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# handout3 - Notes Chapter 3 Numerical Descriptive measures...

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Chapter 3: Numerical Descriptive measures Bin Wang [email protected] Department of Mathematics and Statistics University of South Alabama Mann E6 1/32 3.1 Measures of Central Tendency for Ungrouped Data 3.1.1 Mean Mean of population data : μ = x N Mean of sample data : ¯ x = x n Mann E6 2/32 Example (Identity Fraud Victims in 2004 for Six States) Mann E6 3/32 Example (Identity Fraud Victims in 2004 for Six States) X x = 122 , 129 and ¯ x = x n = 122 , 129 6 = 20 , 354 . 83 Mann E6 4/32 Notes Notes Notes Notes

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3.1 Measures of Central Tendency for Ungrouped Data 3.1.2 Median Definition The median is the value of the middle term in a data set that has been ranked in increasing order. Example The following data give the weight lost (in pounds) by a sample of five members of a health club at the end of two months of membership. 10 5 19 8 3 Find the median. Solution : First, rank the data in increasing order 3 5 8 10 19 Second, find the middle term: 8. Mann E6 5/32 3.1 Measures of Central Tendency for Ungrouped Data 3.1.3 Mode Definition The mode is the value that occurs with the highest frequency in a data set. Example Find the mode of 10 5 8 19 8 3 Remarks: 1) A data set could have no mode, one mode ( unimodal ), two modes ( bimodal ) or more than two modes ( multimodal ). 2) Mode exists for categorical data as well. Mann E6 6/32 3.1 Measures of Central Tendency for Ungrouped Data 3.1.3 Relationship among the mean, median and mode Mann E6 7/32 3.1 Measures of Central Tendency for Ungrouped Data 3.1.3 Relationship among the mean, median and mode Mann E6 8/32 Notes Notes Notes Notes
3.1 Measures of Central Tendency for Ungrouped Data 3.1.3 Relationship among the mean, median and mode Mann E6 9/32 3.2 Measures of Dispersion for Ungrouped Data

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