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Unformatted text preview: Measures of Central Tendency and Variation OneSample Measures OneSample Measures of Central Tendency of Central Tendency 1) Mode The value of a set of observations that occurs with the greatest frequency There may be > 1 mode The mode may be used with data measured on any level OneSample Measures OneSample Measures of Central Tendency of Central Tendency Example : Number of children in 10 families 4,2,0,2,7,3,2,1,0,1 mode=2 Example : Number of cars in 10 families 2,1,1,2,1,2,0,1,2,0 modes = 1,2 ( bimodal) Example : Number of statistics books owned by 10 ISU faculty members 7,5,3,24,58,16,8,6,0,1 no mode [ uniform distribution] OneSample Measures OneSample Measures of Central Tendency of Central Tendency Median (the 50th percentile) The middleranked value, for n odd The average of the two middleranked values, for n even Either way, half the ranked observations lie above the median, and half below OneSample Measures OneSample Measures of Central Tendency of Central Tendency Example : 5 exam scores (n odd) 50, 82, 87, 89, 96 median = case = Example : 6 exam scores (n even) 50, 73, 82, 87, 89, 96 median = + 2 1 n X ( 29 87 3 2 6 = = X X 2 2 1 2 6 2 6 1 2 2 + + + = + X X X X n n ( 29 ( 29 5 . 84 2 87 82 2 4 3 = + = + = X X OneSample Measures OneSample Measures of Central Tendency of Central Tendency A key property of the median is that the sum of the absolute deviations from the median, is a minimum. For example, for the 5 exam scores, = 5087 + 8287 + 8787 + 8987 + 9687 = 37 + 5 + 0 + 2 + 9 = 53   1 Median X n i i =   1 Median X n i i = OneSample Measures OneSample Measures of Central Tendency of Central Tendency 1) Mean center of gravity in a sample; in a population Simple arithmetic average of a set of values, denoted in a sample; in a population is an estimator of X x N X i x = n X X i = X x OneSample Measures OneSample Measures of Central Tendency of Central Tendency In general, , but E( ) = . This says that the expected value of the sample mean, in repeated samples from the same population, is the population mean. This is a statement of the statistical property of unbiasedness , which means here that the longrun average of the values of for all possible samples of a fixed size, n, drawn from a population, is the population mean, ....
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This note was uploaded on 03/26/2008 for the course STAT 401 taught by Professor Shelley during the Spring '08 term at Iowa State.
 Spring '08
 Shelley
 Probability

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