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Quantitative Methods
QMS 102
Amy Peng

Business Statistics I Dr. Changping Wang Session 4 Page 1 Business Statistics I Dr. Changping Wang Example 1. Session 4 Page 2 Business Statistics I Dr. Changping Wang Measures of Position  We have seen several measures of the “centre” of a dataset. Sometimes  we are interested in the relative “position” of a value of the dataset. Here  we introduce the concept of percentile. Percentile:                          k   kth percentile  The kth percentile in a dataset is the value such that at most k% of the  data is lower than the value AND at most (100­k)% of data is higher than  the value. Quartiles: P 25= Q 1 st ---- ndquartile P50= Q 2 ---- 2 quartile; median P75= Q 3 ----3 quartile Remarks: (1)  You can find  Q 1 and  Q 3 when you find mean or median  using a suggested calculator Session 4 Page 3 Business Statistics I Dr. Changping Wang Three steps for finding  Pk     1) Arrange data in an ascending data array. 2) Calculate the rank of  the kth percentile using P r=Rank of  k  =HalfRound(nk/100+1/2)              a)  n=number of the observations in the dataset;    b)  HalfRound(.) means round to the nearest half.        e.g.  HalfRound(2.3)=2.5;            HalfRound(2.1)=2;               HalfRound(3.7)=3.5;            HalfRound(3.8)=4. 3) Find the value  P k . a)  When r=integer,  Pk= x r;   1 b)  When r=m+1/2,  Pk= (2 + m m+1) Session 4 Page 4 Business Statistics I Dr. Changping Wang Example 2.  Refer to table 3:  Marriages by Province and territory  published by Statistics Canada. For 2006, what is the 39  percentile of the  number of marriages? Table 3: Marriages by Province and territory Number of Marriages 2004 2005 2006 2007 2008 Newfoundland 2,850 2,806 2,752 2,698 2,797 PEI 827 829 828 831 824 Nova Scotia 4,729 4,698 4,667 4,633 4,687 New  3,708 3,686 3,646 3,622 3,669 Brunswick Quebec 21,279 22,244 21,900 22,650 22,400 Ontario 64,114 64,677 65,170 65,483 64,959 Manitoba 5,710 5,732 5,746 5,796 5,767 Saskatchewan 5,011 5,000 4,995 5,080 5,080 Alberta 17,909 18,392 19,060 19,837 19,100 British  22,080 20,007 20,660 20,697 20,770 Columbia Yukon 160 159 160 158 161 Northwest  141 140 138 139 138 Terrotories Nunavut 67 69 70 71 71 Source: Statistics Canada, CANSIM, table (for fee) 053­0001 Last Modifed: 2009­06­23     Session 4 Page 5 Business Statistics I Dr. Changping Wang Example 3. The time, t minutes, that each of 100 users stayed on the  internet recently was recorded and the results used to construct the Ogive  below. a. What’s the 40  percentile of the time spending on the internet?                     b. What’s the 75  percentile of the time spending on the internet?                          Session 4 Page 6 Business Statistics I Dr. Changping Wang 4.2. Descriptive Statistics II­Measure of Variability We have discussed three most common measures of central tendency:  mean, median and mode. Advantage of using mean: the mean is a  reliable measure because it takes into account every entry of a data set.  Disadvantage of using mean: the mean is greatly affected by outliers or  extreme values (data entry that is far from the other entries in the data  set).  Dispersion:  It has a technical meaning in statistics. The average measures  the centre of the data. It is one aspect of the observations. Anther feature of the  observations is how the observations are spread about the centre. The observations  may be close to the centre, or they may be spread a
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