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Final

# QMS102 : stats final sheet.docx

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School
Department
Quantitative Methods
Course
QMS 102
Professor
Douglas Mc Kessock
Semester
Fall

Description
Which is a better measure of Central Tendency: mean or median? 10% rule: 1) Calculate the difference A=|Mean-Median|. 2) Calculate the ―10% of the smaller of the mean and median‖, say B. 3) If AB, then median is the preferred measure. ~ mean x 11522.4615 , and median x  4667 . Now we apply the 10% rule: The difference A=| 11522.4615  4667 | 6855.4635 , and the 10% of the smaller, B=10%*4667=466.7. Since A>B, we conclude that the median is a better measure! Mode is data entry that occurs the most 1) Arrange data in an ascending data array Find the value . k when r=integer, k x r; when r=m+1/2, Pk (x  m m1) 2 Find the rank of the 39 percentile: n=13, k=39. So, r = HalfRound(nk/100+1/2) = HalfRound(5.57)=5.5 So, P  (x  x )  (2752  3646 )  3199 39 2 5 6 2 Interquartile Range = Q3 – Q1 Range : Highest number of data set – lowest number For ABC Inc., x  32.21875 and s x 6.735 . So, CV= s x x *100%  21% ; For XYZ Inc., x  32.1023 and sx 6.0278 . So, CV= sx/ x *100% 19% . So, we can conclude that ABC Inc. has more variability. We can use a CASIO calculator to compute the standard deviation:  x for the population standard deviation, and sx for the population standard deviation. (2) To find the variance, we need to square the standard deviation. You were asked to fill in a survey by Ryerson University about the number of courses you intend to take. One of the questions asked is as follow: How many courses do you intend to take in the Winter 2010? Refer to the question above being asked on the survey form. What is the measurement scale of the response data? (a) Nominal (b) Ordinal (c) Interval - Continuous (d) Ratio – Discrete (e) Ratio - ContinuousLIF=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 outliers, using ―o‖ to indicate them; All data values that lie beyond the outer fences are call extremes, using ―*‖ to indicate them. To measure the skewness, one can use the following: 3(mean-median) Skewness= ----------------------------- standard deviation 1) if meanmedian, then skewness>0 (positively skewed, skewed right); 3) if mean=median, then skewness=0 (symmetric). . The quartiles are the values that occupy the quarter positions: First quartile,Q 1 P 25 Second quartile, Q 2 P 50 Third quartile, Q 3 P 75 A five-number summary that consist of X smallest, Q 1 , Median, Q 3 , X largest Class Width = Highest Number - Lowest Number / 5 Right Whisker = greater than Q3 but less than RIF. Value close to RIF Left Whisker = LIF
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