One sample has a mean of and a second sample has a mean of . The two samples are combined into a single set of scores. What is the mean for the combined set if both of the original samples have scores

a) For this case we can use the definition of weighted average given by:

And if we replace the values given we have:

b)

c)

Step-by-step explanation:

Assuming the following question: "One sample has a mean of M=8 and a second sample has a mean of M=16 . The two samples are combined into a single set of scores.

a) What is the mean for the combined set if both of the original samples have n=4 scores "

For this case we can use the definition of weighted average given by:

And if we replace the values given we have:

b) what is the mean for the combined set if the first sample has n=3 and the second sample has n=5

Using the definition we have:

c) what is the mean for the combined set if the first sample has n=5 and the second sample has n=3

Using the definition we have: