We have given, Also, Putting this in above equation Now, given …[1] using this We have, …[2] We know, If x 1 , x 2 , … , x n are observations with frequencies f 1 , f 2 , … , f n i.e. x 1 occurs f 1 times and x 2 occurs f 2 times and so on, then mean( ) of observations is given by From [1] and [2]

If , then =

We have given,

Also,

Putting this in above equation

Now, given …[1]

using this

We have,

…[2]

We know,

If x₁, x₂, … , x_n are observations with frequencies f₁, f₂, … , f_n i.e. x₁ occurs f₁ times and x₂ occurs f₂ times and so on, then mean() of observations is given by

From [1] and [2]