Variables
   Individuals are the objects described by a set of 
   data; may be people, animals or things
   Variable is any characteristic of an individual
                             Statistical Data
                                          What purpose do the data 
                                          have?
                                          Individuals  –  Describe?   
                                          How many?
                                          Variables  –  How  many?   
                                          Definition?        Unit    of 
                                          measurement?
        Types of Variables
   Categorical  variable  places  an  individual  into 
   one of several groups or categories
   Quantitative  variable  takes  numerical  values 
   for which arithmetic operations make sense
   Distribution of a variable tells us what values it 
   takes and how often it takes these values
                   Exploratory Data Analysis
         Examine  each  variable  by  itself…  then 
         relationships among the variables
         Start   with    graphs…  then  add  numerical 
         summaries of specific aspects of the data
           Levels of Measurement
     Nominal
     Ordinal  
     Interval  
     Ratio
     It's  important  to  recognize  that  there  is  a 
     hierarchy  implied  in  the  level  of  measurement 
     idea. At each level up the hierarchy, the current 
     level includes all of the qualities of the one below 
     it  and  adds  something  new.  In  general,  it  is 
     desirable to have a higher level of measurement.