If x1, x​2, x3.....,xn are the means of n groups with nnn3......,nn number of observations respectively, then find the mean x of all the groups taken together

Dear Student,

Please find below the solution to the asked query:

We know :  Mean  = Sum of observationsNumber of observations , So  We get

Sum of observations1n1 = x1 ,

( Sum of observations )1 = n1x1  , Similarly we get 

( Sum of observations )2 = n2x2

( Sum of observations )3 = n3x3 
.
.
.
( Sum of observations )n = nnxn

Then ,

Mean of all group together = x  = n1x1 +n2x2  + n3x3 + . . . + nnxnn1 + n2 + n3 + . . . + nn                                   ( Ans )
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