XYZ Mat 120 Module 1 Lesson 1 6 Part 2 — Transcript

Full transcript

1. 0:00this is module 1 lesson 1.6 part
2. 0:032. we stopped when we were talking about
3. 0:07standard deviation now let's look at
4. 0:08standard deviation for frequency
5. 0:10distribution
6. 0:11this time we have information
7. 0:14in two different lists so i'm going to
8. 0:16pull up my calculator i'm going to go to
9. 0:17stat i'm going to go to enter
10. 0:19and in l1 i'm going to put the aptitude
11. 0:22scores
12. 0:22so i put all the aptitude scores in l1
13. 0:25then i'm going to put the frequencies in
14. 0:28l2 so when i put all the frequencies in
15. 0:30l2 now i have information
16. 0:34in both lists l1 and l2
17. 0:37then i'll go to stat i'll go over to
18. 0:40calc and i'll hit enter
19. 0:42make sure at this point that your list
20. 0:43says l1
21. 0:45and then your frequency list says l2 if
22. 0:47your calculator does not then you have a
23. 0:49little l2 right here above the two so
24. 0:51we'll do
25. 0:52second two to make sure that does say l2
26. 0:55and then we'll come down here and
27. 0:56calculate and the question is what is
28. 0:59the sample standard deviation
29. 1:01remember the sample standard deviation
30. 1:03is the s sub
31. 1:04x so that's going to be 1.77
32. 1:09we rounded it to two decimal places
33. 1:14the next example is we're doing a
34. 1:16frequency distribution
35. 1:18and we want an l1 to have our midpoints
36. 1:22we want the frequencies in l2 so the
37. 1:25midpoints i can find that by
38. 1:27adding the values and dividing by 2. so
39. 1:3050 plus 56 divided by 2 is 106 divided
40. 1:34by 2
41. 1:34which would be 53. so now when i go over
42. 1:38here
43. 1:39i'm going to put all the midpoints in l1
44. 1:42and then i'm going to come over here and
45. 1:44i'm going to put all of the frequencies
46. 1:45in l2
47. 1:46so 53 is going to be the first one then
48. 1:5060. i'm adding 57 plus 3 and then 67
49. 1:54because that's 64 plus 3
50. 1:56and then 74 which is 71 plus 3
51. 2:00and then 81 and then 85 plus 3 would be
52. 2:0488 so those are
53. 2:05all of my midpoints my frequencies
54. 2:0910 18 15
55. 2:138 7 and 3.
56. 2:17and then when we do stat we do calc list
57. 2:20one has l l1 as
58. 2:21frequency has l2 then we'll calculate it
59. 2:24and we're asked to find several things
60. 2:26the sample mean
61. 2:27we want two decimal places 66.196 would
62. 2:32just simply be 66.2 or you could put
63. 2:3566.20
64. 2:36remember the mean is the very first
65. 2:38thing you read the sample standard
66. 2:40deviation is the s
67. 2:429.907 would be 9.91
68. 2:46so that's when we have the
69. 2:50frequency distribution the empirical
70. 2:53rule
71. 2:53the empirical rule is a rule for data
72. 2:56with a bell-shaped distribution
73. 2:58and it's just what it says it's a rule
74. 3:00about 68
75. 3:02of values fall within one standard
76. 3:04deviation of the mean
77. 3:05you have to remember 68 goes to 1.
78. 3:0895 of the values fall within two
79. 3:10standard deviations of the mean
80. 3:12and 99.7 fall within three standard
81. 3:16deviations of the mean
82. 3:17now what does that look like let me get
83. 3:19rid of all this stuff
84. 3:21and the mean is right here
85. 3:24at the center so here's my mean it said
86. 3:2768 of my data values fall within one
87. 3:31standard deviation of the mean so they
88. 3:34go from here to here
89. 3:35half of them on the right side half of
90. 3:37them on the left side
91. 3:38and then we'll stretch it out two
92. 3:41standard deviations of the mean
93. 3:43contain about 95 percent of my data
94. 3:46value so i'm stretching it out further
95. 3:48and then almost all my data values 99.7
96. 3:52percent fall within three standard
97. 3:54deviations of the mean
98. 3:56so that's almost all of my data values
99. 3:59so just remember
100. 4:0068 contains one standard deviation of
101. 4:03the mean
102. 4:0495 contains two and 99.7 contains
103. 4:08three so let's look here at this problem
104. 4:11we have adult males heights are normally
105. 4:14distributed with a mean of 177 standard
106. 4:16deviation of 7.4
107. 4:18so what would be the range for the
108. 4:22heights
109. 4:23at 68 percent of the data well remember
110. 4:2568
111. 4:26is only one standard deviation so that
112. 4:28would be
113. 4:29the mean minus one times the standard
114. 4:33deviation
115. 4:34and the mean plus one times the standard
116. 4:36deviation
117. 4:37the mean is 177 the standard deviation
118. 4:40is 7.4
119. 4:41that's how we get our values 169.6 and
120. 4:45184.4
121. 4:4695 remember that's two standard
122. 4:49deviations
123. 4:50so we're going to do the mean minus 2
124. 4:52times the standard deviation
125. 4:54and the mean plus two times the standard
126. 4:56deviation
127. 4:57so that's going to stretch this out to
128. 4:59162.2
129. 5:01and 191.8 and then three standard
130. 5:04deviations is 99.7 percent of the data
131. 5:07that's the mean minus three times the
132. 5:09standard deviation and the mean plus
133. 5:11three times the standard deviation
134. 5:12that stretches it out even further to
135. 5:14154.8
136. 5:16and 199.2
137. 5:20then when we have a distribution here it
138. 5:23says our
139. 5:24mean score is 76. so let me just kind of
140. 5:27start over here
141. 5:28the mean score is 76 and the standard
142. 5:30deviation
143. 5:31is 14. what's the approximate percentage
144. 5:33of students who scored between 62 and 76
145. 5:36so right here
146. 5:3876 is the mean and we only want this
147. 5:40part
148. 5:41if you remember for one standard
149. 5:44deviation that was 68
150. 5:47we only want half of it so here's one
151. 5:49standard deviation they're asking us for
152. 5:51half so we'll take half of 68 and that's
153. 5:53how i get 34.
154. 5:56then the next question is what is the
155. 5:57approximate percentage who scored
156. 5:58between 64 and 90
157. 6:00well now we know that that is one
158. 6:03standard deviation of the mean so that
159. 6:0568 percent
160. 6:07then it says what is the approximate
161. 6:09percentage who scored less than 48
162. 6:11and then what's approximate percentage
163. 6:13who scored between 48 and 104. now if i
164. 6:15go over here and if i go from 48
165. 6:19to 104 i know that that is now two
166. 6:22standard deviations of the mean
167. 6:24and two standard deviations of the mean
168. 6:26is 95
169. 6:28so that's a total of 95 percent so if we
170. 6:31think about this
171. 6:32all of this is 95 so that's how i'm
172. 6:35going to answer the last question
173. 6:37but how do i answer the question that's
174. 6:39less than 48 so less than 48 is just
175. 6:42this right here
176. 6:43so if the total is 95 1 minus 0.95
177. 6:48is 5 and i only want this side of it so
178. 6:51i'm going to take half of 5
179. 6:53and i'm going to get 0.025 so that means
180. 6:57that 0.025 is right here and .025 is
181. 7:02right here
182. 7:03because if you add those up together
183. 7:04you'll get five percent
184. 7:06you write that as a percentage 2.5
185. 7:09percent
186. 7:12and then the last part um we've got um
187. 7:16the distribution of widget weights is
188. 7:18bell-shaped the widget weights have a
189. 7:20mean
190. 7:20of 42 ounces a standard deviation of
191. 7:22seven
192. 7:23ninety-five percent remember ninety-five
193. 7:26percent
194. 7:27is two standard deviations of the mean
195. 7:29so it would be the mean minus 2 times
196. 7:31the standard deviation and the mean plus
197. 7:322 times the standard deviation
198. 7:34that's how we get 28 and 56. what
199. 7:37percentage
200. 7:38lies between 42 and 63.
201. 7:42so it tells me the mean is 42. so that's
202. 7:44my center
203. 7:45and i want to know between 42 and 63.
204. 7:48well here's one two three standard
205. 7:51deviations of the mean
206. 7:52since it's three standard deviations and
207. 7:55i'm only looking at half of it because
208. 7:57remember the other half is over here
209. 7:59so half of 99.7 is
210. 8:0349.85 percent
211. 8:05and then the last one what percentage
212. 8:07lies between 35 and 49
213. 8:09well here's my 42. so 35
214. 8:13and 49 would be back here and so that's
215. 8:16only
216. 8:167 to the right and 7 to the left so
217. 8:18that's one standard deviation of the
218. 8:20mean
219. 8:21which would be 68 and all of that goes
220. 8:25back to my
221. 8:26rule for the empirical rule
222. 8:29the last thing is consistency and what
223. 8:31you need to know here
224. 8:33standard deviations are more consistent
225. 8:36if they're small
226. 8:37if they're closer to the mean that means
227. 8:38they're close they're consistent
228. 8:40they're less consistent if they're large
229. 8:42if they're farther from the mean
230. 8:44so let's just look at this right here to
231. 8:47determine if ricky is an effective
232. 8:49method for treating pain a pilot study
233. 8:50was carried out where a certified
234. 8:52second second-degree degree reiki
235. 8:55therapist provided treatment on
236. 8:56volunteers pain was measured
237. 8:58using vas immediately before and after
238. 9:01this treatment
239. 9:02so it says the readings before had a
240. 9:05mean
241. 9:05of 4.26 and a standard deviation of 2.19
242. 9:09and then after the treatment the mean
243. 9:12was 2.26 and the standard deviation is
244. 9:152.09
245. 9:16so is it more or less consistent before
246. 9:20so the before had a standard deviation
247. 9:24of 2.9
248. 9:261 9 and then after it was 2.09 so it's
249. 9:31less consistent because it's larger so
250. 9:33if it's larger it's less consistent and
251. 9:35all i'm doing is comparing my standard
252. 9:37deviations that means i'm farther away
253. 9:39i'm more spread out this time we're
254. 9:42going to look at pulse rates from
255. 9:44samples of females who are non-smokers
256. 9:47but do drink alcohol the pulse rates
257. 9:50who exercised had a mean of 74.15 a
258. 9:53standard deviation 11.82
259. 9:55after they ran in place for a minute
260. 9:57they had a mean
261. 9:58126 and a standard deviation of 25. so
262. 10:01let's look at our standard deviations
263. 10:02this one's 25 this one is 11.
264. 10:05the pulse rates before they exercised
265. 10:09so they before they exercise is smaller
266. 10:11therefore it's more consistent
267. 10:14than after they exercised because the
268. 10:17number
269. 10:17is smaller