate the standard deviation
47. 2:20with the following formula.
48. 2:22Sigma is the standard deviation.
49. 2:25N is the number of persons. Xi is the
50. 2:29size of one single person and Xdash is
51. 2:32the mean value of all people.
52. 2:36So the standard deviation is the root of
53. 2:39the sum of squared deviations divided by
54. 2:43the number of values.
55. 2:45For our example, this means that we
56. 2:48calculate the size of the first person
57. 2:50minus the mean and square that. Then the
58. 2:54size of the second person minus the mean
59. 2:56and then square that and so on until we
60. 3:00arrive at the last person.
61. 3:02Then we divide this number by the number
62. 3:04of people. So six and take the root of
63. 3:08it. The result is then 12.06
64. 3:12cm.
65. 3:14So each individual person has some
66. 3:16deviation from the mean. But on average
67. 3:20the people deviate 12.06
68. 3:23cm from the mean which is now our
69. 3:26standard deviation.
70. 3:28Now you might notice one thing. I always
71. 3:31talk about the average deviation from
72. 3:34the mean. But for the average deviation,
73. 3:37I would actually just add up all
74. 3:40deviations and divide it by the number
75. 3:43of participants just like you calculate
76. 3:46a mean value, right? You're absolutely
77. 3:49right. But there are different mean
78. 3:51values. In the case of the standard
79. 3:54deviation, it's not the arithmetic mean
80. 3:57which is used but the quadratic mean. If
81. 4:00the arithmetic mean would be used, the
82. 4:03result would be zero every time.
83. 4:07So far so good, but now there's one more
84. 4:09thing to consider. There are two
85. 4:12slightly different formulas for the
86. 4:14standard deviation. In the first formula
87. 4:17there is a deviation by n and in the
88. 4:19other one there is a deviation by n
89. 4:22minus one. But why that why are there
90. 4:26two different formulas?
91. 4:28Usually you want to know the standard
92. 4:30deviation of the whole population. For
93. 4:32example, you want to know the standard
94. 4:34deviation of hate of all American
95. 4:37professional soccer players.
96. 4:40Now, if you had the hate of all American
97. 4:43soccer players, you would take this
98. 4:45equation with one divided by n.
99. 4:50However, it is usually not possible to
100. 4:53investigate the entire population. So,
101. 4:56you take a sample.
102. 4:58Then you use this sample to estimate the
103. 5:01standard deviation of the population. In
104. 5:04that case, you use this formula.
105. 5:07Therefore, whenever you have data of the
106. 5:09whole population and you want to
107. 5:12calculate the standard deviation for
108. 5:14just this data, you use 1 divided by n.
109. 5:18Therefore, whenever you have data of the
110. 5:21whole population and you want to
111. 5:24calculate the standard deviation for
112. 5:26just this data, you use 1 divided by n.
113. 5:32If you only have one sample and you want
114. 5:34to estimate the standard deviation, you
115. 5:37use n minus one. So to keep it simple,
116. 5:41if your survey doesn't cover the whole
117. 5:43population, you always use the formula
118. 5:46on the right side.
119. 5:48Likewise, if you have conducted a
120. 5:51clinical study, for example, then you
121. 5:53also use the formula on the right side
122. 5:56to inferior the population.
123. 5:59Let's look at the next question now.
124. 6:01What is the difference between the
125. 6:03standard deviation and the variance?
126. 6:07As you now know, the standard deviation
127. 6:09is the average distance from the mean.
128. 6:13The variance now is the squared average
129. 6:16distance from the mean. So we have one
130. 6:20and the same formula. The only
131. 6:22difference is that in order to calculate
132. 6:24the standard deviation, we take the
133. 6:26root. In order to calculate the
134. 6:29variance, we don't do that. To put it
135. 6:32the other way around, the variance is
136. 6:34the squared standard deviation and the
137. 6:37standard deviation is the root of the
138. 6:40variance.
139. 6:41However, this squaring results in a
140. 6:44figure which is quite difficult to
141. 6:47interpret since the unit of the
142. 6:50calculated variance does not correspond
143. 6:52to the original data. For this reason,
144. 6:56it is advisable to always use the
145. 6:58standard deviation to describe a sample
146. 7:01as this makes interpretation a lot
147. 7:04easier for you. The standard deviation
148. 7:06is always in the same unit as the
149. 7:09original data. In our example, this
150. 7:11would be centm.
151. 7:14And finally, as promised, I have a tip
152. 7:15for you. If you want to calculate the
153. 7:18standard deviation, you can easily do it
154. 7:21online with data tab. Just visit
155. 7:24datab.net,
156. 7:26copy your data into the table. Select
157. 7:29the variable you want to calculate and
158. 7:32afterwards you will get the standard
159. 7:34deviation in a very easy way.
160. 7:38I hope you enjoyed the video and see you
161. 7:40next time. Bye-bye.