Lecture02 - Todays Schedule Notation Summary Statistics for...

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17 April 2003 Biostatistics 6650--L2 1 Today’s Schedule Notation Summary Statistics for Quantitative Data location spread
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17 April 2003 Biostatistics 6650--L2 2 Notation Assume we have a random sample of observed data values: Total sample size: n Summation symbol is 1 2 3 1 ... n n i i x x x x x + = = + + + 1 2 , ,..., n x x x
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17 April 2003 Biostatistics 6650--L2 3 Notation Notation Example: We have a sample of n =5 numbers. 5 1 5 3 9 6 10 33 i i x = = + + + + = 1 2 3 4 5 5, 3, 9, 6, 10 x x x x x = = = = =
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17 April 2003 Biostatistics 6650--L2 4 Summary Statistics Summary Statistics Central location Mean Median Mode Spread Range Percentiles Variance/Standard Deviation Coefficient of Variation
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17 April 2003 Biostatistics 6650--L2 5 Central Location Sample Mean Denote observed data from a random sample of size n as: Denote the sample mean as Note: Expected value of = , the pop’n mean 1 2 , ,..., n x x x x 2 1 1 ( ) / ( ) / n n i i x x x x n x n = = + + + = K X μ x
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17 April 2003 Biostatistics 6650--L2 6 Central Location Central Location Example: calculate sample mean from previous 5 data points =(5+3+9+6+10)/5 =33/5 =6.6 . .. . . Mean is ~ center of gravity. 2 1 1 ( ) / ( ) / n n i i x x x x n x n = = + + + = K 6 . x
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17 April 2003 Biostatistics 6650--L2 7 Central Location Central Location Median Middle value when the data are arranged in order from smallest to largest th ( ) (1) (2) ( ) (( 1)/2) ( /2) ( / 2 1) denotes the i largest observation ... median if n is odd [ ]/ 2 if n is even i n n n n x x x x x x x + + = = +
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17 April 2003 Biostatistics 6650--L2 8 Central Location Central Location Median n=8 3.1, 5.6, 7.8, 8.3, 9.2 , 10.1, 12.7, 18.1 • median= x (4) + x (5) 2 = 8.3+9.2 2 = 8.75 n=7 3.1, 5.6, 7.8, 8.3 , 9.2, 10.1, 12.7 • median= x (4) = 8.3
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17 April 2003 Biostatistics 6650--L2 9 Central Location Central Location Mode The observational value(s) that occurs with the highest frequency in the random sample Not influenced by extreme observations More than one mode may exist, or none at all Example 8.5 15.7 15.7 16.6 19.4 19.5 21.8 23.8 23.8 26.5 Modes at 15.7 and 23.8
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17 April 2003 Biostatistics 6650--L2 10 Central Location Central Location Symmetric unimodal distribution Mean, median, and mode about equal Frequency Median=Mean X
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17 April 2003 Biostatistics 6650--L2 11 Central Location Central Location Skewed to the right mean greater than median Median Mean .
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17 April 2003 Biostatistics 6650--L2 12 Central Location Central Location Skewed to the left mean < median Mean Median
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17 April 2003 Biostatistics 6650--L2 13 Central Location Central Location Symmetric distribution, but multimodal
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17 April 2003 Biostatistics 6650--L2 14 Central Location Central Location
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Lecture02 - Todays Schedule Notation Summary Statistics for...

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