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Handout1 - Week 1 Summary Statistics and Box Plots ChE BioE...

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Week 1: Summary Statistics and Box Plots ChE, BioE, EnvE 213 Prof. Milo Koretsky I. Measures of Central Tendency A. Mean ( x ). Measure of location or central tendency. Arithmetic mean is obtained by adding up all the samples and dividing by the number of samples: x = x i i ! n Also called the average. B. Median. Measure of location or central tendency. Middle value in a set of data which is arranged by value. If there is an even number of samples , the median is the average of the two middle ones. C. Mode. Observation that occurs most frequently in a set of data. There may be more than one mode in a frequency distribution, e.g., bimodal. II. Measures of Dispersion Standard Deviation of the sample (s) . A descriptor of the dispersion or variation within a sample. Mathematically it is the square root of the average squared deviation of the data about the mean. s = x i ! x ( ) 2 i " n ! 1 Range ( R ) . A descriptor of the dispersion or variation within a sample. Difference between the largest (in value) and smallest member of the data set: R = x max ! x min III. Box Plots Box plots are useful graphical devices to compare and display sample statistical data. There are
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