One sample of n=20 scores has a mean of M=50. A second sample of n=5 scores has a mean of Mean=10. If the two samples are combined, what is the mean
Mean =∑x/n
50 = ∑x/20
∑x = 100
10 = ∑x/5
∑x = 50
Mean = 150/25 = ?
cf23
To find the mean of the combined samples, you need to calculate the weighted average of the two means based on their sample sizes.
First, let's calculate the total sum of the two samples by multiplying each mean by its respective sample size:
Sample 1 sum = M1 * n1 = 50 * 20 = 1000
Sample 2 sum = M2 * n2 = 10 * 5 = 50
Next, calculate the total sample size (n_total) by adding the two sample sizes:
n_total = n1 + n2 = 20 + 5 = 25
Finally, calculate the mean of the combined samples by dividing the total sum by the total sample size:
Mean_combined = (Sample 1 sum + Sample 2 sum) / n_total
= (1000 + 50) / 25
= 1050 / 25
= 42
Therefore, the mean of the combined samples is 42.