The Problem

A physical therapist suggests that soft tissue massage therapy helps to reduce the number of days per week that patients suffer from headaches. The following tables show the number of days that a sample of 18 patients suffered from headaches before and after 6 weeks of receiving massage therapy.

Patient # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Before 4 5 6 5 5 6 5 4 4 5 5 3 4 4 5 5 5 5

After 5 3 3 4 3 4 3 5 2 4 1 3 2 2 3 4 4 3

Questions 1) What is the level of measurement of each set of data? Explain your reasoning.

2) For each group (before & after), find each of the following (organize your information): a. The mean and median (nearest tenth) b. standard deviation (nearest tenth) c. 5-number summary (nearest tenth as needed) d. Coefficient of variation (write as a percent, rounded to the nearest hundredth).

3) Does soft tissue massage therapy appear to reduce the average number of headaches per day? Support your answer.

4) Which data are more variable: before or after? Explain your reasoning.

5) The box and whisker displays are shown below (they are vertical rather than horizontal). Using those (and any other information you think would be useful), determine the shape of each distribution.

6) Are there any values in either group of data that would be considered unusual? Show your reasoning. (Hint: Remember the criteria for unusual events).

7) Based on these results, do you think that soft tissue massage therapy will be prescribed for people suffering from chronic headaches? Explain your thoughts.

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