Statistics I

Methods of calculating mean of grouped frequency distribution :

Direct Method : Let x_i be class mark and f_i be frequency of i^th class interval. Mean = (Total f_ix_i) / (Total f_i)

Assumed Mean Method : Let x_i be class mark of i^th class interval, A be assumed mean and d_i be x_i - A. 

Mean of d_i = (Total f_id_i) / (Total f_i)

Total mean = A + mean of d_i.

Step Deviation Method : Let d_i = x_i - A, u_i = d_i / h where h is class width. 

Mean of u_i = (Total f_iu_i) / (Total f_i) 

Total mean = A + (mean of u_i)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 f_i, 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 (f_m), determine its class called the modal class.
• Find mode using formula Mode = L + [ (f_m -f₁) / (f_m - f₁ - f₂) ]h where L is lower limit of modal class, f₁ is premodal frequency and f₂ is postmodal frequency.