Q1. Consider the data set 1,2,3,4,5,6,7,8,9
a. Obtain the mean and the median of the data. What is the shape of the distribution?
b. Replace the 9 in the data set by 109 and again compute the mean and the median. What is the shape of the distribution? Decide with measure of central tendency works better here and explain your answer.
c. For the data set in part (b), the mean is neither central nor typical for the data. The lack of what property of the mean accounts for this result?
Q2. Hospital stays. The U.S. National Center for Health Statistics compiles data on the length of stay by patients in short-term hospitals and publishes its findings in Vital and Health Statistics. A random sample of 21 patients yielded the following data on length of stay, in days.
4 4 12 18 9 6 12
3 6 15 7 3 55 1
10 13 5 7 1 23 9
a) Determine the mean, median, and mode
b) Determine the interquartile range
c) Obtain the five number summary
d) Identify potential outlier, if any
e) Determine the variance and standard deviation