Question

One sample of n = 10 scores has a mean of M = 8, and a second sample of n = 5 scores has a mean of M = 2. If the two samples are combined, what is the mean for the combined sample?

Answer 1

Answer:

The mean for the combined sample = 6.

Step-by-step explanation:

We have been given that one sample of n = 10 scores has a mean of M = 8.

So the sum of 10 scores for 1st sample will be: $10\times 8=80$

We are also told that second sample of n = 5 scores has a mean of M = 2.

So the sum of 5 scores for 2nd sample will be: $5\times 2=10$

When the both samples are combined, so total points will be: $80+10=90$ and total scores will be $10+5=15$.

$\text {Mean for the combined sample}=\frac{\text{Total points of both data sets}}{\text{Total scores of both data sets}}$

$\text {Mean for the combined sample}=\frac{90}{15}$

$\text {Mean for the combined sample}=6$

Therefore, the mean for the combined sample will be 6.

Answer 2

The mean of the combined sample is 6

The given parameters:

the number of the first sample = 10

the mean of the first sample = 8

the number of the second sample = 5

mean of the second sample = 2

To find:

• the combined mean of the two samples

The total sample number = 10 + 5 = 15

The sum of the first sample = 10 x 8 = 80

The sum of the second sample = 5 x 2 = 10

The sum of the two samples = 80 + 10 = 90

The mean of the combined samples;

$mean , M = \frac{sum \ of \ the \ sample}{number \ of \ samples} \\\\mean , M =\frac{90}{15} = 6$

Therefore, the mean of the combined sample is 6

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