Data; from Australia stock market
CSR Limited |
||||||||||
Opening Price |
||||||||||
Beginning of Yearly Quarter |
2008 |
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)
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.
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
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,
This will be;
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
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
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
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
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
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:
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).
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
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