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

Note : Allowed to solve only one question per post.

Draw a stem and leaf plot of these data.

1. Arrange the data in ascending order.

2. convert the data to without decimal , that is round up the decimal to who number.

3. We see that max value is 31 and the min value is zero.

Hence we divide the data in the following intervals

4. We put the data in these interval as shown

5. Leaf stem plot

The stem is the tens place of the number in each interval and the units place is the leaf.

Hence the first interval, the stem is 0 and the units place has numbers from 0 to 4.

The 4th interval the stem is 1 and the units place has numbers from 0 to 4. The first number in this branches is 10 and so on.