Basic_Statistics - Basic Statistics Author: John M....

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Basic Statistics Author: John M. Cimbala, Penn State University Latest revision: 16 October 2007 Introduction The purpose of this learning module is to introduce you to some of the fundamental definitions and techniques related to analyzing measurements with statistics . In all the definitions and examples discussed here, we consider a collection (sample) of measurements of a steady parameter. E.g., repeated measurements of a temperature, distance, voltage, etc. Basic Data Analysis using Statistics First some definitions are necessary: o Population – the entire collection of measurements, not all of which will be analyzed statistically. o Sample – a subset of the population that is analyzed statistically. A sample consists of n measurements. o Statistic – a numerical attribute of the sample (e.g., mean, median, standard deviation). Suppose a population – a series of measurements (or readings) of some variable x is available. Variable x can be anything that is measurable, such as a length, time, voltage, current, resistance, etc. Consider a sample of these measurements – some portion of the population that is to be analyzed statistically. The measurements are x 1 , x 2 , x 3 , . .., x n , where n is the number of measurements in the sample under consideration. The following represent some of the statistics that can be calculated: Mean – the sample mean is simply the arithmetic average , as is commonly calculated, i.e., 1 1 n i i x x n = = , where i is one of the n measurements of the sample. o We sometimes use the notation x avg instead of x to indicate the average of all x values in the sample, especially when using Excel since overbars are difficult to add.
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This note was uploaded on 04/05/2008 for the course ME 345 taught by Professor Staff during the Spring '08 term at Pennsylvania State University, University Park.

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Basic_Statistics - Basic Statistics Author: John M....

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