Weighted Mean A student of one of the authors earned grades of 63, 91, 88, 84, and 79 on her five regular statistics tests. She earned a grade of 86 on the final exam and 90 on her class projects. Her combined homework grade was 70. The five regular tests count for 60%

of the final grade, the final exam counts for 10%, the project counts for 15%, and homework counts for 15%. What is her weighted mean grade? What letter grade did she earn (A, B, C, D, or F)? Assume that a mean of 90 or above is an A, a mean of 80 to 89 is a B, and so on.

29. Degrees of Freedom Five pulse rates randomly selected from Data Set 1 “Body Data” in Appendix B have a mean of 78.0 beats per minute. Four of the pulse rates are 82, 78, 56, and 84.

a. Find the missing value.

b. We need to create a list of n values that have a specific known mean. We are free to select any values we desire for some of the n values. How many of the n values can be freely assigned before the remaining values are determined? (The result is referred to as the number of degrees of freedom.)
30. Censored Data Recently, five U.S. presidents were still alive and after their first inauguration, they have lived 37 years, 25 years, 21 years, 13 years, and 5 years so far. We might use the values of 37+, 25+, 21+, 13+, and 5+, where the positive signs indicate that the actual value is equal to or greater than the current value. (These values are said to be censored at the current time that this list was compiled.) If we ignore the presidents who took office because of an assassination or resignation and if we ignore the five presidents who are still alive, the mean of the 33 remaining presidents is 15.0 years. What do we know about the mean if we include the censored values of 37+, 25+, 21+, 13+, and 5+? Do the two results differ by much?
31. Trimmed Mean Because the mean is very sensitive to extreme values, we say that it is not a resistant measure of center. By deleting some low values and high values, the trimmed mean (or truncated mean) is more resistant. To find the 10% trimmed mean for a data set, first arrange the data in order, next delete the bottom 10% of the values and delete the top 10% of the values, and then calculate the mean of the remaining values. Use the LDL measurements of the 300 subjects from Data Set 1 “Body Data” in Appendix B. Compare the mean, the 10%
trimmed mean, and the 20% trimmed mean.