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Quantitative Methods
QMS 102
Changping Wang

Business Statistics I Dr. Changping Wang 4.4. Box-Whisker Plot For numerical data, we can use frequency histogram and relative frequency histogram to get understanding of the shape of the distribution. In this section, we introduce a new concept: the box- whisker-plot. The Box-Whisker Plot is a graphical display that is used to get a general picture of a set of data. The main difference from the box-whisker- plot and previous graphical display is that the box- whisker-plot shows some the values of descriptive statistics. In particular, it shows five-number summary: Minimum, Q1, Median, Q3 and Maximum To draw a Box-Whisker Plot, we need a.Find the five-number summary of the data set. b.Construct an appropriate horizontal scale. c. To form a box with Q1 and Q3 determining the location of the sides. d.The median is indicated by a line across the box; and the mean may be indicated with a “+” sign. e.To draw the whiskers, we follow a)They cannot past the inner fences; b)They must end at a data point. Session 7 Page 1 Business Statistics I Dr. Changping Wang How to calculate the location for the inner and outer fences? LIF=Q1-1.5*IQR; RIF=Q3+1.5*IQR; LOF=Q1-3*IQR; ROF=Q3+3*IQR Note: (1) LIF=Left Inner Fence; LOF=Left Outer Fence; (2) RIF=Right Inner Fence; ROF=Right Outer Fence; (3) All data values that fall between the fences are call suspected outliers, using “o” to indicate them; All data values that lie beyond the outer fences are call outliers, using “*” to indicate them. Session 7 Page 2 Business Statistics I Dr. Changping Wang EXAMPLE 1: The test score of 15 employees enrolled in a CPR training course are listed as follows: 13, 9, 18, 15, 14, 21, 7, 10, 11, 20, 5, 18, 37, 16, 17. Draw a Box-Whisker Plot. Session 7 Page 3 Business Statistics I Dr. Changping Wang EXAMPLE 2: The “Gasoline and fuel oil, average retail prices by urban centre” appeared in Statistics Canada. Gasoline and fuel oil, average retail prices by urban centre (regular unleaded gasoline at self service filling stations) regular unleaded gasoline at self service filling stations Cents per litre July July July July July 2005 2006 2007 2008 2009 St John’s 104.0 116.5 116.5 146.8 109.6 Saint John 100.3 112.8 106.8 137.2 97.1 Halifax 100.4 115.1 112.7 142.2 101.6 Quebec 101.4 115.1 113.3 142.5 102.3 Montreal 98.9 114.1 107.4 143.5 100.1 Ottawa 91.6 105.2 101.2 130.2 89.5 Toronto 90.1 105.7 101.0 132.0 93.9 Thunder 94.6 113.8 114.2 140.3 106.8 Bay Winnipeg 92.5 110.7 112.4 135.6 99.8 Regina 92.7 112.4 113.5 136.0 102.5 Saskatoon 96.9 114.3 114.9 135.5 102.9 Edmonton 88.6 105.8 105.6 130.3 89.6 Calgary 90.2 106.0 109.0 132.2 92.5 Vancouver 99.5 116.0 109.8 146.6 108.1 Victoria 101.4 115.2 111.4 150.5 105.2 Whitehors 106.3 116.3 118.6 144.4 106.3 e Yellowknif 103.5 119.3 127.1 150.0 119.2 e Source: Statistics Canada, CANSIM, table (for fee) 326-0009 and Catalogue no. 62-001-X Last Modified: 2009-08-24 For the date in 2007, draw a Box-Whisker Plot. Session 7 Page 4 Business Statistics I Dr. Changping Wang EXAMPLE 3: The following data was about the rates (¢/min) of calling the world from cell in Canada offered by the Startec Global Communications . 13.9 10.9 Australia 2.9¢ El Salvador ¢ Jordan ¢ Serbia 9.9¢ Austria 3.9¢ France 2.9¢ Korea .S 4.9¢ Spain 2.9¢ Bangladesh3.9¢ Germany 2.9¢ Lebanon 7.9¢ Sweden 3.9¢ Bosnia 9.9¢ Greece 2.9¢ Mexico 1.9¢ Switzerland 3.9¢ Brazil 2.9¢ Guatemala 10.9 Pakistan 13.9 Syria 13.9 ¢ ¢ ¢ Canada 2.9¢ Ireland 2.9¢ Philippines 8.9¢ Taiwan 4.8¢ China 4.8¢ Hong Kong 3.8¢ Poland 2.9¢ Thailand 9.9¢ 1.5 Colombia ¢ India 1.9¢ Portugal 2.9¢ UK 2.9¢ Croatia 2.5¢ Italy 2.9¢ Russia 1.5¢ Ukraine 9.9¢ Egypt 9.9¢ Japan 5.9¢ Moscow 1.5¢ Vietnam 3¢ Help a marketing analyst in the Startec Global Communications to construct a box-whisker plot for the above data by computing each of the following using a CASIO calculator: (If necessary, round your answers to one decimal place. All answers are in ¢/min) Question 1 The first quartile is a) 2.8 b) 2.2 c) 4.3 d) 2.9 e) None of these Question 2 The third quartile is a) 7.9 b) 9.4 c) 3.1 d) 9.0 e) None of these Question 3 The interquartile range is a) 7.9 b) 7.2 c) 9.7 d) 6.5 e) None of these Question 4 The right inner fence is Session 7 Page 5 Business Statistics I Dr. Changping Wang a) 19.2 b) 16.9 c) 19.3 d)12.7 e)None of these Question 5 The right outer fence is a) 22.4 b) 21.4 c) 32.7 d) 28.9 e) None of these Question 6 The smallest value on the left whisker (i.e. the left whisker ends at what value) is a) 2.5 b)1.9 c) - 6.9 d) -16.6 e)None of these Question 7 The largest value on the right whisker (i.e. the right whisker ends at what value) is a) 13.9 b)28.9 c) 4.0 d) 10.5 e)None of these Question 8 In the box-whisker plot, the total number of suspected outliers is: a) 0 b)1 c) 2 d) 3 e)4 Question 9 In the box-whisker plot, the total number of outliers is: a) 0 b)1 c) 2 d) 3 e) None of these Session 7 Page 6 Business Statistics I Dr. Changping Wang 5.1: Basic Probability Concepts We often speak of events and their chance, or probability of occurring. The probability and chance are often the same word. When we do not exactly know the outcome in advance, we speak of chance. e.g. Chance of a team winning; chance of winning a lottery; chance of rolling a six (die); chance of raining tomorrow. We can be certain of few things: e.g. Certain that the sun will rise; certain that there will be school in the winter. To introduce the concept of probability, one has to introduce sample space, events. The general setting is: we perform an experiment (of interest) which can have a number of outcomes. The sample space, denoted by S, is the set of all possible outcomes of the experiment. e.g. If I toss a coin three times and record the result, then S={HHH,HHT, HTH, THH, HTT,THT,TTH,TTT} e.g. If I toss a coin three t
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