Section 1.3-1.4 Exercises

Complete the following exercises from Section 1.3:

• Problem 33 The data represents high workload single leg power of 14 elite endurance cyclists.
  • a) Calculate and interpret the sample mean and median.
  • b) What would be the effect on the mean and median if the first observation was 204 instead of 244?
  • c) Calculate a trimmed mean by choosing a percentage that eliminates the smallest and largest values.
  • d) The article also reports low workload values. The mean for n=13 observations was 119.8. If the 14th observation was 159 (an outlier), what is the value of the mean for the entire sample?
• Problem 36 The data represents escape times for 26 workers from an offshore oil platform in a simulated emergency.
  • a)construct a stem and leaf display. How does it suggest that the sample mean and median will compare?
  • Calculate the sample mean and median
  • By how much could the largest value be increased without changing the median? How much could it be decreased?
  • The data are recorded in seconds. What are the values of the mean and median if the scale is in minutes?
• Problem 39 The data represents time, in units of 10,000 flight hours, for a fatigue crack to reach a given size in 16 fastener holes.
  • a) compute the sample mean and median
  • b) By how much could the largest value be decreased without changing the median?
• Problem 43 In a time to failure experiment, 10 components were tested. Eight had failed by 100 hours when the test was ended, and two had not failed (these were recorded as 100+). Which of the measures of location can be calculated, and what are the values? (In the terminology of survival analysis, the two 100+ components are said to be "right censored", meaning the test ended before they failed).
• Problem 44 Oxygen consumption for 10 firefighters engaged in a simulation are recorded. Compute:
  • The sample range
  • The sample variance s-squared using the formula
  • The sample standard deviation
  • The sample variance using the shortcut method
• Problem 50 The data consists of 27 jury awards for repetetive stress injuries (in thousands of dollars). What is the maximum possible amount that could be awarded in a separate case that would be within two standard deviations of the mean of the sample?
• Problem 51 Oxidation induction times in minutes for 19 commercial motor oils is measured.
  • calculate the sample variance and standard deviation.
  • what would be the sample variance and standard deviation if the scale was changed to hours? Show how you would calculate this without actually rescaling the data.
• Problem 52 The data consists of four deviations from the mean of a sample of 5 measurements of reaction time. What is the fifth deviation? Give a sample for which these are the five deviations from the mean.
• Problem 56 Aluminum contamination in 26 samples of a plastic. Construct a boxplot that shows outliers and comment on its features.