Question

1. The accompanying data set consists of observations on shower-flow rate (L/min) for a sample of houses in Perth, Australia (“An Application of Bayes Methodology to the Analysis of Diary Records in a Water Use Study,” J. Amer. Stat. Assoc., 1987: 705–711):

4.6 12.3 7.1 7.0 4.0 9.2 6.7 6.9 11.5 5.1 11.2 10.5 14.3 8.0 8.8 6.4 5.1 5.6 9.6 7.5 0.2 1.6

7.5 6.2 5.8 2.3 3.4 10.4 9.8 6.6 3.7 6.4 8.3 6.5 7.6 9.3 9.2 7.3 5.0 6.3 13.8 6.2 23.4 0.4 31.1

5.4 4.8 7.5 6.0 6.9 10.8 7.5 6.6 5.0 3.3 7.6 3.9 11.9 2.2 15.0 7.2 6.1 15.3 18.9 7.2 26.7

5.4 5.5 4.3 9.0 12.7 11.3 7.4 5.0 3.5 8.2 8.4 7.3 10.3 11.9 6.0 5.6 9.5 9.3 10.4 9.7 1.2 0.8

5.1 6.7 10.2 6.2 8.4 7.0 4.8 5.6 10.5 14.6 10.8 15.5 7.5 6.4 3.4 5.5 6.6 5.9 15.0 9.6 18.2

7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 33.1 6.8 11.3 9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2 26.1

8.3 3.2 4.9 5.0 2.5 6.0 8.2 6.3 3.8 6.0 1.5 3.1

1. Draw a stem and leaf plot of these data.
2. Group the data into class intervals find corresponding frequencies and relative frequencies
3. Draw the relative frequencies histogram and comment on interesting characteristics. (Central value, symmetry, modality, variability and so on)
4. Draw the cumulative relative frequencies histogram and ogive.
5. Find 5-number-summary and draw the box plot.
6. What proportion of the observations in this sample are less than 6?
7. What proportion of the observations are at least 10?
8. What proportion of the observations are between 4 and 8?

Answer 1