XYZ Mat 120 Module 1 Lesson 1 6 Part 1 — Transcript

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1. 0:00this is module 1 lesson 1.6
2. 0:04we're going to be talking about measures
3. 0:06of variation
4. 0:09measures of variation include the range
5. 0:12which is a very simple measure of
6. 0:14variation
7. 0:15it is the difference between the maximum
8. 0:18and the minimum
9. 0:19data values so all you have to do is
10. 0:22find your maximum value
11. 0:24your minimum value and then you subtract
12. 0:27so the range is very straightforward in
13. 0:30our previous example
14. 0:32when we were doing verizon data speeds
15. 0:34what we're going to do is we're going to
16. 0:36find the range
17. 0:37the maximum value was 55.6
18. 0:40the minimum value was 14.1 when we
19. 0:43subtract
20. 0:44those we'll get 41.5
21. 0:48the second measure of variation is the
22. 0:50standard deviation
23. 0:52the standard deviation is a little bit
24. 0:54more vague
25. 0:55it's the deviation to
26. 0:59see how much data values deviate
27. 1:02away from the mean so your mean
28. 1:06is your central value and the standard
29. 1:09deviation says data values can go above
30. 1:12and below the mean the notation
31. 1:16is for sample standard deviation you'll
32. 1:19use an
33. 1:19s and we'll use another greek letter for
34. 1:22population standard deviation
35. 1:25that is sigma we'll see that on our
36. 1:27calculators in a few minutes
37. 1:29so here's some more notation summary s
38. 1:32is for my sample standard deviation
39. 1:34now if we take s and square it that's
40. 1:37going to be my sample variance
41. 1:40and then sigma is my population standard
42. 1:43deviation
43. 1:44and if i square it i'll get my
44. 1:46population
45. 1:47variance so that's a greek letter sigma
46. 1:50just for standard deviation population
47. 1:55and sample so this one asked us to
48. 1:58calculate the
49. 1:59sample standard deviation and the
50. 2:02population
51. 2:03standard deviation for this set of data
52. 2:06values
53. 2:06so putting these in my calculator i'm
54. 2:08going to go to stat
55. 2:10i'm going to enter in l1 i'm going to
56. 2:14just enter each of these values
57. 2:25and make sure i've got each of those
58. 2:27correct
59. 2:28we want to find the sample standard
60. 2:30deviation and the population standard
61. 2:32deviation we want to round to two
62. 2:33decimal places so we'll go to stat
63. 2:36we'll go over to calc then we'll hit
64. 2:38enter
65. 2:39and in this list this is only one list
66. 2:41we have l1 which is correct
67. 2:44nothing for the frequency list if you
68. 2:46have anything there be sure you clear it
69. 2:48out
70. 2:48calculate and now we're back to where we
71. 2:52were
72. 2:52when we were talking about the mean but
73. 2:54if we look down
74. 2:56you see s sub x that is the standard
75. 2:59deviation for a sample
76. 3:01so we're going to use this value and
77. 3:02then this below is your sigma
78. 3:04sigma sub x is the standard deviation
79. 3:08for a population so the sample standard
80. 3:11deviation is going to be s
81. 3:13we want to use two decimal places so
82. 3:165.549
83. 3:18makes that 5.55
84. 3:21so let's just write that in there 5.55
85. 3:25and we got that just from this s and
86. 3:28then the
87. 3:29population standard deviation is very
88. 3:32close but a little bit different
89. 3:345.066 would be 5.07
90. 3:38so 5.07
91. 3:42so that's how we find and interpret the
92. 3:45sample standard deviation and the
93. 3:47population standard deviation rounded to
94. 3:49two decimal places
95. 3:53another example asked us to do several
96. 3:55things we have a sample of the top
97. 3:57wireless
98. 3:58routers they're tested for performance
99. 4:01and their weights are recorded
100. 4:03so let's find a lot of different values
101. 4:06for this
102. 4:07we'll go back to stat we'll go to enter
103. 4:09we're going to go
104. 4:10up and clear our list so i'm going to
105. 4:12clear this and then i'm going to put
106. 4:15my data values in my calculator
107. 4:21so give me a minute to enter each of
108. 4:24these
109. 4:25data values
110. 4:34now i have all of my data values entered
111. 4:38in my calculator
112. 4:39and i want to find several different
113. 4:41things i want to find the mean and the
114. 4:43median
115. 4:44then the standard deviation and the
116. 4:45range now when i do
117. 4:48stat i do calc
118. 4:51we're doing l1 calculating and we're
119. 4:54going back to that screen that we've
120. 4:55been working with
121. 4:56so the mean is the first thing we see
122. 4:59we'll have
123. 5:00three decimal places where necessary so
124. 5:02the mean is just 2.79 that's the first
125. 5:05thing we see up here our x bar
126. 5:07so 2.79
127. 5:11what about the median now remember we
128. 5:13looked from last time we can find the
129. 5:15median if we just scroll down
130. 5:17and we see med the median is 2.8
131. 5:22now we're asked for the standard
132. 5:24deviation well i showed you a minute ago
133. 5:27that you have both an s and a sigma
134. 5:30our rule is to use the sample standard
135. 5:33deviation unless we're told
136. 5:36that we're looking at a population
137. 5:37standard deviation so the sample
138. 5:39standard deviation is the one we want it
139. 5:41says round to three decimal places so
140. 5:43i'll put 1.174
141. 5:46from the s sub x so
142. 5:49one point
143. 5:54and then the range remember i told you
144. 5:56the range is very easy
145. 5:58the range is the maximum minus the
146. 6:01minimum
147. 6:02so i just scroll down where the median
148. 6:04was and i found 4.2 as my maximum
149. 6:07minimum is 0.5 so i'm going to take 4.2
150. 6:11i'm going to subtract 0.5 and that would
151. 6:15be my range
152. 6:163.7 so this is just like one of your
153. 6:20homework problems
154. 6:22answering both mean and median measures
155. 6:26of
156. 6:28center as well as measures of variation
157. 6:34now we talked about stem plots just a
158. 6:36few minutes ago
159. 6:37and here is a stem plot that gives us
160. 6:40data values
161. 6:41so we know if we were to list these data
162. 6:44values
163. 6:45the first data value would be 12.
164. 6:49there is no value for two you don't see
165. 6:51a zero there
166. 6:53so there is no value for two the next
167. 6:55value would be 31
168. 6:57and 39 then we'll have a 41 and a 46
169. 7:02and another 46 and a 48
170. 7:06then we'll have a 50. notice this time
171. 7:08you see a zero
172. 7:09so that's a 50. a 51 a 54
173. 7:12a 57 and a 58. and then our last one
174. 7:16a 62 a 64 a 66
175. 7:20and a 67 so now i can tell you from this
176. 7:22stem plot
177. 7:24what my data values are so i'll go in my
178. 7:27calculator
179. 7:28up clear enter and i will enter
180. 7:32each of these data values
181. 7:38and then we can do all the calculations
182. 7:41that we need to
183. 7:50after we get them entered in the
184. 7:52calculator
185. 7:55okay i think i've got all of them in
186. 7:57there correctly
187. 7:58and so once we get them in the
188. 8:00calculator they're asking us to find the
189. 8:01mean
190. 8:02so we'll go back to stat to calc
191. 8:06only one list and we're going to find
192. 8:08the mean the mean
193. 8:09is the very first thing you see with the
194. 8:11x bar 49.5
195. 8:14so 49.5 for my mean
196. 8:18the median will scroll down you can see
197. 8:21the median is 50.5
198. 8:2550.5 standard deviation once again i
199. 8:28want to go back
200. 8:29up i want to use the s so it says three
201. 8:33decimal places where necessary
202. 8:35so 14.2688 would be 14.26
203. 8:4314.269
204. 8:45the range would be
205. 8:49the maximum which is 67 the minimum
206. 8:52which is 12 we're going to subtract
207. 8:54so we're going to take 67 subtract 12
208. 8:59and we'll get 55. so 55 for my range
209. 9:02so it's a lot of difference between a 12
210. 9:05and a 67.
211. 9:07that's why our standard deviation is
212. 9:09relatively large because there's a big
213. 9:11difference between your smallest number
214. 9:13and your largest number
215. 9:14and then it says what is the shape of
216. 9:16this data well the shape is it right
217. 9:18skewed symmetric or left skewed so if
218. 9:20you were to plot this
219. 9:22like we were doing before if we were to
220. 9:24plot this and maybe look at this
221. 9:25sideways
222. 9:26you can see that the peak
223. 9:30would be over to the right so if we were
224. 9:33to look at this
225. 9:35on a curve most of our data values are
226. 9:38really high
227. 9:39here and the there's less
228. 9:43to the left so if i kind of turn this
229. 9:45sideways
230. 9:46we would be looking at the higher data
231. 9:48values at this end because we have more
232. 9:50in the 50s and the 60s
233. 9:52therefore what we're going to have is
234. 9:55it's
235. 9:56more skewed to the left and so
236. 9:59it would be left skewed
237. 10:05so that's answering something using a
238. 10:08stem and leaf plot
239. 10:12then we're going to look at a frequency
240. 10:15distribution so i'm going to stop right
241. 10:16here and we'll look at
242. 10:19the frequency distribution on the next
243. 10:21slide