5. Find the weighted mean of the following two samples.
Sample 1: n = 5 and the mean = 20
Sample 2: n = 15 and the mean = 10.
To find the weighted mean of the two samples, you need to consider the sizes (n) of each sample. The weighted mean takes into account the relative importance or weight of each sample.
1. Calculate the total weight: The total weight is the sum of the sample sizes. In this case, the total weight is 5 + 15 = 20.
2. Calculate the weighted sum: Multiply the mean of each sample by its respective weight. For Sample 1, the weighted sum is 5 * 20 = 100. For Sample 2, the weighted sum is 15 * 10 = 150.
3. Calculate the weighted mean: Divide the total weighted sum by the total weight. In this case, the weighted mean is (100 + 150) / 20 = 12.5.
Therefore, the weighted mean of the two samples is 12.5.