18.8 Exercises

Selected answers are available in Sect. D.18.

Exercise 18.1 In the following scenarios, would a standard deviation or a standard error be the appropriate way to measure the amount of variation? Explain.

  1. Researchers are studying the spending habits of customers. They would like to measure the variation in the amount spent by shoppers per transaction at a supermarket.
  2. Researchers are studying the time it takes for inner-city office workers to travel to work each morning. They would like to determine the precision with which their estimate (a mean of 47 minutes) has been measured.
  3. A study examined the effect of taking a pain-relieving drug on children. The researchers wish to describe the sample they used in the study, including a description of how the ages of the children vary.
  4. A study examined the effect of taking a pain-relieving drug in teenagers. The researchers wished to report the percentage of teenagers in the sample that experienced side-effects with some indication of the precision of that estimate.

Exercise 18.2 Which of the following have a standard error?

  1. The population proportion.
  2. The sample median.
  3. The sample IQR.
  4. The sample standard deviation.
  5. The population odds.

Exercise 18.3 A research article made this statement:

Although […] samples should always be summarized by the mean and SD [standard deviation], authors often use the standard error of the mean (SEM) to describe the variability of their sample […] Although the SD and the SEM are related […], they give two very different types of information.

Nagele (2003)

If the standard error of the mean is not used to ‘describe the variability of the sample,’ then what is it used for? How would you explain the difference between the standard error and the standard deviation to researchers who misuse the terms?


Nagele P. Misuse of standard error of the mean (SEM) when reporting variability of a sample. A critical evaluation of four anaesthesia journals. British Journal of Anaesthesia. Oxford University Press; 2003;90(4):514–6.