XYZ Mat 120 Module 1 Lesson 1 3 — Transcript

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1. 0:00this is module 1 lesson 1.3
2. 0:03we're going to talk about a frequency
3. 0:05distribution
4. 0:08so let me move this over just a little
5. 0:09bit a frequency distribution
6. 0:11is also a frequency table we're going to
7. 0:14divide data
8. 0:16into classes by listing the categories
9. 0:19and
10. 0:19the frequency in each class so we're
11. 0:22going to have some definitions
12. 0:24we're going to start off with lower
13. 0:26class limits
14. 0:28so lower class limits are obviously the
15. 0:30smallest numbers in a class
16. 0:34upper class limits are the largest
17. 0:37numbers in a class and then class
18. 0:41boundaries class boundaries are the
19. 0:44numbers used to separate classes
20. 0:47without gaps so i'm going to show you
21. 0:50how all this looks in an example after
22. 0:52we do a few more definitions
23. 0:55the class midpoints are the values
24. 0:58in the middle of each of the classes and
25. 1:01so the midpoint
26. 1:02is a calculation you're going to add the
27. 1:06lower class limit to the upper class
28. 1:08limit
29. 1:09and then you're going to divide by 2. so
30. 1:12we're going to do that calculation a
31. 1:13midpoint is just like you would find a
32. 1:15midpoint in any other math class that
33. 1:16you've done
34. 1:18the class width the width is the
35. 1:21difference
36. 1:22between two consecutive lower class
37. 1:24limits
38. 1:25in a frequency distribution so we're
39. 1:27going to look at all of these things
40. 1:28with an example
41. 1:30so we're going to use the mcdonald's
42. 1:32lunch service times
43. 1:34in the table and we want to construct a
44. 1:37frequency distribution using
45. 1:40five classes so at mcdonald's drive
46. 1:43through
47. 1:44someone gathered time that it took for
48. 1:48each car
49. 1:48to get through the drive-through in
50. 1:50seconds and so they wrote down
51. 1:52all of these data values when you see
52. 1:55the data values it's really meaningless
53. 1:58it's just a bunch of numbers and so in
54. 2:01order to make it make some sense
55. 2:03we create a frequency distribution using
56. 2:06classes
57. 2:07so to have five classes we do class one
58. 2:11is between 75 and 124 seconds
59. 2:15class 2 125 to 174
60. 2:19class 3 175 to 224
61. 2:23225 to 274 and 275 to 324.
62. 2:26later on i'm going to show you how we
63. 2:28determine
64. 2:29this is how we break this down so the
65. 2:32frequency
66. 2:34let's go up here between 75 and 124
67. 2:38so we have got to now look at all the
68. 2:41data
69. 2:41and see how many values fall between 75
70. 2:45and 124
71. 2:46so we can start counting there's one
72. 2:50so i'm going to keep on going here until
73. 2:53i find some more
74. 2:5475 that would be 83
75. 2:58and then 124. here's one here's one
76. 3:02and then i'll count them all up here's
77. 3:04one
78. 3:06and it's a little bit tedious
79. 3:10and we'll find all of these values that
80. 3:13fall
81. 3:13between 75 and 124. you should find 11
82. 3:16of them
83. 3:17did i find 11 1 2 3
84. 3:204 5 6 7 8 9 10. i might have missed
85. 3:24one but that's what we want to do is we
86. 3:27want to find all the data values
87. 3:29between 75 and 124 and we want to
88. 3:33include
89. 3:35those data values so
90. 3:38the next thing we'll do is we'll look at
91. 3:40the next class
92. 3:41and we'll do the numbers between 125 and
93. 3:44174
94. 3:45count them and so we're going to have to
95. 3:47count them and then just mark them off
96. 3:49as we're doing that and you should get
97. 3:5024. i'm not going to sit here and count
98. 3:52all of these
99. 3:53but that's how we create the frequency
100. 3:56distribution
101. 3:57now that's our chart that's what i just
102. 4:00got through doing
103. 4:01i put them in the classes i did the
104. 4:03frequency
105. 4:04so now we want to find the lower class
106. 4:07limits
107. 4:08lower class limits are very easy they're
108. 4:11these numbers the lower class limits and
109. 4:14so we'll list them all
110. 4:16the upper class limits are these numbers
111. 4:20so we'll list all of these so that's
112. 4:23also very easy
113. 4:25the class boundaries what we're going to
114. 4:27do is we're going to add
115. 4:290.5 and subtract 0.5 so we're going to
116. 4:32take our lower number
117. 4:35and we're going to subtract 0.5
118. 4:40and then we're going to take our upper
119. 4:42and we're going to
120. 4:44add 0.5
121. 4:48so my lower number is 75 75
122. 4:51minus 0.5 is 74.5
123. 4:55and then you add 0.5 to 124 and that
124. 4:57would be 124.5
125. 5:00and then you subtract 0.5 from 125
126. 5:03and you get oh the same thing 124.5
127. 5:07and that's where we have without gaps
128. 5:10and then here's 174.5 and then when you
129. 5:13subtract here you get the same thing
130. 5:15174.5 don't write it down but one time
131. 5:18and then for the midpoints we're going
132. 5:20to add up
133. 5:22each of the values so we're going to
134. 5:23take 75 plus 124
135. 5:25and we're going to divide it by 2. so
136. 5:28that's 199.
137. 5:30we're going to divide that by 2. so our
138. 5:32first midpoint is 99.5
139. 5:35and then you're going to do the same
140. 5:36thing for the second one 125 plus 174
141. 5:38divided by 2
142. 5:40and that would be 149.5
143. 5:43class width this is important the class
144. 5:46width
145. 5:47you take the second
146. 5:51lower number which is 125
147. 5:54and you subtract the first one so 125
148. 5:58minus 75 is 50.
149. 6:01now i can do it from here 175
150. 6:04minus 125 is also 50.
151. 6:08225 minus 175 is 50. so the class width
152. 6:12is 50. that's just one number
153. 6:16then we're going to talk about
154. 6:17cumulative frequency cumulative
155. 6:18frequency is very
156. 6:20easy um cumulative frequency just takes
157. 6:23each frequency and adds them up so
158. 6:24here's my original table
159. 6:26so i'm starting with 11 so i'll put 11
160. 6:28here
161. 6:29then i'm going to add 11 plus 24
162. 6:33and that's going to go in my second
163. 6:35class that'll give me 35
164. 6:37and then i'm going to take the 35
165. 6:41and i'm going to add 10 because that's
166. 6:44this one
167. 6:45so 35 plus 10 is 45 and then i'm going
168. 6:49to take my 45
169. 6:50and i'm going to add 3 and i'm going to
170. 6:52get 48
171. 6:54and then i'll take my 48 and i'll add 2
172. 6:56and i'll get a total of 50.
173. 6:58so you should have a total of 50. if you
174. 7:01went back and looked at all those data
175. 7:02values there should be 50 data
176. 7:05data values and so we just take each
177. 7:07class
178. 7:09we add the next one and then take that
179. 7:11total and add the next one that total
180. 7:12and add the next one so that's very
181. 7:14straightforward
182. 7:16relative frequency is a calculation
183. 7:18where you do
184. 7:20frequency for a class divided by the sum
185. 7:22of all frequencies and then we're going
186. 7:23to convert that to a percentage
187. 7:25so let me show you how that looks so
188. 7:28here's the original chart
189. 7:30class 1 the frequency is 11. remember
190. 7:33when we added them all
191. 7:34up we got a total of 50.
192. 7:37so we're going to take each of these
193. 7:39frequencies and divide by 50 so 11
194. 7:41divided by 50 is 0.22
195. 7:4324 divided by 50 is 0.48
196. 7:4610 divided by 50 is 0.2 3 divided by 50
197. 7:51is .06 and then 2 divided by 50 is 0.04
198. 7:55and then you can convert these two
199. 7:56percentages that would be 22 percent
200. 7:59this would be 48 this would be 20
201. 8:04this would be 6 and this would be
202. 8:074
203. 8:10so that is how we do relative frequency
204. 8:13then we're looking at our graphs we have
205. 8:15a histogram
206. 8:17a histogram is just simply one of the
207. 8:19most common graphs that we use and it's
208. 8:21a bar graph and we're going to represent
209. 8:25our data values on the horizontal axis
210. 8:28and the frequencies on the vertical axis
211. 8:30so let's look at some different
212. 8:32shapes of the histogram this is a normal
213. 8:34distribution so here's your histogram
214. 8:36and normal distribution means it goes up
215. 8:39and it comes
216. 8:40down and it makes almost a perfect
217. 8:43bell-shaped curve
218. 8:44it's not exactly perfect but it's in the
219. 8:46shape of a
220. 8:47perfect bell-shaped curve where most of
221. 8:49the things are in the middle
222. 8:51sometimes they're not like that
223. 8:52sometimes they're skewed
224. 8:54so this one is positively skewed so if
225. 8:58it's
226. 8:58positively skewed it means it's skewed
227. 9:00to the right
228. 9:01now what is skew it's got a longer
229. 9:04right tail it peaks really fast on the
230. 9:07left side
231. 9:08but it's got more data values over here
232. 9:10on the right so that would be positively
233. 9:12skewed or skewed to the right
234. 9:14whereas negatively skewed or skewed to
235. 9:17the left
236. 9:18is going to have a longer left tail
237. 9:21so that would be a negative skew example
238. 9:24and then the last thing we're going to
239. 9:26do is construct a frequency
240. 9:29distribution for an example and this
241. 9:31comes from your homework problems
242. 9:34so your homework problems gives you a
243. 9:36data set and it looks like this
244. 9:38it says calculate the class width and
245. 9:40then construct a frequency distribution
246. 9:42using five classes so that's really
247. 9:44important we want five classes
248. 9:46here's a rule that we need to follow in
249. 9:48order to know what numbers to put
250. 9:51in each of the classes the width is the
251. 9:54range divided by the number of classes
252. 9:56well the range is the maximum minus the
253. 9:58minimum
254. 10:00the number of classes they tell us we
255. 10:02want five
256. 10:03so the maximum value in this data set
257. 10:06you have to look at the data set and see
258. 10:07the maximum value is 113
259. 10:10and the minimum value is 16 that's the
260. 10:12smallest so that's the largest that's
261. 10:13the smallest when we subtract we'll get
262. 10:1597
263. 10:16we're going to divide it by 5 which is
264. 10:17our number of classes
265. 10:19it doesn't divide evenly so we always
266. 10:21want to
267. 10:22round up don't round using your rounding
268. 10:26rules but
269. 10:27round up so 19.4 is going to round to
270. 10:3020.
271. 10:31so 20 is going to be our width now let's
272. 10:34see how that looks
273. 10:36remember width goes here and here and
274. 10:39here and here so we're going to have 20
275. 10:40between each of those
276. 10:42we always want to start with our
277. 10:43smallest number smallest number 16
278. 10:45that's going to be the first one
279. 10:47now if 20 is your width we're going to
280. 10:50take 16 and add 20 and we're going to
281. 10:51get 36 and put it right here
282. 10:54and then we're going to add 20 and get
283. 10:5556 and we're going to add 20
284. 10:57and then we're going to add 20 more now
285. 10:59this one has to be one less
286. 11:02than the 36 so that's got to be 35
287. 11:06and then we're going to add 20 that's 55
288. 11:08and we'll add 20 and we'll add 20 and
289. 11:09we'll add 20
290. 11:10and that way i'll have a class for
291. 11:14all of my data values then i have to
292. 11:18go back to my original data values and
293. 11:22find the frequencies
294. 11:23so how many values fall between 16 and
295. 11:2635
296. 11:27this is where you just have to count so
297. 11:29between 16
298. 11:31and 35 i find three data values
299. 11:35how many are between 36 and 55
300. 11:38so between 36 and 55
301. 11:42there's 1 2 3 4
302. 11:455 and then
303. 11:48that would be my total for my frequency
304. 11:50and you do the same thing for the rest
305. 11:51of them so that you get all of your data
306. 11:53values
307. 11:53and it's a total of 16. so that's how
308. 11:56you construct
309. 11:57a frequency distribution using classes