Suppose that the data are arranged in increasing order, T% of the observations are removed from each end and the sample mean of the remaining numbers is calculated. The resulting quantity is called a trimmed mean. The trimmed mean x generally lies between the sample mean and the sample median x. Why?
(a) Calculate the 10% trimmed mean for the yield data in Exercise 6-17.
(b) Calculate the 20% trimmed mean for the yield data in Exercise 6-17 and compare it with the quantity found in part (a).
(c) Compare the values calculated in parts (a) and (b) with the sample mean and median for the yield data. Is there much difference in these quantities? Why?