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Measures of Central Tendency

Mean raw data :- Let x₁,x₂,x₃, … … xn. be n observations, then the mean is obtained by the formula :

Mean = ∑ x_i / n 

Where ∑ denotes the summation of all the observations.

Mean of grouped data :- Let f₁,f₂, … … fk be the frequencies of x₁, x₂ … … xk respectively, then mean is obtained by the formula :

Mean   =   ∑ f_i x_i  / n, where n= f₁ + f₂ + … … + fk.

To make the calculation easy, we suppose A as our assumed mean. The we use the following two formulae. Of the two second one is easy.

1.  Mean   = A + ∑ f_i d_i / n, where d_i = x_i – A   
2. Mean   = A + {∑ f_i u_i / n}× h, where, h is the class size,and  ui = (x_i – A)/h