Question

One sample has n = 4 scores and M = 10. A second sample has n = 6 scores and M = 5. If the two samples are combined, then what is the mean for the combined sample?

Answer 1

First sample:

$$n_1=4, M_1=10, \sum_ix_i=4(10)=40$$

Second sample:

$$n_2=6, M_2=5, \sum_iy_i=6(5)=30$$

Combined sample:

$$n_{comb}=n_1+n_2=4+6=10$$

$$\sum_iu_i=\sum_ix_i+\sum_iy_i=40+30=70$$

$$M_{comb}=\dfrac{\sum_iu_i}{n_{comb}}=\dfrac{70}{10}=7$$

The mean for the combined sample is $M_{comb}=7.$