A sample of n=5 scores has a mean 50. Another sample has n=10 scores and a mean of 60. If the two samples are combined, will the combined sample mean be greater than 55

[n1(mean1)+n2(mean2)]/(n1+n2)

no

To determine if the combined sample mean will be greater than 55, we can use the concept of weighted means.

The formula to calculate the weighted mean is:
Weighted Mean = (Sum of (Value * Weight)) / (Sum of Weights)

In this case, the weights are the number of scores in each sample (n), and the values are the means of the samples.

For the first sample with n=5 and mean 50:
Weighted Mean of Sample 1 = (50 * 5) / 5 = 50

For the second sample with n=10 and mean 60:
Weighted Mean of Sample 2 = (60 * 10) / 10 = 60

To find the combined sample mean, we'll calculate the weighted mean of the two samples combined.

Let's say the combined sample has a total of N scores, where N = n1 + n2, and n1 and n2 are the number of scores in the first and second samples, respectively.

Weighted Mean of Combined Sample = [(Weighted Mean of Sample 1 * n1) + (Weighted Mean of Sample 2 * n2)] / N

Let's substitute the values we know:
Weighted Mean of Combined Sample = [(50 * 5) + (60 * 10)] / (5 + 10)
= (250 + 600) / 15
= 850 / 15
= 56.67

Therefore, the combined sample mean is 56.67.

Since 56.67 is indeed greater than 55, the combined sample mean will be greater than 55.