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# Unit 2 - Statistics V3100018.001 UNIT 2 Tables and Charts...

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Statistics – V3100018.001 UNIT 2 – Tables and Charts Giuseppe Arbia , Catholic University of the Sacred Hearth, Roma, Italy

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25/01/12 2 Population and sample
A deductive exercise to start Suppose that we have an urn that contains 6 balls each numbered progressively from 1 to 6. This is our POPULATION. And we draw 4 balls from the urn without replacing the ball in the urn after drawing (sampling without replacement). We can draw 15 different samples . 6 4 " # \$ % & = 6! 4!2! = 15; n ! = n ( n ( 1)( n ( 2). ..1

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A deductive exercise to start
A deductive exercise to start Let us compute the mean in each sample True mean = (1+2+3+4+5+6)/6 = 3.5 Different samples lead to different means.

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A deductive exercise to start Let us compute the mean of all possible sample means The mean of all possible sample means is equal to the true mean !!
A deductive exercise to start The highest frequency corresponds to the true value. This is called the sampling distribution of the mean Let us now count how many times a certain value occur and graph it.

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Each row represents an observation (individual). Each column represents a variable. Structure of a statistical database
Statistical variable: e. g. : gender, year of birth, birthplace, . Modality of the variable: e. g.: The variable gender has two modalities: M and F The variable year of birth has modalities e. g. 1988, 1989, 1990. .. Definitions

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Qualitative No order between modalities = Nominal variables (e.g. gender, working status etc.) With an intrinsic order = Ordinal variables (e.g. degree) Quantitative Continuous = A variabile defined on a Scale (e. g. duration of an internet connection) Discrete = Formally it is like an ordinal (e. g. number of accesses to a web page ) Typologies of statistical variables
We make such a distinction because Different typologies of data require different statistical methodologies

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Notice: sometimes in a questionnaire ordinal variables are coded with numbers: e.g. 1= bad; 2=sufficient; 3= good; 4= very good. The coding is
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Unit 2 - Statistics V3100018.001 UNIT 2 Tables and Charts...

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