Question

what is the mean for the combined set if the first sample has n=3 and the second sample has n=6

Answer 1

The combined mean for two sets will depend on also the means for the each respective set:

$x_{a+b} = \frac{n_ax_a+n_bx_b}{n_a+n_b}$ ,

where:

$x_a$ = the mean of the first set,

$n_a$ = the number of items in the first set,

$x_b$ = the mean of the second set,

$n_b$ = the number of items in the second set,

$x_{a+b}$ = the combined mean.

Using the information we have,

$n_a = 3; n_b = 6, \\ x_{a+b} = \frac{1}{9}(3x_a+6x_b) = \frac{1}{3}(x_a+2x_b).$