Stemandleaf displays and frequency plots
(a)List all the quarterly opening price values in two tables, one for MQG and the other for PPT. Then construct a stemandleaf display with one stem value in the middle, and MQG leaves on the right side and PPT leaves on the left side. (Must use EXCEL or similar for the plot.)
(b)Construct a relative frequency histogram for MQG and a frequency polygon for PPT on the same graph with equal class widths, the first class being “$0 to less than $10”. Use two different colours for MQG and PPT. Graph must be done in EXCEL or similar software.
(c)Draw a bar chart of market capitals (or total assets) in 2017 (in million Australian dollars) of 6 companies listed in ASX that trade in financials with over AUD500 million in market capital. Graphing must be done in EXCEL or with similar software.
If one wishes to invest in MQG or PPT, what is the market recommendation (for example, from Morningstar, Fatprophets, InvestSmart, etc.)? If you cannot find the information, what would be your recommendation based on your research of these two companies (trend, P/E ratio, dividend yield and Beta)?
...
(a)ompute the mean, median, first quartile, and third quartile of average priceearnings ratio for each company using the exact position, (n+1)f, where n is the number of observations and f the relevant fraction for the quartile.
(c)Draw a box and whisker plot for the average priceearnings ratio of each company and put them side by side on one graph with the same scale so that the P/Es can be compared. (This graph must be done in EXCEL or similar software and cannot be handdrawn.)
Write a paragraph on priceearnings ratio values related to it being indicative of a share being a good investment or a poor investment.
(a)Based on the table above, what is the probability that an Australian selected at random will die from neoplasms?
(b)Based on the table above, what is the probability that an Australian selected at random will die from a disease of the circulatory system and is a female?
(c)Based on the table, which disease has the highest proportion of male deaths compared to female deaths, and also, which disease has the highest proportion of female deaths compared to male deaths?
Visit the ABS website (Data Cube 1) and determine the probability of an Australian selected at random of dying from diabetes mellitus.
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 5mm and 15mm of rainfall?
(ii) What is the amount of rainfall if only 10% of the weeks have that amount of rainfall or higher?
(a) Test for normality of all the variables separately using normal probability plot, except the first and last column variables.
(b) Construct a 90% confidence interval for each of the variables in part (a) which can be considered as normally distributed separating the data between float glass and nonfloat glass. In the last column, the numbers 1 and 3 represent float glass, all other numbers indicate nonfloat glass. In other words, there will be two confidence interval constructions for each normally distributed variable – one for the float glass observations and the other for the nonfloat glass observations. After all the confidence intervals have been constructed, identify the variable(s) which are significantly different in composition between float and nonfloat type of glasses (i.e., identify the variables where the confidence intervals do not overlap).
Stemandleaf displays and frequency plots
 Quarterly opening prices
Year 
Quarter 
MQG 
PPT 
Year 
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 StemandLeaf 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)
 Histogram and Frequency polygon for MQG and PPT
Figure 1: Histogram and Frequency polygon of MQG and PPT
 Market capitals for 6 companies listed in ASX with over AUD 500 million
Figure 2: Market capitals
 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 Priceearning 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).
 Mean, median, 1^{st}and 3^{rd} 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 
 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)
 Box and Whisker Plots
Figure 3: Box and Whisker Plots
 A discussion on the priceearnings ratio values
Higher values of priceearnings 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 3^{rd} and 1^{st} quartile, hence lower deviation from the median. It is very risky to invest in VOC stock because it is hard to estimate its ideal priceearnings 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).
 The probability that an Australian will die from neoplasms.
 The probability of a Female Australian to die from disease of the circulatory system
 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%.
 The probability of dying from diabetes mellitu
(McCluskey & Lalkhen, 2007)
 Probability of rainfall
 The probability that there will be no rainfall in any given day
 The probability of 2 or more days of rainfall in a week
 Assuming that the weekly rainfall follows a normal distribution
The mean weekly rainfall is 9.9132mm and a standard deviation of 12.297mm
 The probability of having rainfall between 5mm to 15mm
 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
 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(Abdalsahib et al., 2013; Tsokos et al., 2016).
 Confidence intervals of Float and nonfloat 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: NonFloat 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
Abdalsahib, 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=2s2.030344484585&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/B9780128029671.000073
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