Statistics I

Methods of calculating mean of grouped frequency distribution :
Direct Method : Let xi be class mark and fi be frequency of ith class interval. Mean = (Total fixi) / (Total fi)
Assumed Mean Method : Let xi be class mark of ith class interval, A be assumed mean and di be xi - A. 
Mean of di = (Total fidi) / (Total fi)
Total mean = A + mean of di.
Step Deviation Method : Let di = xi - A, ui = d/ h where h is class width. 
Mean of ui = (Total fiui) / (Total fi
Total mean = A + (mean of ui)h.

Method of calculating median of grouped frequency distribution :
  • Write given class intervals in column 1, respective frequencies in column 2, cumulative frequency less than type in column 3.
  • Find total frequency N = Total fi, find N/2, and then find c.f. less than type which is > or = N/2. That class is median class.
  • find median using formula Median = L(N/2 - c.f.).h/f where L is lower limit and h is width of median class.

Method of calculating mode of grouped frequency distribution :
  • Find maximum frequency (fm), determine its class called the modal class.
  • Find mode using formula Mode = L + [ (fm -f1) / (fm - f1 - f2) ]h where L is lower limit of modal class, f1 is premodal frequency and f2 is postmodal frequency.