5 A researcher in an alcoholism treatment center. interested in summarizing the length of stay in the center for first-time patients, randomly selects ten records of individuals insu- tutionalized within the previous two years. The lengths of stay in the center. in days. are as follows. 11. 6. 20. 9, 13, 4. 39, 13, 44, and 7

a) Construct a stem and leaf plot.

TABLE 3.11 Place of Birth Number Europe 4.0 Former Soviet Union .3 Asia 50 Canada 7 Mexico 43 Canbbean 19 Central America 1.) South America 10 Afnca .4 .1 Total 18.8 Source Statistical Abstract of the United States 1994

b) Find the mean, and interpret.

c) Find the median, and interpret.

d) Find the standard deviation, and interpret.

e) For a similar study 25 years ago at the same institution, lengths of stay for ten sampled individuals were 32, 18, 55, 17. 24, 31, 20. 40, 24, and 15 days. Compare results to those in the new study using (i) a back-to-back stem and leaf plot, (ii) the mean, (iii) the median. (iv) the standard deviation. Interpret any differences you find.

f) Actually, the new study also selected one other record That patient is still institution- alized after 40 days Thus, that patient's length of stay is at least 40 days, but the actual value is unknown Can you calculate the mean or median for the complete sample of size 11 including this partial observation? Explain. (An observation such as this is said to be censored, meaning that the incasured value is "cut short" of its true, unknown value.)