Statistics for Analytical Decisions and Probability Computation

This article covers statistical analysis of Australian stock market, prices of apartments in Australian state capital city centers, and daily rainfall amount from the Australian Bureau of Meteorology. It also includes probability computation for various events.

Statistics for Analytical Decisions
Statistical Analysis Paper
Student’s Name
Institution Affiliation

Statistics for Analytical Decisions
Question One
Data; from Australia stock market
a. Tables of the quarterly opening price values of CSR and the other for SFR
CSR imitedL
Opening Price
Beginning of Yearly
Quarter
2008 200
9
201
0
201
1
2012 2013 2014 2015 2016 2017
anuaryJ 22.1 4.42 7.84 5.37 53.3
1
52.9
5
62.0
4
49.3 29.8
2
36.8
2
April 18 3.9 7.74 4.67 52.2 49.3
2
66.4
3
37.7
4
33.6
5
37.7
ulyJ 13.3
8
7.38 4.57 5.28 47.6
3
45.3
7
63.7 38.8
3
32.8
1
37.7
2
ctoberO 14 7.15 5.6 6.4 52.7
1
58.2 44.7
7
30.0
5
41.2
8
48.3
9
S R imitedF L
Opening Price
Beginning of Yearly
Quarter
200
8
2009 201
0
201
1
2012 2013 2014 2015 2016 2017
anuaryJ 37.4
6
31.4
2
52.8
3
57.5
7
57.2
8
115.7
5
122.4
1
131.8
6
139.2
3
144.4
5
April 34.6
6
28.5
2
51.9
9
59.5
8
71.1
6
138.6
9
123.4
2
136.1
1
148.7
8
173.1
3
ulyJ 34.2
9
39.3
5
45.5
4
59.4 78.8
8
113.4
6
127.5
7
141.8
5
159.3
4
207.5
ctoberO 31.2
1
42.7
3
47.4
7
49.2 88.2
7
109.4
9
127.8
7
152.5 146.6
8
191.7

Statistics for Analytical Decisions
Stem and leaf display
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)

Statistics for Analytical Decisions
b. Histograms

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c. Bar chart of total market capital for other 6 companies listed in ASX.
Adelaide
rightonB imitedL
Alumina
imitedL Amcor
imitedL luescopeB Steel
imitedL
oralB
imitedL ortescueF Metals
roup DG LT
0
2,000,000,000
4,000,000,000
6,000,000,000
8,000,000,000
10,000,000,000
12,000,000,000
14,000,000,000
16,000,000,000
18,000,000,000
20,000,000,000
d. 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)

Statistics for Analytical Decisions
Question Two
Data: The prices of apartments with 2 bedrooms and 2 bathrooms sold between January and July
of 2018 in Australian state capital city centers.
a. 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
b. 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 for Analytical Decisions
Statistics
Sydney
Absolute
deviation
Melbourne
Absolute
deviation
Brisbane
Absolute
deviation
Adelaide
Absolute
deviation
Perth
Absolute
deviation
Hobart
Absolute
deviation
N
Vali
d
19 41 38 14 18 5
Miss
ing
22 0 3 27 23 36
Mean 511.9942 160.7211 136.6395 150.0613 72.4433 91.6000
c. 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

Statistics for Analytical Decisions
d. 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
Question Three
Data: Australian Bureau of Statistics (ABS)
The table below shows a well-organized data for the computation of probabilities

Statistics for Analytical Decisions
Column1 Males Females Persons
Occupation Major Group
Full
Time
Part
Time
Tot
al
Full
Time
Part
Time
Tot
al
Full
Time
Part
Time
Tota
l
Managers
909.
9 70.0
979
.9
385.
6
133.
4
519
.0
1295.
5 203.4
1498
.9
rofessionalsP
1043
.1 158.2
120
1.3
835.
7
526.
0
136
1.8
1878.
9 684.2
2563
.1
echnicians and tradesT
workers
1344
.9 138.7
148
3.6
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
124
8.7
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
aborersL
464.
4 272.7
737
.1
129.
2
247.
5
376
.7 593.6 520.3
1113
.9
Total
5179
.4
1090.
4
626
9.8
2784
.6
2519
.4
530
4.0
7964.
0
3609.
8
1157
3.8
a. The probability that a randomly selected employee in Australia is a professional.
According to Ross (2014), the probability of an event is given by
Prob ( event ) = Number of outcomes∈an event
Total number of possible outcomes
Therefore,
Prob ( Professional )= Number of professionals
Total numbe r of employees = 2563.1
11573.8 =0.2215

Statistics for Analytical Decisions
b. The probability that a randomly selected employee in Australia is a Male and Sales
worker.
This will be;
Number of Male Sales workers
Total Number of Employe e s
¿ 393.8
11573.8 =0.0340
c. 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.
Number of Female Clerical working Part time
Total Number of Employees
¿ 510
11573.8 =0.0441
d. The ratio for the total persons in 2013 between owners manager of incorporated
enterprises to Owner managers of unincorporated enterprises.
The ratio will be given by
Incorporated
Unincorporated = 782.6
1156.2 =0.6769
nterpriseE Full Time Part-Time otalT
ncorporatedI 619.8 162.7 782.6
nincorporatedU 725.1 431.1 1156.2

Statistics for Analytical Decisions
Therefore, the ratio for the total persons in 2013 between owners manager of incorporated
enterprises to Owner managers of unincorporated enterprises is 1 :0.6769
Question Four
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
(Question Four)
a. Probability:
i. That there’s no rainfall on any given week.
According to Hasset & Stewart (2006), probability by counting principle is given
by
Prob ( event ) = Number of outcomes∈an event
Total number of possible outcomes
Therefore, the probability that there’s no rainfall on any given week, will be given
by
Number weeks with no rain
Total number of weeks∈a year = 7
52 =0.135
ii. That there’s at least 3 days of rainfall in a week
To compute this you need to compute the probability having rain in any week, which is
given by
1−Prob ( no rain∈any givenweek ) =1−0.135=0.865

Statistics for Analytical Decisions
And probability of having rain in at most two days in a week:
Pro ( Rain , one day )+ Prob ( rain, two da ys )=0.124 +0.247=0.371
The probability of raining at least 3 days in a week is given by
1−Pro ( rains , at most 2 days )=1−0.371=0.629
b. Assuming normal distribution for the above data:
Computation of mean and standard deviation of weekly total
This was done on Microsoft Excel
Mean=9.485
Standard de viation=13.846
i. Probability that the in a given week there will be between 3mm and 9mm of
rainfall.
This will be given by
Prob ( 9 ) −Prob (3)
Due to the assumption of normal distribution, the probability will be computed from z-scores of
the two limits of rainfall amount, 3mm and 9mm.
According to Francis (2004) z-scores is computed by the formula
z= x−mean( x )
Standard deviation
z1= 3−9.485
13.846 =−0.035
z2= 9−9.485
13.846 =−0.468

Statistics for Analytical Decisions
The probabilities of z-scores are read from the z-tables. This leads to
P( z1)=0.3198 and P( z2)=0.4860
Therefore
Prob ( 9 )−Prob ( 3 ) =0.486−0.3198=0.1663
ii. 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;
15 %∗52=7.8
The mount within the range of 3mm and 9mm, will be:
7.8∗( 3+9
2 )=46.8 mm
The amount rainfall will be at least 46.8 mm

Statistics for Analytical Decisions
Question Five
Data: Absenteeism from work
a. 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 p-value of the test is interpreted as
follows:
 Small p-value: Null hypothesis of normality is rejected: data is not data is not
from normal distribution
 Large p-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

Statistics for Analytical Decisions
The p-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). b

Statistics for Analytical Decisions

Statistics for Analytical Decisions

Statistics for Analytical Decisions
b. 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

Statistics for Analytical Decisions
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

Statistics for Analytical Decisions

Statistics for Analytical Decisions
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

Statistics for Analytical Decisions
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

Statistics for Analytical Decisions
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]

Statistics for Analytical Decisions
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.
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