51632435 (1).ppt - Descriptive Statistics Sanjay Rastogi...

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Sanjay Rastogi, IIFT ,New Delhi Descriptive Statistics
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Sanjay Rastogi, IIFT ,New Delhi Measures of Central Tendency: Ungrouped Data Measures of central tendency yield information about “particular places or locations in a group of numbers.” Common Measures of Location Mode Median Mean Percentiles Quartiles
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Sanjay Rastogi, IIFT ,New Delhi Mode The most frequently occurring value in a data set 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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Sanjay Rastogi, IIFT ,New Delhi The mode is 44. There are more 44s than any other value. 35 37 37 39 40 40 41 41 43 43 43 43 44 44 44 44 44 45 45 46 46 46 46 48 Mode -- Example
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Sanjay Rastogi, IIFT ,New Delhi Median Middle value in an ordered array of numbers. Applicable for ordinal, interval, and ratio data Not applicable for nominal data Least affected by extremely values.
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Sanjay Rastogi, IIFT ,New Delhi Median: Computational Procedure First 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. Second Procedure The median’s position in an ordered array is given by (n+1)/2.
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Sanjay Rastogi, IIFT ,New Delhi Median: Example with an Odd Number of Terms Ordered Array 3 4 5 7 8 9 11 14 15 16 16 17 19 19 20 21 22 There are 17 terms in the ordered array. Position of median = (n+1)/2 = (17+1)/2 = 9 The median is the 9th term, 15. If the 22 is replaced by 100, the median is 15. If the 3 is replaced by -103, the median is 15.
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Sanjay Rastogi, IIFT ,New Delhi Median: Example with an Even Number of Terms Ordered Array 3 4 5 7 8 9 11 14 15 16 16 17 19 19 20 21 There are 16 terms in the ordered array. Position of median = (n+1)/2 = (16+1)/2 = 8.5 The median is between the 8th and 9th terms, 14.5. If the 21 is replaced by 100, the median is 14.5. If the 3 is replaced by -88, the median is 14.5.
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Sanjay Rastogi, IIFT ,New Delhi Arithmetic Mean Commonly called ‘the mean’ is the average of a group of numbers Applicable for interval and ratio data Not applicable for nominal or ordinal data Affected by each value in the data set, including extreme values Computed by summing all values in the data set and dividing the sum by the number of values in the data set
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Sanjay Rastogi, IIFT ,New Delhi Population Mean X N N X X X X N 1 2 3 24 13 19 26 11 5 93 5 18 6 ... .
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Sanjay Rastogi, IIFT ,New Delhi Sample Mean X X n n X X X X n 1 2 3 57 86 42 38 90 66 6 379 6 63 167 ...
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