lecture1 - ISYE 2028 A and B Spring 2009 Lecture 1 Dr. Kobi...

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ISYE 2028 A and B Spring 2009 Lecture 1 Dr. Kobi Abayomi January 8, 2009 1 Introduction: What is Data In statistics we worry about what there is to observe (what we expect to see) and what we have actually observed (what we do in fact see). Data are the quantitative characterizations of what we see, often based upon what we expect (or often even desire to see). Data are our observations: observed and quantified. We call the population the set of all possible observations. We call a sample the observations we see at a glance, inspection or study. A statistic is any quantity we derive from the observed data – i.e. any quantity we can generate from the sample. A parameter is any quantity we cannot observe about the data; one that is specific to the population. We often seek to estimate parameters using samples from the population. 1 2 Classifying and Observing Data We often call the individual objects described by a set of data call units of observation or cases . A variable is an object that holds information about the same characteristic for many cases. A data table is an arrangement of data – the convention is to let rows represent cases and columns represent variables. Here is an example of a possible data table. ID Name ShoeSize TestScore Classlevel FashionLevel 1 Kobi 11 95 Graduate Low 2 Djleroy 11 100 PhD. High 3 Ronald 22 50.15 Pre-K Very Low ... ... ... ... ... 1 These are my heuristic definitions. .. 1
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We classify variables as either quantitative - where the numbers act as numerical values or categorical - which are either word or numerals that are treated as non-numeric. For the above example, which variables are which. Quantitative data can be either discrete – in that we can list all the possible values – or continuous in that we cannot. A more particular distinction is to say a variable is discrete if it can take countably many values and that a variable is continuous otherwise. The distinction is often apparent in use. Quantitative variables in which the order (in the greater than, less than sense) and distance be- tween data can be determined are called interval variables. Percent scores are examples of interval variables. Quantitative variables in which the order of data points can be determined, but not the distance are called ordinal . Examples are letter grades. . Categorical variables which are determined by categories that cannot be ordered, such as gender and color, are called nominal . In math notation a data table is a multivariate vector – i.e. matrix x with dimension n x k or ( n,k ) or n rows and k columns. The observations are the rows n ; the number of measurement types is k , the number of columns. We select the ith observation of the jth variable with element x i,j from x . In
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lecture1 - ISYE 2028 A and B Spring 2009 Lecture 1 Dr. Kobi...

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