Let x_n and s²_n be the sample mean and variance for the sample {x₁, x₂, x₃, . . . , x_n}, and let x_n+1 and s²_n+1 be the sample mean and variance when we add a new observation x_n+1 to the sample.

Show that s²_n+1can be computed from x_n+1, x_n , and s²_n

Hint:

Show that ns²_n+1 satisfies ns²_n+1 = (n 1)s²_n + (n/(n + 1 ))(x_n+1 x_n)²