13.10 Exercises

Selected answers are available in Sect. D.13.

Exercise 13.1 The histogram of the direct HDL cholesterol from the NHANES study is shown in Fig. 13.1. Should the mean or median be used to measure location?

Exercise 13.2 The average monthly SOI values in August from 1995 to 2000 are shown in Table 13.10. Use your calculator (where possible) to calculate the:

1. sample mean
2. sample median.
3. range.
4. sample standard deviation.
TABLE 13.10: The average monthly SOI values in August from 1995 to 2000
Year Monthly average SOI
1995 0.8
1996 4.6
1997 -19.8
1998 9.8
1999 2.1
2000 5.3

Exercise 13.3 The activity below contains histogram and boxplots.

1. Match the histogram with the corresponding boxplot.

2. For which data sets would the mean and standard deviation be the appropriate numerical summary?

For which data sets would the median and IQR be the appropriate numerical summary?

Exercise 13.4 A study of the productivity of construction workers recorded, among other things, the rate at which concrete panels could be installed by workers. Data for three different female workers in the study are shown in Table 13.11. Construct the boxplot comparing the three workers. What does it tell you?
TABLE 13.11: The productivity of three females workers installing concrete panels (in panels per minute)
Worker 1 Worker 2 Worker 3
Mean 1.24 1.73 1.36
Minimum 0.59 1.13 0.86
1st quartile 0.88 1.51 1.16
Median 1.35 1.70 1.38
3rd quartile 1.49 1.91 1.58
Maximum 1.88 3.00 2.17
Range 1.28 1.87 1.31

References

Gatti UC, Migliaccio GC, Bogus SM, Schneider S. An exploratory study of the relationship between construction workforce physical strain and task level productivity. Construction Management and Economics. 2013;1–7.