STATISTICS_PLS

# STATISTICS_PLS - Department of Mechanical Engineering...

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Department of Mechanical Engineering STATISTICS ES 140 Section 5 Fall 2006

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Department of Mechanical Engineering Theory – Measures of Center Mode -the most frequent data point in a set Median -the middle score in the set Mean, Average, or Arithmetic Mean -the sum of the scores in the set divided by the number of scores Example: Set A: 12,34,36,42,52,54,68,72,81,93 Set B: 152,154,155,155,156,158,159,161,163,164
Department of Mechanical Engineering Mode The most frequent data point in a set (Hint: some sets have no mode) Set A: 12,34,36,42,52,54,68,72,81,93 Set B: 152,154,155,155,156,158,159,161,163,164

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Department of Mechanical Engineering Median The middle score in the set (Hint: if there are an even number of terms, use a value halfway between middle terms) Set A: 12,34,36,42,52,54,68,72,81,93 Set B: 152,154,155,155,156,158,159,161,163,164
Department of Mechanical Engineering Mean Average, or Arithmetic Mean -the sum of the scores divided by the number of scores Set A: 12,34,36,42,52,54,68,72,81,93 Set B: 152,154,155,155,156,158,159,161,163,164 Σ Set A =544 #scores=10 average A =54.4 Σ Set B =1577 #scores=10 average B =157.7

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Department of Mechanical Engineering Comparison of Measures SET MODE MEDIAN MEAN A None 53 54.4 B 155 157 157.7 Note: The different “center” values for a given set may not always be close to each other. e.g. SET C: 1, 3, 3, 59, 68, 76, 1000 C 3 59 172.86
Department of Mechanical Engineering Effect of outlying data The most important difference between the mean and the median is shown below. Observe what happens to a set of five scores when the largest one is made considerably larger: Set D: 12, 13, 23, 32, 43 Mean = 24.6 Median = 23 Set D Altered: 12, 13, 23, 32, 143 Mean = 44.6 Median = 23

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Department of Mechanical Engineering Measures of Variability Range Variance Standard Deviation
Department of Mechanical Engineering Range The difference between the smallest and the largest value Set E: 80 85 79 90 95 98 92

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Department of Mechanical Engineering Variance ( 29 ( 29 value Data data the of Mean points data of Number 1 Variance 1 2 2 = = = - - = = i n i i x n n x s μ Set E: 80 85 79 90 95 98 92
Department of Mechanical Engineering Variance Calculations ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 62 . 53 6 43 . 88 92 43 . 88 98 43 . 88 95 43 . 88 90 43 . 88 79 43 . 88 85 43 . 88 80 1 ) ( 43 . 88 7 92 98 95 90 79 85 80 2 2 2 2 2 2 2 2 1 2 2 1 = - + - + - + - + - + - + - = - - = = + + + + + + = = = = D n i i D n i i D s n x s n x μ

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Department of Mechanical Engineering Standard Deviation ( 29 ( 29 value Data data the of Mean points data of Number 1 Deviation Standard 1 2 = = = - - = = i n i i x n n x s μ Set E: 80 85 79 90 95 98 92 32 . 7 62 . 53 2 = = = D D s s
Department of Mechanical Engineering Interpretation of Standard Deviation If the values in a set are more "spread out" (i.e.

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## This test prep was uploaded on 04/08/2008 for the course ES 140 taught by Professor Varies during the Fall '07 term at Vanderbilt.

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STATISTICS_PLS - Department of Mechanical Engineering...

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