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GGR270 Lecture #3 Sept. 26 2012.pdf

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Damian Dupuy

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GGR270  Lecture  #3     September  26,  2012     • Mean  example:   o Temperature  data:     7.3;  10.7;  9.1;  8.4;  13.9;  9.4;  8.2     =  67/7   =9.57   ∴  the  mean  is  9.6     ***  Always  round  off  to  the  number  of  decimal  places  that  the  original  data  has.     Measures  of  the  Centre  II     • Median   o The  value  that  occupies  the  “middle  position”  in  an  ordered  set  of   observations  (smallest  #  -­‐  largest  #).   o Order  the  observations  lowest  to  highest.   o Formula:  =½(n+1)  –  this  gives  the  position  not  the  value.***   o When  trying  to  find  the  median  of  even  numbers;  if  3.5  is  the  position,   add  3  and  4  position  and  divide  by  half.       Measures  of  the  Centre  III     • Mode   o The  value  that  occurs  with  the  highest  frequency.   o Allows  you  to  locate  the  peak  of  a  relative  frequency  histogram.   Number  of   Frequency   Households   1   15   2   30   3   100   4   25   5   30   o 100  is  the  highest  frequency,  the  mode  is  3.   o The  range  of  values  that  occur  most  often.   o On  the  graph,  the  mode  is  the  bar  that  is  the  tallest.       Choosing  an  Appropriate  Measure   • Mean  is  usually  the  best  measure  as  it  is  sensitive  to  change  in  a  single   observation.     • BUT  not  a  good  measure  when:   o Distribution  is  bimodal.   GGR270  Lecture  #3     September  26,  2012     o Skewed  distributions.   o Outliers  (extreme  values)  are  present  in  the  data  set.  E.g.  2,  5,  6,  8,  9,   21,  22           Measures  of  Dispersion  I   • Range:   o Simplest  measure  of  dispersion   o Takes  the  difference  between  the  smallest  and  largest  value  in  the   data  set,  at  the  interval/ratio  scale   o Influenced  by  outliers   o Formula:  Range  =  X max  -min   • Quartiles:   o Can  yield  more  information  and  lessen  the  impact  of  outliers   o Data  is  divided  into  quartiles  (4  groups)     Measures  of  Dispersion  II   • Standard  Deviation  and  Variance:   o Two  of  the  most  commonly  used  measures  of  dispersion.     o Comparing  the  value  of  each  measure  to  the  mean.  
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