3.2 DISPLAYING DATA Snoises Mean, Median, and Histogram Mental Health Contact Hours (291052 20 (GM) end doinw 8 bioW 101 noitudhzib grit 2900 .E -6pen 10 wexz svitizog 6 9ver 0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 STATISTICAL GUIDE Figure 1. Mental health professionals' reported family contact time. The mean, median, and mode, the measures of central tendency, have See Note. Professionals' family contact hours per week (N = 69); Mean = 3.5; Adjusted Exercise 3. Mean = 3.02; Median = 2.0 important relationships with a histogram. Understanding these relation- ships helps to illuminate the basic contours of a distribution. As we saw to review histogram . in the previous exercise, the mode is the highest bar in a histogram. In See Exercise 2. STUDY QUESTIONS this exercise, we will focus on how the mean and median relate to the to review histogram. (Note: the mean is sometimes referred to as the average.) mean and Factual Questions And just as a quick review, two points: (1) Small numbers of scores median that are far from the bulk of the scores are called outliers. (2) A distribu- 1. What is the sample size? 5. Going by Figure 1, what is the tion with extreme scores to the right (but not the left) is said to have a 2. In the histogram, are the out- mode of the distribution? What positive skew, while one with extreme scores to the left (but not to the liers far to the left or far to the s the relationship between the right? right) is said to have a negative skew. onhussam 101 lu mode and the median in this Insmevojami enibes 3. By how many points do the case? mean of 3.5 and the median 6. Is the distribution in the histo- EXCERPT FROM THE RESEARCH ARTICLE' Slevel sbsip-tenit differ? 169291 9rit 9zogque .S gram skewed? Explain. 4. How have the outliers influ- enced the mean? This study surveyed a sample of. . . mental health professionals employed by two community mental health agencies in rural north- Questions for Discussion ern and central Michigan. ... The survey sample included social 7. Do you think that the mean of (7.39 and 2.58). Which average workers (65.8%), psychologists (11%), counselors (8.2%), and 3.5 or the median of 2.0 is bet- do you think was reported: the other professionals (4%). ter for describing the central mean or the median? Figure 1 demonstrates that community mental health professionals tendency of the distribution in 10. The sample included various reported 0 to 16 hrs/week of family contact time [i.e., contact time the histogram? Explain subgroups of mental health with family members of those with psychiatric disabilities]. The mean 8. What kind of information professionals (e.g., social of reported family contact hours per week was 3.5; the mean was does the adjusted mean pro- workers and psychologists). 3.02 with two large outliers omitted. Given the large positive skew vide that the mean of 3.5 does In your opinion, would it have of the distribution. . ., a useful measure of central tendency is the not provide? (See the text and been more informative to pro- median of 2 hrs/week of reported family contact time. The average the figure to determine what vide separate histograms for number of hours per week of family contact time for professionals the adjusted mean is.) each type of professional? who served children was 7.39; the average number of hours per week 9. In the last sentence, the of family contact time for professionals who served adults was 2.58. researcher reports two averages