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Study Guide Exam 1

by: Olivia Sorenson

Study Guide Exam 1 STAT 201 003

Olivia Sorenson

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These notes included everything except the material covered in the last two lectures (Wednesday and Friday) before the exam.
Elementary Statistics
Dr. Tass
Study Guide
50 ?




Popular in Elementary Statistics

Popular in Statistics

This 8 page Study Guide was uploaded by Olivia Sorenson on Saturday January 23, 2016. The Study Guide belongs to STAT 201 003 at Brigham Young University taught by Dr. Tass in Winter 2016. Since its upload, it has received 130 views. For similar materials see Elementary Statistics in Statistics at Brigham Young University.


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Date Created: 01/23/16
key  terms  are  bolded  –  know  their  definitions   equations  are  all  given  in  red  boxes   –  know  how  to  use  them  and  when     Introduction  to  Statistics   Statistics   The  science  that  deals  with  the  collection,  classification,  analysis,  and  interpretation  of  numerical         facts  or  data,  by  use  of  mathematical  theories  of  probability  in  the   presence  of  variation   Statistical  inferences     Conclusions  are  made  based  on  the  sa mple  and  applied  to  the  population :           (1)  Based  upon  data  that  is  collected  by  observation  or  experimentation             (2)  There  is  a  degree  of   uncertainty,  which  should  be  reported     Probability   The  language  of  variability  and  the  mathematical  structure   that  the  science  of  statistics  is  based  on     The  Science  of  Statistics                   Scientific  Method   • Ask  question   • Make  hypothesis  (current  knowledge)         Statistics:   • Design  Experiment               Step  1   • Gather  Data   • Conclusion  (analyze  data  to  update  knowledge)       Step  2:  based  on  probability   CHAPTER  1:  Collecting  Data   Population   The  set  of  all  possible  outcomes  for  which  data  is  sought       Conceptual   All  the  values  that  can  be  observed  in  experimental  conditions       Tangible   A  type  of  population  you  can  touch   Sample   The  subset  of  the  population  that  is   actually  studied  and  from  which  data  is  collected       Simple  Random  Sample   sample  is  chosen  at  random,  everyone  is   equally  likely  to  be  chosen   Randomness   Allows  us  to  assume  items  in  the  sample  are   independent  (they  do  not  affect  each  other)       Knowing  the  measurement  for  one  item  does  not  tell  us  any  information  about  any  other  item   Data     Measurements  from  the  sample ;  “n”  is  the  number  of  data  points  in  the  sample   Variable     Characteristic,  number,  or  quantity  that  can   be  measured  or  counted;  a  data  item       Numerical   quantitative,  measureable,  any  type  of  number       Categorical   qualitative,  items  are  placed  into  categories       Response  variable   the  outcome,  dependent  variable,  y-­‐axis,  the  data  you  are  observing       Explanatory  variable     the  input,  independent  variable,  x-­‐axis,  controlled  by  researcher               categorical  explanatory  variables  are  called   factors   Observational  Study     observe  factors  as  they  are,  researcher  does  not  control  factors           cannot  conclude  causation   Controlled  Experiment   factors  are  controlled           causation  conclusions  are  justified     Summarizing  Data   1.  Center   represents  “typical  value”  of  the  sample       Sample  Mean   average  of  sample  values,  susceptible  to  outliers       Median     “middle”  of  the  ordered  sample  values             (If  there  is  an  even  number,  take  the  average  of  the  middle  two)   • If  the  mean  and  the  median  are  different,  then  the  data  is  skewed   • If  they  are  the  same,  the  data  is  symmetric   2.  Spread   variation  and  standard  deviation  (conveys  the  uncertainty  in  the  data)       Sample  Variance   X i=  each  data  point             ????  =  sample  mean           Standard  Deviation   also  susceptible  to  outliers     • Smaller  deviation  means  more  certainty  in  the  data   • These  two  are  ALWAYS  positive  numbers!     Relative  Position     Percentile     denoted  “p”  and  expressed  as  a  decimal         EXAMPLE:  40  percentile  is  the  value  at  which  40%  of  the  data  is  below  it;  p  =  0.4         Calculate  percentile:  1.  order  data  from  smallest  to  largest               2.     x  =  p  (n+1)               3.  Count  x  data  points  along  in  the  ordered  data     (if  x  is  a  decimal,  take  average  of  the  two         Interquartile  Range   IQR  =  Q3  –  Q1   closest  ordered  values)         Special  Cases:     Q1  =  25  percentile,       so  p  =  0.25           th             Median  =  50  percentile,     so  p  =  0.5               Q3  =  75  percentile,       so  p  =  0.75     3.  Shape   visual  representations,  graphs       Histogram   useful  for  large  sample  sizes,  **no  spaces  between  bars!           data  is  divided  into  “bins”  (intervals)  and  the  frequency  of  each  bin  is  plotted   ***TEST  QUESTION:  be  able  to  find  1  quartile  by  looking  at  a  histogram!           Boxplot   centerline  =  median                                    box  =(so  50%  of  the  data  is  in  the  box)                                        whiskers  =  smallest  and  largest  data  points  within:            1.5(IQR)                      outliers  =  plotted  individually         Bar  chart   used  for  categorical  data,  **spaces  between  bars!           order  is  random  so  shape  does  not  matter           better  than  pie  charts  because  it  is  easy  to  compare  bars  just  by  looking   Other:  Dotplot,  stem-­‐and-­‐leaf  plot     4.  “Unusual”  values     outliers  in  the  data     CHAPTER  2:  Probability   Probability     denoted  P(A);  in  terms  of  the  long  run  as  if  the  experiment  is  repeated  infinitely     Experiment     process  that  results  in  an  outcome  that  could  not  have  been  predicted  with  certainty   Sample  Space   set  of  all  possible  outcomes   Event       denoted  A   a  subset  of  sample  space,  a  particular  set  of  outcomes  of  interest   Union       denoted  A∪B,  which  reads  “A  and  B”     Intersection     denoted  A∩B,  which  reads  “A  or  B”       Compliment     denoted  A ,  which  reads  “not  A”       Mutually  exclusive   two  events  can  never  happen  at  the  same  time         their  Venn  diagrams  do  not  overlap  (no  elements  in  common)         A∩B  =  ∅  (empty  set)       The  Axioms  of  Probability   1.  Let  S  be  the  sample  space.  Then  P(S)  =  1   2.  For  any  event  A,  0  ≤  P(A)  ≤  1.   3.  If  A  and  B  are  mutually  exclusive  events,  then  P(A∪B)  =  P(A)  +  P(B).     ALSO:   P(A )  =  1  –  P(A)     P(∅)  =  0   Additive  Rule:  If  A  and  B  are  NOT  mutually  exclusive  events,  then  P(A∪B)  =  P(A)  +  P(B)  –  P(A∩B)     Conditional  Probability     A  probability  that  is  based  on  part  of  the  sample  space  –  no  longer  random           Look  for  words:  If,  given,  assuming,  suppose                       Independence   knowing  the  probability  of  one  event  does  not  change  what  you  know  about  the           probability  of  another  event         If  two  events  are  independent,  so  are  their  compliments         P(B|A)  =  P(B)         P(A∩B)  =  P(A)  P(B)     (Multiplicative  Rule)     Mutually  Exclusive             vs.     Independence   If  B  happened,  I  know  A  did  not  happen       If  B  happened,  I  still  know  nothing  about  A     • An  event  cannot  be  mutually  exclusive  and  independent  at  the  same  time!     Law  of  Total  Probability   When  mutually  exclusive  sets  join  together  to  form  a  partition           If  A ,…A 1  are  mutunlly  exclusive,  then:             Special  case,  when  n  =  2,  then:           Bayes’  Rule     Allows  us  to  flip  the  conditions  in  conditional  probability:     A|B     B|A         If  A ,…A 1  are  mutunlly  exclusive,  then:             Special  case:         Random  Variable   assigning  a  numerical  value  to  each  outcome  of  an  experiment         Discrete   possible  values  form  a  discrete  set         Continuous   possible  values  contain  an  interval   Probability  Distribution   all  the  possible  values  of  the  random  variable  and  the  probability  of  each           this  can  be  a  table,  equation  or  a  graph         Discrete:   probability  =  height  of  graph  (y-­‐axis)         Continuous:   probability  =  area  under  the  curve             density  =  height  of  graph  (y-­‐axis)               discrete         continuous     Probability  Mass  Function   probability  distribution  of  a  discrete  random  variable             pmf  is  denoted  p(x)  =  P(X  =  x)   p(x)  ≥  0   Σp(x)  =  1   Cumulative  Distribution  Function   cdf  is  denoted  as  F(x)  =  P(X  ≤  x)   Facts  about  cdf:     F(x)  is  non-­‐decreasing   The  location  of  the  jumps  and  their  magnitude  represent  pmf…  aka  p(x)     If  we  think  of  discrete  random  variables  as  the  population:   Theoretical/Population  Mean     the  mean  of  all  discrete  random  variables     Theoretical/Population  Variance   the  variance  of  all  discrete  random  variables           Theoretical/Population  Standard  Deviation   the  standard  deviation  of  all  discrete  random  variables              


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