Summary_Statistics_p

Summary_Statistics_p - SummaryStatistics Objectives...

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Summary Statistics
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Objectives Objectives To determine "typical" values of the  variables.  To look ways of checking the assumptions  for statistical procedures.  To determine how to check the quality of  the data. 
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Graphically Graphically Graphs communicate complex ideas with  clarity, precision, and efficiency.
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Frequency Table Frequency Table No. of Lifts (Xi) No. of Buildings  (fi) Relative  Frequency (%) 0 41 28.5 1 43 29.9 2 29 20.1 3 18 12.5 4 11 7.6 5 2 1.4 144 100.0 
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Bar Chart and Pie Chart Bar Chart and Pie Chart Relative Frequency 0.0% 10.0% 20.0% 30.0% 40.0% 1 2 3 4 5 6 No. of L if ts Relative Frequency % 1 2 3 4 5 6
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Histogram Histogram Exam Marks: {31,13,20,21,24,  25,25,27,28,40,29,  30,31,23,31,32,35,28, 36,37,38,40,50,17} 20.00 30.00 40.00 50.00 Exam_Mark 2 4 6 8 Count MR Exam Marks
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Right and Left Skewness  (Asymmetry)
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Stem-and-Leaf Diagram and  Stem-and-Leaf Diagram and  Cumulative Distribution Function Cumulative Distribution Function Exam Marks: {31, 13, 20, 21, 24, 25, 25,  27,28,40,29,30,31,23,31,32,35,28,36,37,38,40,5 0,17}
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Scatterplot Scatterplot Day Temperature  (F) Water  Consumption  (oz) 1 99 48 2 85 27 3 97 48 4 75 16 5 92 32 6 85 25 7 83 20
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Measures of Location Mean is an appropriate measure of the  center of the data if the data has a  symmetric distribution with light tails. Median if the distribution has heavy tails or  is asymmetric. Median is resistant.
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value common most The : Mode 4 n : 1.5 is {0,1,2,3} of Median 3 n : 1 is {0,1,2} of Median even. is n if ] [ 2 1 odd is n if Median ... sample ordered the of middle Median ... average Mean ) 2 2 ( ) 2 ( 2 ) 1 ( max ) ( ) 2 ( ) 1 ( min 1 2 1 = = + = = = = = = + + + = = + + = n n n n n i i n x x x x x x x x n x n x x x x Measures of Location
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) , , ( deviation standard and variance, mean, population the of analogs sample are deviations standard and variance, mean, Sample : deviation standard Sample ) ( 1 1 ) ( 1 1 : variance Sample Q1 - Q3 range(IQR) ile Interquart minimum - maximum Range 2 2 2 1 2 1 2 2 σ μ s s x n x n x x n s n i i n i i = - - = - - = = = = = Measures of Dispersion
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Box and Whiskers Plots
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Sample Correlation Coefficient A single numerical summary statistic which measures  the strength of a linear relationship between  and  y . r = covar(x,y)/(stddev(x)*stddev(y))
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Summary_Statistics_p - SummaryStatistics Objectives...

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