Data Analysis And Statistics Exercises

Stem-and-leaf displays and frequency plots

  1. Quarterly opening prices

Year

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Quarter

MQG

PPT

Year

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Quarter

MQG

PPT

2007

1

79.65

78.45

2013

1

37.86

38.84

2

85.56

80.91

2

38.54

41.20

3

81.13

77.50

3

43.16

39.90

4

82.66

74.26

4

50.11

46.00

2008

1

63.92

58.30

2014

1

54.09

47.04

2

62.37

54.84

2

57.70

46.90

3

50.58

40.76

3

58.52

48.82

4

28.91

34.93

4

61.17

46.45

2009

1

25.56

30.72

2015

1

62.15

49.18

2

32.93

32.18

2

77.97

54.16

3

43.29

33.51

3

82.15

44.85

4

49.17

37.62

4

85.70

44.91

2010

1

49.33

35.05

2016

1

71.58

41.31

2

49.46

34.55

2

63.50

42.75

3

36.58

29.03

3

74.39

45.50

4

35.60

37.85

4

79.80

45.24

2011

1

39.95

31.29

2017

1

84.60

46.80

2

34.58

28.89

2

93.00

52.78

3

27.11

23.58

3

85.83

50.48

4

24.50

22.75

4

98.35

48.48

2012

1

25.08

20.25

 

2

28.73

25.50

 

3

24.57

23.91

 

4

31.37

27.94

 

              MQG and PPT Stem-and-Leaf Plot

                     Stem &  Leaf

               98753320 . 2 .  4455788

            98775443210 . 3 .  12456789

       9887666655442110 . 4 .  33999

                   4420 . 5 .  00478

                        . 6 .  12233

                    874 . 7 .  14799

                      1 . 8 .  1224555

                        . 9 .  38

 Each leaf: 1 case(s)

(Fletcher, 2009)

  1. Histogram and Frequency polygon for MQG and PPT

Figure 1: Histogram and Frequency polygon of MQG and PPT

  1. Market capitals for 6 companies listed in ASX with over AUD 500 million

Figure 2: Market capitals

  1. Invest in MQG or PPT

Based on the series of previous share prices from 2007 to March 2018, I would advise on investing with PPT because the prices are down and there is a possibility of a rise in a few moments. This is in comparison to MQG whose prices have been rising since 2010 and just as any other stock price, there are very high chance of the prices losing value. Therefore, it would be more advisable to invest in a stock whose price has a higher chance of increasing than decreasing. In addition, PPT has a higher dividend yield of 6.65% compared to MQG which is 4.66%. Further, PPT has a lower Price-earning Ration compared to MQG, which make PPT stock better to invest in because their future growth has higher chances of growth(Aspara, 2009; Lynott, 2005).

  1. Mean, median, 1stand 3rd Quartiles

TLS

SPK

TPM

CNU

VOC

Mean

13.37

13.33

18.65556

11.76667

21.34

Median

13.75

12.85

15.8

10.95

22.25

First Quartile

10.85

11.5

14.2

6.7

12.625

Third Quartile

15.475

15.55

25.3

17.475

28.9

  1. Standard Deviation, Mean Absolute Distance and Range statistics

TLS

SPK

TPM

CNU

VOC

Standard Deviation

2.322951

2.148046

6.225951

4.764335

10.46501

Mean Absolute Distance

2.056

1.936

5.617284

4.533333

8.56

Range

6.8

6.2

19.2

11.3

36.6

(Cohen, Manion, & Morrison, 2011)

  1. Box and Whisker Plots

Figure 3: Box and Whisker Plots

  1. A discussion on the price-earnings ratio values

Higher values of price-earnings ratio show that the stock is overpriced while stocks with small values are seen to be better because they have higher growth potentials. Therefore, CNU has the highest growth potential compared to the others because the median measure small compared to the others. However, SPK has the least margin for the 3rd and 1st quartile, hence lower deviation from the median. It is very risky to invest in VOC stock because it is hard to estimate its ideal price-earnings ratio because of the higher variation. Therefore, it will be safer to invest in CNU, SPK and TLS stock as opposed to TPM and VOC(Titman, Wei, & Xie, 2004).

  1. The probability that an Australian will die from neoplasms.
  1. The probability of a Female Australian to die from disease of the circulatory system
  1. Proportions of deaths

The disease with the highest proportion of male deaths compared to female deaths is Neoplasms with a difference of 6.3%. Diseases of circulatory system such as heart disease have the highest difference in proportion between female deaths and male deaths with a difference of 3.4%.

  1. The probability of dying from diabetes mellitu

(McCluskey & Lalkhen, 2007)

  1. Probability of rainfall
  2. The probability that there will be no rainfall in any given day
  1. The probability of 2 or more days of rainfall in a week
  1. Assuming that the weekly rainfall follows a normal distribution

The mean weekly rainfall is 9.9132mm and a standard deviation of 12.297mm

  1. The probability of having rainfall between 5mm to 15mm
  1. Amount of rainfall if only 10% of the weeks have that amount of rainfall or higher

 (Tsokos, Wooten, Tsokos, & Wooten, 2016)

The amount of rainfall will be  

  1. Normality Test

Refractive Index

Figure 4: Refractive index for refractive index

Sodium

Figure 5: Probability plot for Sodium

Magnesium

Figure 6: Probability plot of Magnesium

Aluminium

Figure 7: Probability plot of Aluminium

Silicon

Figure 8: Probability plot of Silicon

Potassium

Figure 9: Probability plot of Potassium

Calcium

Figure 10: Probability plot of Calcium

Barium

Figure 11: Probability plot of Barium

Iron

Figure 12: Probability plot of iron

Refractive index, Silicon, Aluminium, and Sodium are the only variables which are approximately normally distributed(Abdal-sahib et al., 2013; Tsokos et al., 2016).

  1. Confidence intervals of Float and non-float glass

Table 1: Float Glass Confidence intervals for normally distributed variables

Statistic

Std. Error

Refractive index

Mean

1.5185708

.00023735

95% Confidence Interval for Mean

Lower Bound

1.5180990

Upper Bound

1.5190426

Sodium

Mean

13.2803

.05402

95% Confidence Interval for Mean

Lower Bound

13.1730

Upper Bound

13.3877

Aluminum

Mean

1.1711

.03080

95% Confidence Interval for Mean

Lower Bound

1.1099

Upper Bound

1.2324

Silicon

Mean

72.5772

.06030

95% Confidence Interval for Mean

Lower Bound

72.4574

Upper Bound

72.6971

Table 2: Non-Float Glass Confidence intervals for normally distributed variables

Statistic

Std. Error

Refractive index

Mean

1.5186186

.00043613

95% Confidence Interval for Mean

Lower Bound

1.5177497

Upper Bound

1.5194874

Sodium

Mean

13.1117

.07618

95% Confidence Interval for Mean

Lower Bound

12.9599

Upper Bound

13.2635

Aluminum

Mean

1.4082

.03652

95% Confidence Interval for Mean

Lower Bound

1.3354

Upper Bound

1.4809

Silicon

Mean

72.5980

.08311

95% Confidence Interval for Mean

Lower Bound

72.4325

Upper Bound

72.7636

References

Abdal-sahib, R., Altammar, S. M., Azlan, H. A., Aytemur, A., Balters, S., Steinert, M., … Canny, J. (2013). Testing for Normality. Frontiers in Psychology, 98(1), 1–8. https://doi.org/10.3389/fpsyg.2014.01470

Aspara, J. (2009). Aesthetics of stock investments. Consumption Markets & Culture, 12(2), 99–131. https://doi.org/10.1080/10253860902840917

Cohen, L., Manion, L., & Morrison, K. (2011). Descriptive Statistics. In Research methods in education (pp. 622–640). https://doi.org/10.1213/ANE.0000000000002471

Fletcher, J. (2009). Normal distribution. BMJ, 338(feb18 2), b646–b646. https://doi.org/10.1136/bmj.b646

Lynott, W. J. (2005). Stock investments. Water Well Journal, 59(12), 39. Retrieved from https://www.scopus.com/inward/record.url?eid=2-s2.0-30344484585&partnerID=40&md5=ba73235c348c82cf518a1f10cd84cbe4

McCluskey, A., & Lalkhen, A. G. (2007). Statistics III: Probability and statistical tests.s, 7(5), 167–170. https://doi.org/10.1093/bjaceaccp/mkm028

Titman, S., Wei, K. C. J., & Xie, F. (2004). Capital Investments and Stock Returns. Journal of Financial and Quantitative Analysis, 39(04), 677. https://doi.org/10.1017/S0022109000003173

Tsokos, C., Wooten, R., Tsokos, C., & Wooten, R. (2016). Normal Probability. In The Joy of Finite Mathematics (pp. 231–263). https://doi.org/10.1016/B978-0-12-802967-1.00007-3