Construct a stem-and-leaf display for the data

Assignment Help Applied Statistics
Reference no: EM131051263

Question 1:      

Visit the Australian Stock Exchange website, www.asx.com.au and from "Prices and research" drop-down menu, select "Company information". Type in the ASX code "CCL" (Coca-Cola Amatil Limited), and find out details about the company. Your task will be to get the opening prices of a CCL share for every quarter from January 2001 to December 2015. If you are working with the monthly prices, read the values in the beginning of every Quarter (January, April, July, October) for every year from 2001 to 2015. It is part of the assignment task to test your ability to find the information from an appropriate website. If you are unable to do so, you may read the values from the chart provided below obtained from Etrade Australia. Obviously, reading from the chart will not be accurate and you may expect around 60 percent marks with such inaccuracy. After you have recorded the share prices, answer the following questions:

(a) List all the values in a table and then construct a stem-and-leaf display for the data. 

(b) Construct a relative frequency histogram for these data with equal class widths, the first class being "$4 to less than $6".

(c) Briefly describe what the histogram and the stem-and-leaf display tell you about the data. What effects would there be if the class width is doubled, which means the first class will be "$4 to less than $8"?

(d) What proportion of stock prices were above $10?

557_Figure.png

(Note: Use only the original values of share prices and not adjusted values.)

Question 2:

The following table provides the median weekly rents of a 3-bedroom house of a few randomly selected suburbs in four capital cities of Australia - Sydney, Melbourne, Brisbane and Perth - for March 2016. The data is obtained from the website https://www.realestate.com.au/neighbourhoods/. From the data answer the questions below for the capital cities.

Median weekly rent of a 3 bedroom house In Australian capital cities

 

Sydney  Melbourne Brisbane Perth
Suburb name  Rent ($) Suburb name  Rent ($) Suburb name  Rent ($) Suburb name Rent ($) 
Newtown 890 Carkon 700 Fortitude Valey 610 Stbaco 725
Ranchvick 999 Footsaay 413 Wookoongabba 480 Innaloo 470
Maroubra 850 Kew 645 McDowell 450 Balculta 395
Rockdale 600 Toorak 895 Underwood 395 Duncrarg 440
Camsie 550 Coburg 480 Manly 450 Dalkeirn 715
Hurstwile 580 Camberwell 605 Jindalee 415 Bassendean 400
Auburn 485 Ringwood 380 Cleveland 425 Kewdale 395
Ryde 650 Moorabbin 465 Teneriffe 700 Beckenham 380
Cabramatta 420 Wernbee 300 Tingalpa 420 Langford 340
Bella Vista 658 Truganna 330 Algester 390 Kardinya 430
Artarmon 950 Taylors Lakes 370 Aspley 420 Cottesloe 800
Bankstown 500 Bundoora 370 Herston 535 Stratton 350
Chatswood 850 Craigiebum 340 New Farm 685

Epping 630 Epping 340





Pod Melbourne 813



(a) Compute the mean, median, first quartile, and third quartile for each capital city (with only the data provided for that city, do not add/delete values for any new/given suburb of question 2) using the exact position, (n+1)f, where n is the number of observations and f the relevant fraction for the quartile.

 (b) Compute the standard deviation, range and coefficient of variation from the sample data for each city.

 (c) Draw a box and whisker plot for the median weekly rents of each city and put them side by side on the same scale so that the prices can be compared.  

(d) Compare the box plots and comment on the distribution of the data.             

Question 3:

The Table below is taken from the Australian Bureau of Statistics website. It provides data on energy use of households - almost all houses use mains electricity but some use additional energy sources such as gas and solar. (You can get the data from Table 1 from the URL: https://www.abs.gov.au/AUSSTATS/[email protected]/DetailsPage/4602.0.55.001Mar%202014?OpenDocument.) Missing cells indicate data not published, and totals may be higher since all possibilities may not be listed. The totals are not incorrect.).

931_Figure2.png

 Based on the information available in the table above -

(a) What is the probability that an Australian household, randomly selected, uses solar as a source of energy?

(b) What is the probability that an Australian household, randomly selected, uses mains gas and is located in Victoria?

(c) Given that a household uses LPG/bottled gas, what is the probability that the household is located in South Australia?

(d) Is the percentage of Australian households using mains gas independent of the state?

Question 4:       

(a) The following data collected from the Australian Bureau of Meteorology Website  (https://www.bom.gov.au/climate/data/?ref=ftr) gives the daily rainfall data for the year 2015 in Brisbane. The zero values indicate no rainfall and the left-most column gives the date. Assuming that the weekly rainfall event (number of days in a week with rainfall) follows a Poisson distribution (There are 52 weeks in a year and a week is assumed to start from Monday. The first week starts from 29 December 2014 - you are expected to visit the website and get the daily values which are not given in the table below. Make sure you put the correct station number. Ignore the last few days of 2015 if it exceeds 52 weeks.):

(i) What is the probability that on any given week in a year there would be no rainfall?

(ii) What is the probability that there will be 2 or more days of rainfall in a week?

Observations of Dail) rainfall are nominally made at 9 am local clock time and record the total for the preaous 24 hours. Rainfall includes all forms of precipitation that reach the ground, such as rain, drizzle, had and snow. About rainfall data

Station: Brisban     Number 40913   Opened: 1999   Now: Open

                           Lat 27.48's       Lon:153.04*E   Elevation: 8m

Key: Units = mm 12.3= Not Quality controlled = Pan of accumulated total

2015 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Graph











1st 12.2 17.2 0 68.2 56.2 0 0.2 0 0 0 0 0
2nd 0.2 0 0 8.8 182.6 0 0 0
0 0 0.4
3rd 1.2 2.2 0 38.4 0 0 0 0 2.4 0 0 2
4th 16.8 0 0 0.4 0 0 0 0 0.2 0 11.6 0.2
5th 0 0 0 1.8 0 0 0 0 0 0 0 0
6th 21.6 2.8 0 0
0 0 0 0 0 19 0
7th 0 0.2 0 0 0 0 0 0 0 0 0 0
8th 1.8 0.2 0 0
0.2 0 0 0 0 0.4 0
9th 3.6 0 0 0 0 0 0 0 0 5.8 14 0
10th 0 5.2 0 0 0 0 2 0 0 0.2 0 0
11th 0 12.2 0 0 0 0 0 0 0 0 0 0.6
12th 14.6 8.4 0 0 0 4.6 0.6 0.2 0 0 0 1
13th 38.6 1.6 0 0 0 1.2 0.2 3.6 0 0 0 9.8
14th 0.2 0.4 0 0 0 4.2 0 0 0 0.2 1 0.8
15th
0.2 0 0 0 4 0 0 0 4.4 10.6 0
16th 0 0.4 0 0.2 0 1 0 0 0 0 0.2 0
17th 0 0.4 0 0 1 3.4 0 0 10.2 0 0.6 3.8
18th 0 0.2 0 3.4 6.6 2.4 0 0 18 0 0 3.2
19th 0 4.6 7.6 0.4 0.8 0 0 0 0.6 0 0 0
20th 35.8 54 0 14.6 0 0 0 0 0 0 0 0
21st 0.2 89.2 0.2 2 0.2 0 0.2 0.4 1.6 0 0 0
22nd 1 68.4 68 0.2 1.4 0 2.8 2.2 0 0 0 0
23rd 100.4 4.4 81.8 0 0 0 4.4 0 0 20.8 0 0
24th 65.2 0.4 0 0 0 0 0 0 0.6 0 0 3.2
25th 0 0.2 0 0 0 0 0 2.2 0.2 1.2 0 9.2
26th 0 1.8 3.8 0 0 0.2 0.2 0 0 0 0 0.4
27th 0 0.2 0 0
0 0 0 0.4 4.8 0 0.8
28th 5.2
0 0 0 2.4 0 5 12.2 13.2 0 0.8
29th 0
0
0 7 0 0.2 0 5 0 0
30th 3.8
0 7.8 4 4 0 13.6 7.8 0.2 0.2 0
31st 0
0
0
0 0.2
0 16.6 0
Highest Daily 100.4 89.2 81.8 68.2 182.6 7 4.4 13.6 18 20.8 19 9.8
Monthly Total 322.4 274.8 161.4 146.2 248.8 34.6 9.2 27.6 54.2 55.6 74.2 36.2

(b) Assuming that the weekly total amount of rainfall (in mm) from the data provided in part (a) has a normal distribution, compute the mean and standard deviation of weekly totals.

(i) What is the probability that in a given week there will be between 5 mm and 10 mm of rainfall?

(ii) What is the amount of rainfall if only 13% of the weeks have that amount of rainfall or higher?

Question 5:

The following data is taken from the UCI machine learning data repository (https://archive.ics.uci.edu/ml/datasets/Wine+Quality). It lists a few attributes of red wine, randomly sampled from thousands of bottles, which can be classified as of good, medium and poor quality.

(a) Test for normality of all the variables separately for good wine using normal probability plot.      

(b) Construct a 95% confidence interval for each of the variables for good wine.               

(c) Find the mean of each of the variables for medium quality red wine. Do the same for the poor quality red wine.

 (d) Check if the means calculated for the medium and poor quality red wines fall within the corresponding confidence intervals of the good quality wine. For those attributes whose means lie outside the confidence interval, the attributes are significant in determining the quality.  This assumption is, however, partially compromised if the attribute fails the normality test. Identify the significant and non-significant variables, and comment.        

Good quality red wine

Alcohol

Residual sugar

Chlorides

Total sulfur dioxide

Density

pH

Sulphates

Citric acid

10

1.2

0.065

21

0.9946

3.39

0.47

0

9.5

2

0.073

18

0.9968

3.36

0.57

0.02

10.5

1.8

0.092

103

0.9969

3.3

0.75

0.56

9.7

2.1

0.066

30

0.9968

3.23

0.73

0.28

9.5

1.9

0.085

35

0.9968

3.38

0.62

0.16

10.5

1.8

0.065

16

0.9962

3.42

0.92

0.16

13

1.2

0.046

93

0.9924

3.57

0.85

0.08

10.3

1.4

0.056

24

0.99695

3.22

0.82

0.47

10.8

2.6

0.095

28

0.9994

3.2

0.77

0.74

10.8

2.6

0.095

28

0.9994

3.2

0.77

0.74

10.5

2.1

0.054

19

0.998

3.31

0.88

0.58

12.2

1.6

0.054

106

0.9927

3.54

0.62

0.04

9.2

2.2

0.075

24

1.00005

3.07

0.84

0.44

9.2

2.2

0.075

24

1.00005

3.07

0.84

0.44

10.5

2.6

0.085

33

0.99965

3.36

0.8

0.47

10.2

1.8

0.071

10

0.9968

3.2

0.72

0.52

12.8

3.6

0.078

37

0.9973

3.35

0.86

0.46

12.6

6.4

0.073

13

0.9976

3.23

0.82

0.45

10.5

5.6

0.087

47

0.9991

3.38

0.77

0.32

9.9

3.5

0.358

10

0.9972

3.25

1.08

0.68

10.5

5.6

0.087

47

0.9991

3.38

0.77

0.32

10.6

2.5

0.091

49

0.9976

3.34

0.86

0.09

10.6

2.5

0.091

49

0.9976

3.34

0.86

0.09

11.5

3.2

0.083

59

0.9989

3.37

0.71

0.39

11.5

3.2

0.083

59

0.9989

3.37

0.71

0.39

11.5

3.65

0.121

14

0.9978

3.05

0.74

0.66

11.7

2.5

0.078

38

0.9963

3.34

0.74

0.01

12.2

3.4

0.128

21

0.9992

3.17

0.84

0.53

9.8

2.3

0.082

29

0.9997

3.11

1.36

0.54

12.3

2.7

0.072

34

0.9955

3.58

0.89

0.02

11.7

2.95

0.116

29

0.997

3.24

0.75

0.66

10.4

3.1

0.109

23

1

3.15

0.85

0.66

10

5.8

0.083

42

1.0022

3.07

0.73

0.66

10

5.8

0.083

42

1.0022

3.07

0.73

0.66

12

2.4

0.074

18

0.9962

3.2

1.13

0.53

11.8

4.4

0.124

15

0.9984

3.01

0.83

0.71

12

2.4

0.074

18

0.9962

3.2

1.13

0.53

10

2.5

0.096

49

0.9982

3.19

0.7

0.31

12.9

1.4

0.045

88

0.9924

3.56

0.82

0.05

13

4.2

0.066

38

1.0004

3.22

0.6

0.76

10.8

3

0.093

30

0.9996

3.18

0.63

0.66

11.7

6.7

0.097

19

0.9986

3.27

0.82

0.53

11.8

2.4

0.089

67

0.9972

3.28

0.73

0.33

12.3

2.3

0.059

48

0.9952

3.52

0.56

0.03

11

2.1

0.066

24

0.9978

3.15

0.9

0.47

12.3

2.3

0.059

48

0.9952

3.52

0.56

0.03

11

2.1

0.066

24

0.9978

3.15

0.9

0.47

9.8

2.2

0.072

29

0.9987

2.88

0.82

0.72

11.2

3.7

0.1

43

1.0032

2.95

0.68

0.76

11.6

2.7

0.077

19

0.9963

3.23

0.63

0.49

12.5

1.7

0.054

27

0.9934

3.57

0.84

0.01

11.2

2.8

0.084

22

0.9998

3.26

0.74

0.63

13.4

5.2

0.086

19

0.9988

3.22

0.69

0.67

11.2

2.8

0.084

22

0.9998

3.26

0.74

0.63

11.7

2.8

0.08

17

0.9964

3.15

0.92

0.56

10.8

2.8

0.081

67

1.0002

3.32

0.92

0.55

13.3

2.5

0.055

25

0.9952

3.34

0.79

0.5

13.4

2.6

0.052

27

0.995

3.32

0.9

0.51

11

2.6

0.07

16

0.9972

3.15

0.65

0.53

11

2.6

0.07

16

0.9972

3.15

0.65

0.53

12

6.55

0.074

76

0.999

3.17

0.85

0.73

12

6.55

0.074

76

0.999

3.17

0.85

0.73

10.9

1.9

0.078

24

0.9976

3.18

1.04

0.47

10.8

1.8

0.077

22

0.9976

3.21

1.05

0.42

12.5

2.9

0.072

26

0.9968

3.16

0.78

0.63

10.8

1.8

0.075

21

0.9976

3.25

1.02

0.46

11.4

2.8

0.084

43

0.9986

3.04

0.68

0.75

11.8

2.4

0.107

15

0.9973

3.09

0.66

0.64

11.8

2.4

0.107

15

0.9973

3.09

0.66

0.64

Medium quality red wine

alcohol

residual sugar

chlorides

total sulfur dioxide

density

pH

sulphates

citric acid

9.4

1.9

0.076

34

0.9978

3.51

0.56

0

9.8

2.6

0.098

67

0.9968

3.2

0.68

0

9.8

2.3

0.092

54

0.997

3.26

0.65

0.04

9.4

1.9

0.076

34

0.9978

3.51

0.56

0

9.4

1.8

0.075

40

0.9978

3.51

0.56

0

9.4

1.6

0.069

59

0.9964

3.3

0.46

0.06

10.5

6.1

0.071

102

0.9978

3.35

0.8

0.36

9.2

1.8

0.097

65

0.9959

3.28

0.54

0.08

10.5

6.1

0.071

102

0.9978

3.35

0.8

0.36

9.9

1.6

0.089

59

0.9943

3.58

0.52

0

9.1

1.6

0.114

29

0.9974

3.26

1.56

0.29

9.2

3.8

0.176

145

0.9986

3.16

0.88

0.18

9.2

3.9

0.17

148

0.9986

3.17

0.93

0.19

9.3

1.7

0.368

56

0.9968

3.11

1.28

0.28

9.7

2.3

0.082

71

0.9982

3.52

0.65

0.31

9.5

1.6

0.106

37

0.9966

3.17

0.91

0.21

9.4

2.3

0.084

67

0.9968

3.17

0.53

0.11

9.3

1.4

0.08

23

0.9955

3.34

0.56

0.16

9.5

1.8

0.08

11

0.9962

3.28

0.59

0.24

9.5

1.6

0.106

37

0.9966

3.17

0.91

0.21

9.4

1.9

0.08

35

0.9972

3.47

0.55

0

10.1

2.4

0.089

82

0.9958

3.35

0.54

0.07

9.8

2.3

0.083

113

0.9966

3.17

0.66

0.12

9.2

1.8

0.103

50

0.9957

3.38

0.55

0.25

10.5

5.9

0.074

87

0.9978

3.33

0.83

0.36

10.5

5.9

0.074

87

0.9978

3.33

0.83

0.36

10.3

2.2

0.069

23

0.9968

3.3

1.2

0.22

9.5

1.8

0.05

11

0.9962

3.48

0.52

0.02

9.2

2.2

0.114

114

0.997

3.25

0.73

0.43

9.5

1.6

0.113

37

0.9969

3.25

0.58

0.52

9.2

1.6

0.066

12

0.9958

3.34

0.56

0.23

9.2

1.4

0.074

96

0.9954

3.32

0.58

0.37

9.2

1.7

0.074

23

0.9971

3.15

0.74

0.26

9.4

3

0.081

119

0.997

3.2

0.56

0.36

9.5

3.8

0.084

45

0.9978

3.34

0.53

0.04

9.6

3.4

0.07

10

0.9971

3.04

0.63

0.57

9.4

5.1

0.111

110

0.9983

3.26

0.77

0.12

10

2.3

0.076

54

0.9975

3.43

0.59

0.18

9.2

2.2

0.079

52

0.998

3.44

0.64

0.4

9.3

1.8

0.115

112

0.9968

3.21

0.71

0.49

9.8

2

0.081

54

0.9966

3.39

0.57

0.05

10.9

4.65

0.086

11

0.9962

3.41

0.39

0.05

10.9

4.65

0.086

11

0.9962

3.41

0.39

0.05

9.6

1.5

0.079

39

0.9968

3.42

0.58

0.11

10.7

1.6

0.076

15

0.9962

3.44

0.58

0.07

10.7

2

0.074

65

0.9969

3.28

0.79

0.57

9.5

2.1

0.088

96

0.9962

3.32

0.48

0.23

9.5

1.9

0.084

94

0.9961

3.31

0.48

0.22

9.6

2.5

0.094

83

0.9984

3.28

0.82

0.54

10.5

2.2

0.093

42

0.9986

3.54

0.66

0.64

10.5

2.2

0.093

42

0.9986

3.54

0.66

0.64

10.1

2

0.086

80

0.9958

3.38

0.52

0.12

9.2

1.6

0.069

15

0.9958

3.41

0.56

0.2

9.4

1.9

0.464

67

0.9974

3.13

1.28

0.7

9.1

2

0.086

73

0.997

3.36

0.57

0.47

9.4

1.8

0.401

51

0.9969

3.16

1.14

0.26

Poor quality red wine

alcohol

residual sugar

chlorides

total sulfur dioxide

density

pH

sulphates

citric acid

9

2.2

0.074

47

1.0008

3.25

0.57

0.66

8.4

2.1

0.2

16

0.9994

3.16

0.63

0.49

10.7

4.25

0.097

14

0.9966

3.63

0.54

0

9.9

1.5

0.145

48

0.99832

3.38

0.86

0.42

11

3.4

0.084

11

0.99892

3.48

0.49

0.02

10.9

2.1

0.137

9

0.99476

3.5

0.4

0

9.8

1.2

0.267

29

0.99471

3.32

0.51

0

10.2

5.7

0.082

14

0.99808

3.4

0.52

0.05

9.95

1.8

0.078

12

0.996

3.55

0.63

0.02

9

4.4

0.086

29

0.9974

3.38

0.5

0.08

9.8

1.5

0.172

19

0.994

3.5

0.48

0.09

9.3

2.8

0.088

46

0.9976

3.26

0.51

0.3

13.1

2.1

0.054

65

0.9934

3.9

0.56

0.15

9.2

2.1

0.084

43

0.9976

3.31

0.53

0.26

9.1

1.5

0.08

119

0.9972

3.16

1.12

0.2

10.5

1.4

0.045

85

0.9938

3.75

0.48

0.04

9.4

3.4

0.61

69

0.9996

2.74

2

1

9.2

1.3

0.072

20

0.9965

3.17

1.08

0.02

9

1.6

0.072

42

0.9956

3.37

0.48

0.03

9.1

1.8

0.058

8

0.9972

3.36

0.33

0.03

11.4

2.1

0.061

31

0.9948

3.51

0.43

0.06

10.4

2

0.089

55

0.99745

3.31

0.57

0.36

9.4

2

0.087

67

0.99565

3.35

0.6

0.04

9.8

3.3

0.096

61

1.00025

3.6

0.72

0

9.6

4.5

0.07

49

0.9981

3.05

0.57

0.49

9.6

2.1

0.07

47

0.9991

3.3

0.56

0.49

10

2.3

0.103

14

0.9978

3.34

0.52

0.24

10

2.1

0.088

23

0.9962

3.26

0.47

0.27

11.3

3.4

0.105

86

1.001

3.43

0.64

0.22

11

2.2

0.07

14

0.9967

3.32

0.58

0.01

11

4.4

0.096

13

0.997

3.41

0.57

0.02

9.6

2.6

0.073

84

0.9972

3.32

0.7

0.48

9.7

1.6

0.078

14

0.998

3.29

0.54

0.04

11.2

3.1

0.086

12

0.9958

3.54

0.6

0.1

11.4

2.1

0.102

7

0.99462

3.44

0.58

0.24

10.9

2.5

0.058

9

0.99632

3.38

0.55

0.07

9.9

1.6

0.147

51

0.99836

3.38

0.86

0.44

Reference no: EM131051263

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