XYZ Mat 120 Module 1 Lesson 1 5 Part 1 — Transcript

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1. 0:00this is module 1 lesson 1.5
2. 0:04we're going to talk about several
3. 0:06measures
4. 0:07of central tendency so measures of
5. 0:10central tendency
6. 0:12are actually measures of center and we
7. 0:16have
8. 0:16a few that we want to talk about the
9. 0:18first one is the mean
10. 0:19which is probably the most common one
11. 0:21that you're aware of
12. 0:22the mean is a set of data values
13. 0:26measured to find the measure of center
14. 0:28and we'll add
15. 0:29all the data values and we'll divide by
16. 0:32the total number of data values so the
17. 0:33calculation is very straightforward
18. 0:36we're going to take our values we'll add
19. 0:39them all up and divide by the total
20. 0:40number of values
21. 0:42now in statistics you're going to see
22. 0:44some notation
23. 0:46for sample mean this is the sample mean
24. 0:50and it's pronounced x bar this is a
25. 0:53summation symbol
26. 0:55we're looking at greek letters here the
27. 0:57sum of all
28. 0:58x's divided by the total number of
29. 1:01values
30. 1:01so x's are all your data values and then
31. 1:05so x bar is for the sample mean mu
32. 1:09is a greek letter and that is the
33. 1:12population mean
34. 1:14how do we calculate it the same way the
35. 1:16sum of all the x's
36. 1:17divided by the total number of values
37. 1:19just for the population
38. 1:20we're going to use a capital n and for
39. 1:23the sample we'll use a small
40. 1:24n so if you see x bar or mu you know
41. 1:28we're talking about the mean
42. 1:29the calculation is done exactly the same
43. 1:32way for both
44. 1:34so let's look at an example we have
45. 1:36airport data speeds
46. 1:38and we're going to find the mean for the
47. 1:40first five data speeds for verizon
48. 1:42so here are my data values 38.5 55.6
49. 1:4722.4 14.1 and 23.1
50. 1:52so what we want to do is we want to find
51. 1:54the mean
52. 1:55and this is a sample so we'll use x bar
53. 1:58by
54. 1:59adding all of our data values dividing
55. 2:02by five
56. 2:02well they're five data values so when
57. 2:04you count them you get five
58. 2:06so you end up with 153.7
59. 2:09divided by 5. now we can actually do
60. 2:13this in our calculator
61. 2:16if we go to stat
62. 2:19this is the button for stat and we hit
63. 2:22enter
64. 2:24now in my calculator
65. 2:27let's see here let's um clear these
66. 2:31out and you should see l1
67. 2:35so put in your values 38.5
68. 2:4055.6
69. 2:4322.4
70. 2:4714.1 and 23.1
71. 2:51so when i put all those data values in
72. 2:54that's in list
73. 2:54one so i'll hit stat again
74. 2:58this time i'm going to use my arrow to
75. 2:59go over to calc up at the top of the
76. 3:01screen
77. 3:02so i just clicked on the arrow and
78. 3:04you'll see one variable stats
79. 3:06so we'll hit enter and your calculator
80. 3:09probably shows this
81. 3:10l1 is the default for this list that's
82. 3:13where my values are so i'm going to
83. 3:15leave that
84. 3:18you don't see it l1 is right here above
85. 3:20the one
86. 3:22and we'll do second one to get that
87. 3:25there's nothing for the frequency list
88. 3:27so leave that blank and then we'll click
89. 3:29on calculate
90. 3:30now there's your x bar at the very top
91. 3:33you see 30.74
92. 3:35and so that would be my values and
93. 3:37that's how we enter that
94. 3:38in the calculator
95. 3:41now let's look at a second measure of
96. 3:44center
97. 3:45which would be the median the median is
98. 3:48simply
99. 3:49the middle value when you arrange
100. 3:52your data values in order of increasing
101. 3:56or decreasing
102. 3:57generally we'll do increasing magnitude
103. 4:00so the middle value is what we're
104. 4:01looking for for the mean
105. 4:03median i'm sorry median so if we have an
106. 4:06odd number of data values
107. 4:08it's very easy i have five data values
108. 4:12if i put them all in order i just figure
109. 4:14out which one sits in the middle
110. 4:16so here's my solution we have all of our
111. 4:20verizon data values arranged in order
112. 4:23the one that sits in the middle is 23.1
113. 4:27so that's easy to see because we'll have
114. 4:292 on the sine and 2
115. 4:30on that side and then we'll have our
116. 4:31middle value but that is not always what
117. 4:34happens
118. 4:35sometimes we have an even number of data
119. 4:38values
120. 4:39this time if we have an even number of
121. 4:41data values so we're going to add one
122. 4:42more number to this data set
123. 4:45then what we're going to have to do is
124. 4:47we're going to have to
125. 4:49take the two middle values because now
126. 4:52there are 2
127. 4:52in the middle we'll add those and divide
128. 4:55by 2.
129. 4:57so when you add the two middle values
130. 4:58divided by 2 we get
131. 5:00a different median it will not be one of
132. 5:03your data values because it does not
133. 5:05sit right in the middle because it's not
134. 5:07an odd number of values
135. 5:09so if you have an even number of data
136. 5:11values
137. 5:12you have to arrange them in order and
138. 5:16then take
139. 5:16the middle value now can we find the
140. 5:20median in our calculator
141. 5:22sure we can so let's go back here's stat
142. 5:25that's where i always want to start then
143. 5:28we'll do enter
144. 5:29and these are my data values i have my
145. 5:3238 i have my 55
146. 5:3522.4 my 14 my 23.1 let's add the 24.5 to
147. 5:40this set
148. 5:42so let's come down here and let's add
149. 5:4624.5 to this data set
150. 5:49then when i go to stat i go over to calc
151. 5:54i hit enter for my one variable
152. 5:56statistics
153. 5:57make sure you see l1 you see the
154. 5:59frequency list and you see calculate
155. 6:01now the mean changed because i added a
156. 6:04data value but if i keep scrolling
157. 6:06you just notice i'm hitting this little
158. 6:08arrow down you see
159. 6:10median so i scroll down by hitting my
160. 6:13arrow
161. 6:14and right there you see your median is
162. 6:1723.8
163. 6:19so that can be done on the calculator
164. 6:22finding that value
165. 6:25a third measure of center is the mode
166. 6:28the mode is the value that occurs the
167. 6:31most
168. 6:32the one that has the greatest frequency
169. 6:35now
170. 6:36sometimes we're going to have one mode
171. 6:40sometimes we'll have two modes sometimes
172. 6:42we'll have three and sometimes we don't
173. 6:44have a mode at all
174. 6:45so mode just depends on the values that
175. 6:49occur the most
176. 6:50so if we look at this sprint data speeds
177. 6:54we see 0.3.3.3 occurs three times
178. 6:57therefore the mode is 0.3 because it
179. 7:01occurs
180. 7:01the most 0.6 occurred twice
181. 7:04but 0.3 occurred more
182. 7:08and then the last one is the mid-range
183. 7:10the mid-range is a mathematical
184. 7:11calculation
185. 7:13where we're going to look at the maximum
186. 7:15data value
187. 7:16plus the minimum data value add those up
188. 7:19divide by two
189. 7:20so all we care about for the mid-range
190. 7:22is the high
191. 7:23plus the low divided by two
192. 7:27so for my mid-range on this one back to
193. 7:30the verizon data speeds
194. 7:32if we take the maximum we'll have
195. 7:3655.6 from these data values
196. 7:40the minimum 14.1 from these data values
197. 7:44and we'll divide by 2. so when we added
198. 7:46them up divide by 2 we'll get
199. 7:4934.85 now
200. 7:51if i look at this and i want to know the
201. 7:53mid-range on my calculator i really
202. 7:55can't find it
203. 7:56this one remember i added a value so
204. 7:58it's not exactly what you see on the
205. 8:00screen
206. 8:01well it is the maximum is 55.6 because
207. 8:04we added a middle value
208. 8:05the minimum is 14.1 so when i scrolled
209. 8:09down to find the median i can also find
210. 8:11the maximum
211. 8:12minimum but it doesn't say the answer is
212. 8:1534.85
213. 8:16we have to add those two values and then
214. 8:18divide by two
215. 8:22then we're going to have some homework
216. 8:24examples to work through
217. 8:26so let's look at this homework example
218. 8:28and then i'm going to stop and i'll
219. 8:29split this
220. 8:30up so that we can do the next topic we
221. 8:32have a data set
222. 8:33so let's take our data set let's go back
223. 8:35here
224. 8:37and let's enter these data
225. 8:40values
226. 8:49i'm just entering each of these after i
227. 8:51clicked on stat
228. 9:05all right so now i have all my data
229. 9:06values in l1 we want to find
230. 9:08the mean so in l1 i'm going to go back
231. 9:11to stat
232. 9:12i'm going to go to calc i'm going to go
233. 9:14to enter
234. 9:15and it's in l1 so
235. 9:18the mean is
236. 9:23108.65 that's not what i had gotten
237. 9:26earlier but um checking my data values
238. 9:29let me just kind of
239. 9:31erase what i have here i might have
240. 9:32typed in something wrong here
241. 9:34but let's go back and let's look at that
242. 9:38so my mean 108.65
243. 9:44it said two decimal places the median
244. 9:48remember i said we can find the median
245. 9:50on our calculator 107.6
246. 9:55and the mode for this one looking at
247. 9:57this
248. 9:58you can see that the mode is 122. 122
249. 10:02is there three times and so that's
250. 10:04obviously the mode
251. 10:06so i'm going to stop this and then we'll
252. 10:07look at another part to finish
253. 10:09up this lesson