Lecture 3 - Lecture3 DescriptiveStatistics...

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Lecture 3 Descriptive Statistics Descriptive Statistics
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Statistics in Business What tools might a stockbroker use  to evaluate investment options? Cyril Jinks, Bell Potter Securities
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Learning Objectives Distinguish  between measures of central  tendency, measures of variability, measures  of shape, and measures of association Understand the meanings of mean, median,  mode, quartile, percentile, and range Compute  mean, median, mode, percentile,  quartile, range, variance, standard deviation,  and mean absolute deviation on ungrouped  data Differentiate  between sample and population  variance and standard deviation
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Learning Objectives (cont’d) Understand the meaning of standard  deviation as it is applied by using the  empirical rule and Chebyshev’s theorem Understand box and whisker plots,  skewness, and kurtosis Compute  a coefficient of correlation and  interpret it
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Measures of Central  Tendency:  Ungrouped Data Measures of central tendency yield  information about the centre of a group of  numbers – e.g. a typical, middle, or average  value Common Measures of Central Tendency Mode Median Mean Percentiles Quartiles
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Mode   Applicable to all levels of data  measurement (nominal, ordinal,  interval, and ratio) Bimodal – Data sets that have two  modes Multimodal – Data sets that contain  more than two modes
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Mode - Example Offer prices for 20 Australian small capital floats  in 2004 ($) The most frequently occurring value is $1 0.40  0.80  1.00  1.00  1.00  1.00  1.00  1.20  1.20  1.25  1.35  1.50  1.80  1.85  1.90  2.00  2.10  2.30  2.40  2.50      Page 56   
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Median   Applicable for ordinal, interval, and ratio  data Not applicable for nominal data Unaffected by extremely large and  extremely small values
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Median   Computational Procedure  Arrange the observations in an ordered  array If there is an odd number of terms, the  median is the middle term of  the ordered  array If there is an even number of terms, the  median is the average of the middle two  terms The median’s position in an ordered array  is given by
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Median:  Example  with an Odd Number of Terms A business researcher wants to determine the median of the  following numbers 15 11 14 3 21 17 22 16 19 16 5 7 19 8 9 20 4 First, present these numbers as an ordered array 3 4 5 7 8 9 11 14 15 16 16 17 19 19 20 21 22
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Median:  Example with  an Even Number of Terms The value 22 has been eliminated from the dataset.  The  ordered array is 3 4 5 7 8 9 11 14 15 16 16 17 19 19 20 21
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Arithmetic Mean Commonly called ‘the mean’
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Lecture 3 - Lecture3 DescriptiveStatistics...

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