Analysis Of Australian Stock Market & Rainfall Data

Stock Market Data

Data; from Australia stock market

1. Tables of the quarterly opening price values  of CSR and the other for SFR

CSR  Limited
	Opening Price
Beginning of Yearly Quarter	2008 Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	2009	2010	2011	2012	2013	2014	2015	2016	2017
January	22.1	4.42	7.84	5.37	53.31	52.95	62.04	49.3	29.82	36.82
April	18	3.9	7.74	4.67	52.2	49.32	66.43	37.74	33.65	37.7
July	13.38	7.38	4.57	5.28	47.63	45.37	63.7	38.83	32.81	37.72
October	14	7.15	5.6	6.4	52.71	58.2	44.77	30.05	41.28	48.39

SFR  Limited
	Opening Price
Beginning of Yearly Quarter	2008	2009	2010	2011	2012	2013	2014	2015	2016	2017
January	37.46	31.42	52.83	57.57	57.28	115.75	122.41	131.86	139.23	144.45
April	34.66	28.52	51.99	59.58	71.16	138.69	123.42	136.11	148.78	173.13
July	34.29	39.35	45.54	59.4	78.88	113.46	127.57	141.85	159.34	207.5
October	31.21	42.73	47.47	49.2	88.27	109.49	127.87	152.5	146.68	191.7

CSR Stem-and-Leaf Plot

 Frequency    Stem &  Leaf

 12.00        0 .  344455567777

 3.00        1 .  348

 2.00        2 .  29

 8.00        3 .  02367778

 7.00        4 .  1457899

 5.00        5 .  22238

 3.00        6 .  236

Stem width:     10.00

Each leaf:       1 case(s)

SFR Stem-and-Leaf Plot

Frequency    Stem &  Leaf

11.00        0 .  23333334444

     9.00        0 .  555555778

    15.00        1 .  011222233334444

     4.00        1 .  5579

     1.00        2 .  0 

 Stem width:    100.00

 Each leaf:       1 case(s)   

1. Histograms    

1. Bar chart of total market capital for other 6 companies listed in ASX. 

1. Advice

From the trends displayed in the graph CSR shares are a viable investment, since its yield is associated with lower risk (standard deviation, 20.49) that of SFR shares ( standard deviation, 51.37)  

Data: The prices of apartments with 2 bedrooms and 2 bathrooms sold between January and July of 2018 in Australian state capital city centers.

1. Computation of Mean, Median, first Quartile and third Quartile of sold price for each city. These were statistics were computed on SPSS

Statistics
	Melbourne	Brisbane	Adelaide	Perth	Hobart	Sydney
N	Valid	41	38	14	18	5	19
Missing	0	3	27	23	36	22
Mean	733.171	572.05	650.143	506.83	737.00	1778.11
Median	650.000	518.50	605.000	480.00	730.00	1810.00
Percentiles	25	600.000	448.75	518.750	440.00	626.00	1190.00
50	650.000	518.50	605.000	480.00	730.00	1810.00
75	795.500	650.00	699.500	537.50	851.50	2300.00

Computation of Standard deviation, Mean absolute deviation and range of sold price for each city. These were statistics were computed on SPSS 

Statistics
	Melbourne	Brisbane	Adelaide	Perth	Hobart	Sydney
N	Valid	41	38	14	18	5	19
Missing	0	3	27	23	36	22
Std. Deviation	240.4076	173.076	247.8296	103.290	116.831	674.212
Range	1197.0	665	1055.0	450	278	2740

The means in the table below are the means absolute deviations of the sold price for each city. These were statistics were computed on SPSS 

Statistics
	Sydney Absolute deviation	Melbourne Absolute deviation	Brisbane Absolute deviation	Adelaide Absolute deviation	Perth Absolute deviation	Hobart Absolute deviation
N	Valid	19	41	38	14	18	5
Missing	22	0	3	27	23	36
Mean	511.9942	160.7211	136.6395	150.0613	72.4433	91.6000

Drawing a box and whisker plot for the sold prices of each city and put them side by side on one graph with the same scale    

1. Comment on the 2 bed, 2 bath apartment prices of each city, number of apartments sold, and recent trends in apartment prices in the Australian capital cities.

From the result,  it clear that the number of apartments sold in any city depends on the selling prices. When the price  is high the  number  sold is low for example in Sydney city,  the number sold, 2000 is lower than those, 7000,  in Hobart, since   the average price, 1778.11  is much higher than that in Hobart, 737.00 

Data: Australian Bureau of Statistics (ABS)

 The table below shows a well-organized data for the computation of probabilities

Column1	Males	Females	Persons
Occupation Major Group	Full Time	Part Time	Total	Full Time	Part Time	Total	Full Time	Part Time	Total
Managers	909.9	70.0	979.9	385.6	133.4	519.0	1295.5	203.4	1498.9
Professionals	1043.1	158.2	1201.3	835.7	526.0	1361.8	1878.9	684.2	2563.1
Technicians and trades workers	1344.9	138.7	1483.6	131.6	109.7	241.3	1476.5	248.4	1724.9
Community and personal service workers	225.8	129.8	355.6	303.7	502.0	805.7	529.5	631.8	1161.3
Clerical and administrative workers	354.4	58.3	412.7	738.7	510.0	1248.7	1093.1	568.3	1661.4
Sales workers	232.4	161.3	393.8	207.8	471.6	679.4	440.2	632.9	1073.1
Machinery operators and drivers	604.4	101.4	705.8	52.3	19.2	71.4	656.7	120.5	777.2
Laborers	464.4	272.7	737.1	129.2	247.5	376.7	593.6	520.3	1113.9
Total	5179.4	1090.4	6269.8	2784.6	2519.4	5304.0	7964.0	3609.8	11573.8

The probability that a randomly selected employee in Australia is a professional.

According to Ross (2014), the probability of an event is given by

Therefore,  

1. The probability that a randomly selected employee in Australia is a Male and Sales worker.

This will be; 

1. The probability that a randomly selected employee in Australia belongs to the category of Clerical and administrative workers given that she a female working part-time. 

1. The ratio for the total persons in 2013 between owners manager of incorporated enterprises to Owner managers of unincorporated enterprises.

Enterprise	Full Time	Part-Time	Total
Incorporated	619.8	162.7	782.6
Unincorporated	725.1	431.1	1156.2

The ratio will be given by

Therefore, the ratio for the total persons in 2013 between owners manager of incorporated enterprises to Owner managers of unincorporated enterprises is

Data: Daily Rainfall Amount from the Australian Bureau of Meteorology.

Every data needed in  the computation of probabilities has been worked out on the excel file

1. Probability:
2. That there’s no rainfall on any given week.

According to Hasset & Stewart (2006), probability by counting principle is given by

Therefore, the probability that there’s no rainfall on any given week, will be given by 

1. That there’s at least 3 days of rainfall in a week

CSR and SFR opening prices

To compute this you need to compute the probability having rain in any week, which is given by

 And probability of having rain in at most two days in a week:

The probability of raining at least 3 days in a week is given by

1. Assuming normal distribution  for the above data:

Computation of mean and standard deviation of weekly total

This was done on Microsoft Excel

Probability that the in a given week there will be between 3mm and 9mm of rainfall.

This will be given by

Due to the assumption of normal distribution, the probability will  be computed from -scores of the two limits of rainfall amount, 3mm and   9mm.

According to Francis (2004) -scores is computed by the formula

The probabilities of -scores are read from the -tables. This leads to and Therefore  

1. The amount of rainfall if only 15% of the weeks have that amount of rainfall or higher?

To compute this you need the number of weeks in 15% of the year;

The mount within the range of 3mm and 9mm, will be:

The amount rainfall will be at least 46.8 mm

Data: Absenteeism from work

1. Normality Test

According to Ruppert(2014) normality test is used to determine whether the  data set is from  the normal distribution. The commonly used normality tests are Kolmogorov-Smirnov and Shapiro-Wilk (Thode, 2002). The -value of the test is interpreted as follows:

• Small -value:  Null hypothesis of normality is rejected: data is not data is not from normal distribution
• Large -value: Null hypothesis  of normality is accepted; data is  from normal distribution

 The below is results for the normality test of Absenteeism from work Data; Transportation expense, Distance from Residence to Work, Service time, Age, and Body mass index. The test was done using SPSS software. 

Tests of Normality
	Kolmogorov-Smirnova	Shapiro-Wilk
Statistic	df	Sig.	Statistic	df	Sig.
Transportation expense	.153	740	.000	.946	740	.000
Distance from Residence to Work	.178	740	.000	.878	740	.000
Service time	.109	740	.000	.943	740	.000
Age	.126	740	.000	.928	740	.000
Body mass index	.179	740	.000	.946	740	.000
a. Lilliefors Significance Correction

The -values of the five variables, Transportation expense, Distance from Residence to Work, Service time, Age, and Body mass index, are  very small (.000), thus null hypothesis is rejected as  an evidence that the variables are not form normal distribution (Ruppert 2014). 

1. Construction of 90% confidence interval for each variable in a above separating the data between absenteeism time below 10 hours above 10 hours.

Confidence interval for five variables when the absenteeism time is less than 10 hours 

This was computed using SPSS

Descriptives
	Statistic	Std. Error
Transportation expense	Mean	221.32	2.567
90% Confidence Interval for Mean	Lower Bound	217.09
Upper Bound	225.54
5% Trimmed Mean	218.77
Median	225.00
Variance	4460.894
Std. Deviation	66.790
Minimum	118
Maximum	388
Range	270
Interquartile Range	81
Skewness	.413	.094
Kurtosis	-.257	.188
Distance from Residence to Work	Mean	29.97	.573
90% Confidence Interval for Mean	Lower Bound	29.02
Upper Bound	30.91
5% Trimmed Mean	29.91
Median	26.00
Variance	222.307
Std. Deviation	14.910
Minimum	5
Maximum	52
Range	47
Interquartile Range	34
Skewness	.284	.094
Kurtosis	-1.296	.188
Service time	Mean	12.52	.171
90% Confidence Interval for Mean	Lower Bound	12.23
Upper Bound	12.80
5% Trimmed Mean	12.65
Median	12.00
Variance	19.824
Std. Deviation	4.452
Minimum	1
Maximum	29
Range	28
Interquartile Range	7
Skewness	.036	.094
Kurtosis	.670	.188
Age	Mean	36.42	.248
90% Confidence Interval for Mean	Lower Bound	36.01
Upper Bound	36.82
5% Trimmed Mean	36.06
Median	37.00
Variance	41.764
Std. Deviation	6.462
Minimum	27
Maximum	58
Range	31
Interquartile Range	9
Skewness	.643	.094
Kurtosis	.281	.188
Body mass index	Mean	26.76	.166
90% Confidence Interval for Mean	Lower Bound	26.48
Upper Bound	27.03
5% Trimmed Mean	26.66
Median	25.00
Variance	18.625
Std. Deviation	4.316
Minimum	19
Maximum	38
Range	19
Interquartile Range	7
Skewness	.287	.094
Kurtosis	-.347	.188

Confidence interval for five variables when the absenteeism time is greater than 10 hours 

This was computed using SPSS

Descriptives
	Statistic	Std. Error
Transportation expense	Mean	221.48	8.721
90% Confidence Interval for Mean	Lower Bound	206.91
Upper Bound	236.04
5% Trimmed Mean	219.27
Median	228.00
Variance	4791.544
Std. Deviation	69.221
Minimum	118
Maximum	369
Range	251
Interquartile Range	134
Skewness	.233	.302
Kurtosis	-.879	.595
Distance from Residence to Work	Mean	26.02	1.716
90% Confidence Interval for Mean	Lower Bound	23.15
Upper Bound	28.88
5% Trimmed Mean	25.59
Median	25.00
Variance	185.435
Std. Deviation	13.617
Minimum	5
Maximum	52
Range	47
Interquartile Range	23
Skewness	.609	.302
Kurtosis	-.680	.595
Service time	Mean	12.97	.451
90% Confidence Interval for Mean	Lower Bound	12.21
Upper Bound	13.72
5% Trimmed Mean	13.20
Median	13.00
Variance	12.838
Std. Deviation	3.583
Minimum	3
Maximum	18
Range	15
Interquartile Range	5
Skewness	-.679	.302
Kurtosis	.507	.595
Age	Mean	36.83	.843
90% Confidence Interval for Mean	Lower Bound	35.42
Upper Bound	38.23
5% Trimmed Mean	36.30
Median	36.00
Variance	44.792
Std. Deviation	6.693
Minimum	28
Maximum	58
Range	30
Interquartile Range	7
Skewness	1.260	.302
Kurtosis	1.962	.595
Body mass index	Mean	25.83	.488
90% Confidence Interval for Mean	Lower Bound	25.01
Upper Bound	26.64
5% Trimmed Mean	25.79
Median	25.00
Variance	15.017
Std. Deviation	3.875
Minimum	19
Maximum	38
Range	19
Interquartile Range	7
Skewness	.446	.302
Kurtosis	.245	.595

From the above  result of confidence,  the variable that is likely to influence absenteeism time is Distance from residence to  work. Its confidence interval does not overlap.

Below 10 hours: [29.02, 30.91]

Above 10 hours: [23.15, 28.88]

References

Francis, A., 2004. Business mathematics and statistics. Cengage Learning EMEA.

Hassett, M.J. and Stewart, D., 2006. Probability for risk management. Actex Publications.

Ruppert, D., 2014. Statistics and finance: an introduction. Springer.

Ross, S., 2014. A first course in probability. Pearson.

Thode, H.C., 2002. Testing for normality (Vol. 164). CRC press.

https://www.asx100list.com/#second

https://www.historicalstockprice.com

Data; from Australia stock market