



 
Murtaza,
You know the mean and variance s^{2} (square of the standard deviation) and the number of items in the data set n. Let
S_{x} is n times the mean so you can find the value of S_{x} as n times the mean. Once you have this value then using the expression for the variance in my earlier response you can find
Now suppose you are given a new x value, x_{n+1} As you remarked you can find the sum of the x values as
and hence the new mean is
But you can also find the new SS_{x} by
and
I hope this helps,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 