Final answer:
The mean of the given data set is approximately 494.44, and the 5% trimmed mean is 500 after removing the lowest and highest values from the ordered data.
Step-by-step explanation:
To compute the mean of the given data set (425, 475, 450, 600, 800, 575, 550, 150, 425), first, we need to add all the numbers together and then divide by the number of data points. There are 9 numbers in this set.
Mean = (425 + 475 + 450 + 600 + 800 + 575 + 550 + 150 + 425) / 9 = 4450 / 9 = 494.44 (approx).
Next, to compute the 5% trimmed mean, we first need to remove the lowest 5% and highest 5% of the data points. Since we have 9 data points, 5% of 9 is less than 1, so we will remove one data point from each end after ordering the data. First, we order the data set from lowest to highest: 150, 425, 425, 450, 475, 550, 575, 600, 800. Removing the lowest and highest values, we then have: 425, 425, 450, 475, 550, 575, 600.
Trimmed Mean = (425 + 425 + 450 + 475 + 550 + 575 + 600) / 7 = 3500 / 7 = 500.