Statistics Summary

Chapter  1  Intro  and  Basic  Concepts  

N:  Population  elements  

n:  Sample  elements  

Qualitative:    

Nominal:  Cannot  be  ordered  

Ordinal:  Can  be  ordered  

Quantitative:   Interval:  Differences  of  values  are  meaningful,  ratios  not.  

Ratio:  Differences  and  ratios  are  meaningful.  

Discrete  variables:  Set  of  possible  variables  can  be  counted.  

Continuous  variables:  Set  of  possible  variables  with  same  real  interval,  with  uncountable  many  

numbers.  

Descriptive  Statistics:  Gathering  the  data,  summarization  (tables,  graphs;  statistics)  

Probability  (theory):  Chance;  probability;  rules  

Sampling  (theory):  How  to  draw  a  sample?  Properties  of  random  sampling  

Inferential  Statistics:  Drawing  conclusions  about  the  population  on  the  basis  of  a  sample  from  it  

Chapter  2  Tables  and  Graphs  

Frequency  distribution:  Overview  of  all  values  with  accompanying  frequencies  

Relative  frequency  distribution:  Overview  of  all  values  with  accompanying  relative  frequencies  

-­‐

Frequency/total  observations  

CDF  (cumulative  distribution  function  F):  F(a)  =  relative  frequency  of  the  observations  £  a;  real  

numbers  a  

Classified  freq  distribution:  Overview  of  classes  and  accompanying  frequencies  

-­‐  depends  on  the  classification  

-­‐  preferably  equal  class  width  

Frequency  density:  Overview  of  classes  and  relative  frequencies  divided  by  corresponding  

class  widths  

Linear  interpolation:      

 (or  see  book  page  42)  

Chapter  3  Measures  of  Location  

Mode:  value  with  the  largest  frequency  

Median:  middle  of  ordered  observations  

Mean  (=  arithmetic  mean):  Average  (population  =  µ,  sample  =   )  

Weighted  mean:  

Geometric  mean:  

Property:  

Population  mean:    

Sample  mean:      

 ...