Exercises page for Biostats Course VHM 801 at AVC - Fall Semester 2026

Follow this link to datasets (in Minitab (.mtw) and comma-separated (.csv) file formats).
Follow this link to extra exercises (labeled as x:number) and this link to AI discussion exercises.

This page contains links to solutions (either as text files, to be opened directly in a web browser or in Notepad (or similar), or as .pdf files, to be opened in a suitable reader, such as Adobe Acrobat) for selected exercises of VHM 801. The solutions have been compiled by the Biostats 801 course instructor, Henrik Stryhn.

Solutions to exercises

1. 1, 10, 16, 22, 42, 51, 65, 77,
2. 7, 67, 69,
3. 4, 10, 14, 18, 19, 40, 52, 94, 95,

Stata do-files for exercises

1. 10, 42, 51, 72, 77,
2. 7,
3. 14, 40,

R program files for exercises

1. 10, 42, 51, 72, 77,
3. 14, 40,

Data files

Data files (.mtw)

• Chapter 1: 10, 16, 23, 42, 51,
• Chapter 2: 7,
• Chapter 3: 14, 40,
• Extra: parasite, PEI migration, crab, poplar

Data files (.csv)

• Chapter 1: 10, 16, 23, 42, 51,
• Chapter 2: 7,
• Chapter 3: 14, 40,
• Extra: parasite, PEI migration, crab,

Extra exercises

• x:1. This exercise uses the Mean and Median applet (use link from homepage) which allows you to place observations on a line and see their mean and median displayed visually. Follow the instructions to the left of the display. Put some points to get a sense of how it works.
  1. Now put two observations on the line. Why does only one arrow appear?
  2. Try next with three observations, where two are close together near the center and one somewhat to the right of these two. Move the rightmost point away and towards the other points, and observe how the mean and median behave. Explain your findings. Then move the rightmost across the two centre points to the left: what happened to the mean and median as you did that? Again, explain your findings.
  3. Finally, put five (distinct) observations on the line. Try to add one point without changing the median: where is your new point? Explore what happens to the median when you add another point; explain your findings.
  4. (Optional) If you have interest in exploring further, you may also try some of the suggestions below the display.

• x:2. In this exercise, we use the guinea pig data from Exercise 1.51 to explore how the number of bins in a histogram affects its shape and the impression it gives of the distribution.
  1. Draw first the default histogram (in your software). How many bins does it have?
  2. In Minitab, in order to change the binning of a histogram, you have to right-click on the bars, select the menu item Edit bars and the submenu Binning. Try to construct histograms with the maximal and minimal number of bins. How many bins did you get, and how does it affect your impression of the distribution?
  3. Experiment further with the binning to determine your preferred number of bins; how many bins did you choose? Does your preferred choice agree with the software default or any of the guidelines mentioned in Lecture 1? Do you think the shape of the distribution will affect the "best" number of bins? (For example, you may think about whether we should use the same number of bins for a symmetrical and a skewed distribution.)

• x:3. Randomization may be based on tables of random digits (e.g., Table A of PSLS or Table B of IPS). Discuss whether each of the following statements about such tables are true.
  1. Among 40 random digits (corresponding one row in the table), there are exactly 4 nines.
  2. Each pair of digits has a chance/probability of 1/100 of being 99.
  3. The number 9999 can never appear as a group because it is not a random pattern.

Solutions to extra exercises:

Topics for discussion with a Generative AI bot

#	Topic	Suggested/Template questions
1	Choice of descriptive statistic	when to use a mean and when to use a median? (follow-up: if computing the median for ordinal categorical data, it may produce a nonsensical value?); what is a good descriptive statistic for spread of a distribution?; is the standard deviation appropriate for skewed distributions?
2	Outliers	what is an outlier?; are observations indicated by asterisks in a boxplot outliers? (follow-up: what do you mean, are they potential or actual outliers?); should outliers be removed from the data?
3	Association vs causation	can I conclude a causal effect from an observed effect?; can an experiment prove causation?; does association in a randomized controlled trial imply causation?