A researcher in an alcoholism treatment center, to study the length of stay in the center for first- time patients, randomly selects ten records of individuals institutionalized within the previous two years. The lengths of stay, in days, were 11, 6, 20, 9, 13, 4,39, 13, 44, and 7. (a)Construct a stem-and-leaf plot. (b) Find the mean and the standard deviation, and interpret. (c) For a similar study 25 years ago, lengths of stay for ten sampled individuals were 32, 18,55, 17, 24, 31, 20, 40, 24, 15. Compare results to those in the new study using (i) a back-to-back stem-and-leaf plot, (ii)the mean, (i) the standard deviation. Interpret any differences you find. (d)Actually, the new study also selected one other record. That patient is still institutionalized 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.