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Lecture

GGR270 Lecture #4 Oct. 3 2012.pdf

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Department
Geography
Course
GGR270H1
Professor
Damian Dupuy
Semester
Fall

Description
GGR270  Lecture  #4     October  3,  2012     Measures  of  Dispersion   • Coefficient  of  variation  (continued)   o Would  calculate  for  each  individual  sample  and  note  which  one  has   the  highest  degree  of  variability.     Practical  Significance  of  Standard  Deviation   • Tchebysheff’s  Theorem  and  Empirical  Rule   o We’re  relating  the  standard  deviation  to  the  normal  curve   o On  a  normal  distribution  (bell  curve)  we  know  the  mean  is  in  the   center.   o  And  then  we  ask  how  do  we  interpret  the  standard  deviation?   o We  always  say  that  the  standard  deviation  is  equal  to  plus/minus.   o Typically  we  don’t  go  further  than  +/-­‐  3  standard  deviations  on  a   normal  curve.     o We  use  it  in  terms  of  understanding  distributions  of  marks  and   predicting  the  possibility  of  particular  values  cropping  up,  we  can  also   view  it  in  terms  of  probability.   o Empirical  rule  only  works  with  normal  data.   o See  charts  on  notes.   • Z  scores   o Standardizes  any  value  on  the  above  curve,  so  that  we  can  compare   any  value  that  we  have  to  our  mean  and  standard  deviation.   o Standard  scores  are  referenced  to  as  Z  Scores.   o They  indicate  how  many  standard  deviations  separate  a  particular   value  from  the  mean.   o The  standard  deviation  is  +/-­‐  1  value  from  the  mean  for  example,  1  is   our  standardized  distance  –  but  this  approach  takes  any  value  for   example  1.2  standard  deviations.   o Z  scores  can  be  +  or  –  depending  on  if  they  are  >  or  <  than  the  mean.     o Z  score  of  the  mean  is  0  and  the  standard  deviation  is  +  or  –  1.   o Table  of  Normal  Values  provides  probability  information  on  a   standardized  scale.    We  can  also  calculate  Z  scores.   o Formula  involves  comparing  values  to  the  mean  value,  and  dividing  by   the  standard  deviation.   o Result  is  interpreted  as  the  ‘number  of  standard  deviations  an   observation  lies  above  or  below  the  mean’.   o Z  =  X  -­‐                /  S      Where:  S  –  Standard  deviation.    X  –  is  each  value  in  the  data  set.              −  is  the  mean  of  all  values  in  the  data  set.           GGR270  Lecture  #4     October  3,  2012     Bivariate  Data   • Simple  bivariate  graphs:   o Comparative  pie  charts.   o Stacked  bar  graph.   o In  these  you  are  not  getting  the  sense  of  the  relationship  because  we   need  to  see  how  one  variable  relates  to  another.   • Correlation   o Allows  us  to  observe,  statistically  the  relationship  between  two   variables.   o How  strong  is  the  relationship  –  is  it  positive  or  negative.   o You  can  say  a  lot  except  that  one  causes  the  other.   o Looking  at  strength  and  direction  of  the  relationship  between  these   two  variables.   o Most  common  graphic  technique  that  we  use  is  the  Scatterplot.    Consists  of  pairs  of  variables  such  as  years  of  schooling  or   income.      Says  even  though  you  aren’t  saying  one  thing  causes  something   else,  you  are  saying  one  works  as  a  function  of  something  else   o Direction  of  the  bivariate  relationship    Positive:  as  X  increases,  Y  increases.  U
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