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Week 1 Notes - Lecture 2

by: Debra Tee

Week 1 Notes - Lecture 2 STATS 250

Marketplace > University of Michigan > Statistics > STATS 250 > Week 1 Notes Lecture 2
Debra Tee
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About this Document

Raw Data, Types of Variables, Summarizing one or two categorical variables, Numerical Summaries.
Introduction to Statistics
Brenda Gunderson
Class Notes
summarizing, Histograms, boxplots, categorical, quantitative




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This 6 page Class Notes was uploaded by Debra Tee on Wednesday September 21, 2016. The Class Notes belongs to STATS 250 at University of Michigan taught by Brenda Gunderson in Fall 2016. Since its upload, it has received 17 views. For similar materials see Introduction to Statistics in Statistics at University of Michigan.


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Date Created: 09/21/16
Lecture  2:  Turning  Data  into  information     -   “Simple  summaries  of  data  can  tell  an  interesting  story  and  are  easier  to   digest  than  long  lists.”     2.1   Raw  Data   -   Raw  data  correspond  to  numbers  and  category  labels  that  have  been   collected  or  measured  but  have  not  yet  been  processed  in  any  way.       Definition:   -   A  variable  is  a  characteristic  that  differs  from  one  individual  to  the  next.   -   Sample  data  are  collected  from  a  subset  of  a  larger  population.   -   Population  data  are  collected  when  all  individuals  in  a  population  are   measured.   -   A  statistic  is  a  summary  measure  of  sample  data.   -   A  parameter  is  a  summary  measure  of  population  data.     2.2  Types  of  Variables   -­‐  We  have  2  variables  in  our  data  set.  We  want  to  distinguish  between  the   different  types  of   variables  -­‐  different  types  of  variables  provide  different  kinds  of  information  and   the  type  will  guide  what  kinds  of  summaries  (graphs/numerical)  are  appropriate.         -   Think  about  it:   ▯  Could  you  compute  the  “AVERAGE  AMOUNT  OF  SLEEP”  for  these  86  students?   YES   ▯  Could  you  compute  the  “AVERAGE  SLEEP  DEPRIVED  STATUS”  for  these  86   students?  NO  (could  code,  but  it  would  be  arbitrary:  0  and  1,  or  could  use  any  two   values  like  1  and  203)   -   SLEEP  DEPRIVED  STATUS  is  said  to  be  a  CATEGORICAL  variable,   -   AMOUNT  OF  SLEEP  is  a  QUANTITATIVE  variable.     Definitions:   -   A  categorical  variable  places  an  individual  or  item  into  one  of  several   groups  or  categories.   -   When  a  categorical  variable  has  ordered  categories,  it  is  called  an  ordinal   variable.   -   A  quantitative  variable  takes  numerical  values  for  which  arithmetic   operations  such  as   adding  and  averaging  make  sense.  Other  names  for  quantitative  variable   are:   measurement  variable  and  numerical  variable       Exercise:     ▯ -­‐    Age  (years):  QUANTITATIVE   ▯  -­‐  Typical  Classroom  Seat  Location  (Front,  Middle,  Back):  CATEGORICAL   ▯  -­‐  Number  of  songs  on  an  iPod:  QUANTITATIVE   ▯  -­‐  Time  spent  studying  material  for  this  class  in  the  last  24-­‐hour  period  (in  hours) :   QUANTITATIVE   ▯  -­‐  Soft  Drink  Size  (small,  medium,  large,  super-­‐sized):  CATEGORICAL  (ordinal)     2.3   Summarizing  One  or  Two  Categorical  Variables   -   Numerical  Summaries:  percentages,  proportions,  frequency  distributions   -   Visual  summaries:  graph,  pie  charts,  histogram   -   Maximum,  Minimum   -   Categorical  Data:  Use  bar  graphs   Interpreting  Histograms:   1.   Location  (center,  average)   -   Approximately  the  middle  value  or  where  it  would  balance   2.   Spread  (variability)   -   Range  (overall  and  then  where  most  of  the  observations  are)   3.   Deviations  from  overall  Pattern   -   Outliers   Examples:           Numerical  Summaries:   -   Mean:  numerical  average  value   -   Median:  the  middle  value  when  data  is  arranged  from   smallest  to  largest   -     -   Range  =  Max  –  Minimum   -   Percentiles:  The  pth  percentile  is  the  value  such  that  p%  of   the  observations  fall  at  or  below  that  value.     th -   Median:  50  percentile   -   First  percentile:  25  percentile   th -   Third  quartile:  75  percentile   -   Interquartile  Range:  Measures  the  spread  over  the  middle   50%  of  the  data.  IQR  =  Q3-­‐  Q1   -   Outliers:  Uses  1.5*  IQR  rule     BOXPLOT:     -   Side  by  side  boxplots  are  good  for  comparing  2  or  more   sets  of  observations   -   Can’t  confirm  shape  from  a  boxplot  alone.  (Histograms   better  for  showing  shape).       Quantitative  Variables:   -   Histogram   -   QQ  Plots   -   Time  Plots   -   Boxplots   -   Scatter  plots     Categorical  Variables:     -   Bar  Charts   -   Pie  Charts   -   Freq.  Tables  


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