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Chapter 1: Q14E (page 25)

The accompanying data set consists of observations,on shower-flow rate (L/min) for a sample of n=129,houses in Perth, Australia (鈥淎n Application of Bayes,Methodology to the Analysis of Diary Records in a

Water Use Study,鈥� J. Amer. Stat. Assoc., 1987: 705鈥�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

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

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

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

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

7.8 7.0 6.9 4.1 3.6 11.9 3.7 5.7 6.8 11.3

9.3 9.6 10.4 9.3 6.9 9.8 9.1 10.6 4.5 6.2

8.3 3.2 4.9 5.0 6.0 8.2 6.3 3.8 6.0

  1. Construct a stem-and-leaf display of the data.
  2. What is a typical, or representative, flow rate?
  3. Does the display appear to be highly concentrated or spread out?
  4. Does the distribution of values appear to be reasonably symmetric? If not, how would you describe the departure from symmetry?
  5. Would you describe any observation as being far from the rest of the data (an outlier)?

Short Answer

Expert verified

a.

The stem and leaf display is:

2

23

3

2344567789

4

01356889

5

00001114455666789

6

0000122223344456667789999

7

00012233455555668

8

02233448

9

012233335666788

10

2344455688

11

2335999

12

37

13

8

14

36

15

0035

16


17


18

9

b. A typical or representative flow rate is 7 L/min.

c. The display is concentrated.

d. The distribution of values does not appear to be reasonably symmetric. The departure from symmetry implies non-identical sides of the graph from reference mid point.

e. Observation 18.9 is the outlier., far from rest of the points.

Step by step solution

01

Given information

Theobservations on shower-flow rate (L/min) for a sample of n=129houses in Perth, Australia is provided.

02

Construct a stem and leaf diagram

a.

A stem-and-leaf display provides a visual representation of the dataset.

The steps to construct a stem-and-leaf display are as follows,

1) Select the leading digit for the stem and trailing digits for the leaves(only numbers at unit鈥檚 place).

2) Represent the stem digits vertically and similarly the trailing digits corresponding to the stem digits.

3) Mention the units for the display.

The stem and leaf display for the provided scenario is,

2

23

3

2344567789

4

01356889

5

00001114455666789

6

0000122223344456667789999

7

00012233455555668

8

02233448

9

012233335666788

10

2344455688

11

2335999

12

37

13

8

14

36

15

0035

16


17


18

9

Unit: 10|2=10.2

03

Provide a representative flow rate

b.

Referring to part a. the stem and leaf plot is,

2

23

3

2344567789

4

01356889

5

00001114455666789

6

0000122223344456667789999

7

00012233455555668

8

02233448

9

012233335666788

10

2344455688

11

2335999

12

37

13

8

14

36

15

0035

16


17


18

9

A representative flow rate is the middle flow rate; that is, 7 L/min.

Thus, a typical or representative flow rate is 7 L/min.

04

Check whether the data is highly concentrated or spread out

c.

From the stem and leaf plot display, the data appears to be clustered around the stem values of 5 to 10, with only one extreme value of 18.9.

Thus, it can be concluded by the observations in the plot that the display is concentrated.

05

Check whether the distribution is symmetric

d.

Referring to (a) part of the question,

From the stem and leaf display, it can be observed that the distribution appears to be positively skewed and not symmetric as the shape is not bell-shaped and most of the values lie at the top of the display.

A symmetric graph must have the almost same type of appearance on either end of the reference point(mostly the central point of the graph).

In this case, assuming the central value close to 9, the data is concentrated on the left end as compared to the right side.

06

Check if there is any outlier

e.

Referring to (a) part of the question,

From the stem and leaf display, it can be observed that observation 18.9 lies far away from other observations. This is an outlier that is present in the dataset.

Thus, observation 18.9 is the outlier.

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Most popular questions from this chapter

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