Statistics Assignment (Solution)

STATISTICS

Table of Contents
QUESTION 1...................................................................................................................................1
(a) Data for CSR Ltd and SFR Ltd along with stem-and-leaf diagram using Excel..............1
(b) Construction of Relative frequency for CSR Ltd and frequency polygon for SFR Ltd:. .4
(c) Bar Chart for six listed companies in Material Sector according to market capital.........6
(d) Recommendations to invest in CSR Ltd or SFR Ltd. based on fundamental analysis and
expert advice...........................................................................................................................7
QUESTION 2...................................................................................................................................8
(a) Calculation of Mean, Median, first quartile, and third quartile of sold prices for each city
using excel..............................................................................................................................8
(b) Calculation of standard deviation, mean absolute deviation and range for each city using
excel........................................................................................................................................8
c) Box and Whisker Plot for the sold prices of each city.......................................................9
d) Recent trends in apartment prices in Australia..................................................................9
QUESTION 3.................................................................................................................................10
a) Calculation of probability that an employee in Australia.................................................11
b) Probability of male sale worker employed in Australia...................................................11
c) Probability of female employee working in part time of clerical and administrative workers
..............................................................................................................................................11
d) Ratio for total persons in 2013 between Owner managers of incorporated enterprises to
Owner managers of unincorporated enterprises...................................................................12
b) Professional......................................................................................................................14
QUESTION 4.................................................................................................................................14
b)...........................................................................................................................................14
QUESTION 5...................................................................................................................................1
CONCLUSION................................................................................................................................2
REFERENCES................................................................................................................................3
APPENDIX......................................................................................................................................4

QUESTION 1
(a) Data for CSR Ltd and SFR Ltd along with stem-and-leaf diagram using Excel
The sample data for two ASX listed companies viz. CSR Limited and SFR Limited have
been provided below along with their unadjusted opening prices for the time period January 2008
to December 2017. (Price and research of SFR Limited, 2019)
Date Opening Prices (Unadjusted)
2008 CSR LTD. (in $ AUD) SFR LTD. (in $ AUD)
January 8.21 0.34
April 8.45 0.3
July 6.59 0.27
October 6.78 0.17
2009
January 5.19 0.08
April 3.53 0.08
July 4.93 1
October 5.54 3.4
2010
January 5.4 3.7
April 5.31 3.62
October 5.4 6.91
2011
January 5.07 8.11
April 3.28 6.81
July 2.93 7.11
October 2.26 5.88
1

2012
January 1.96 6.58
April 1.81 8.04
July 1.42 7.27
October 1.55 8.36
2013
January 1.96 8.63
April 2.06 6.02
July 2.22 5.13
October 2.44 6.43
2014
January 2.65 6.46
April 3.5 5.85
July 3.5 6.18
October 3.3 5.77
2015
January 3.9 4.55
April 4.03 4.37
July 3.59 5.71
October 2.88 5.65
2016
January 2.89 5.63
April 3.25 5.67
July 3.68 5.25
2

October 3.65 5.08
2017
January 4.62 5.64
April 4.5 6.37
July 4.22 5.62
October 4.72 5.76
Stem-and-leaf Display:
As the name suggests, stem and leaf diagram is a table produced by Excel that splits the
given data into stems and leaves. It is an analytical tool that helps in bifurcation of given data
into more legible and easier manner for the analysts to make sense of the collected data (Al-
Omari, 2016).
Given below is an output of values in stem and leaf pattern which shows stem values
ranging between 0 to 8 and includes CSR and SFR values on the right side and left side
respectively (Armstrong and Taylor, 2014). Here, the data values are broken down into stems
and just like the stem holds the leaves of a plant, the leaves values originate from these given
stem values. For instance, Stem Value 0 produces an SFR leaf depicting the value for unadjusted
opening prices for January 2008 0.34 in decimal values. Since, CSR prices have no value with a
zero in it, the CSR leaves for stem value 0 has been left empty. For Stem Value 1, SFR Leaves
produces a value zero since there is only one opening price for SFR in the above data that
touches $1 for July 2009. Therefore, SFR leaf shows zero in front of Stem-value 1 since zero
plus one would render a value of one (Boehm and Thomas, 2013).
The value 0.3430271708 for Stem-value 0 can be read as the prices $0.34, $0.30, $0.27,
$0.17 and $0.08. This is applicable for both SFR and CSR Leaves. It is easier to see through this
plot the ranges of opening prices at which the Company stocks have been frequent. For instance,
SFR Share price has not touched price $2 at all, it has either touched $5 and $6 as its highest
opening prices and $0.08 as its lowest opening price between January 2008 and December 2017
(Price and research of CSR Limited, 2019).
3

SFR Leaves Stem CSR Leaves
0.3430271708 0
0 1 0.9681425596
2 0.9326062245
0.40706221 3 0.5328553959
0.5537 4 0.9398036252
0.8813857772 5 0.1954431407
0.9181580243 6 0.5978
0.1127 7
0.11043663 8 0.2145
(b) Construction of Relative frequency for CSR Ltd and frequency polygon for SFR Ltd:
i. Relative Frequency histogram for CSR Ltd.:
Relative Frequency is the percent unit for how many times a frequency has occurred in
relation to the total of frequency for given range values. The following table shows relative
frequency table and histogram for CSR Ltd:
Relative Frequency table for CSR Ltd.:
Ranges CSR LTD. ( frequency) CSR Ltd. (Relative Frequency )
$0 to less than $1 0 0
$1 to less than $2 5 0.125
4

$2 to less than $3 8 0.2
$3 to less than $4 10 1
$4 to less than $5 7 0.175
$5 to less than $6 6 0.15
$6 to less than $7 2 2
$7 to less than $8 0 0
$8 to less than $9 2 0.05
Total 40
The above table shows classification of the sample data given with first range describing
how many times an opening price for CSR Limited has fallen between '$0 to less than $1', '$1 to
less than $2' and so on.. After finding the frequency, relative frequency for each range has been
ascertained by dividing frequency of CSR Limited from total observations, that is, 40 (Brozović
and Schlenker, 2011).
This table has then been converted into a Relative Frequency histogram shown below
using Excel for getting a better picture of the behaviour of share opening prices between January
2008 to December 2017. It can clearly show that the opening prices have frequently fallen
between the class width '$6 to less than $7' and least between the class width '$7 to less than $8'.
Relative Frequency histogram for CSR Ltd.:
5

CSR Ltd. (Relative Frequency )
0
0.5
1
1.5
2
2.5
0 0.125 0.2
1
0.175 0.15
2
0.05
$0 to less than $1
$1 to less than $2
$2 to less than $3
$3 to less than $4
$4 to less than $5
$5 to less than $6
$6 to less than $7
$7 to less than $8
$8 to less than $9
ii. Frequency polygon for SFR Ltd.:
Frequency polygon refers to the graphical representation of frequency of a given sample
data with equal class widths (Embrechts and Hofert, 2014). The following table shows frequency
table and polygon for SFR Ltd:
Frequency table for SFR Ltd.:
Ranges Frequency (f)
$0 to less than $1 6
$1 to less than $2 1
$2 to less than $3 0
$3 to less than $4 4
$4 to less than $5 2
$5 to less than $6 13
$6 to less than $7 8
$7 to less than $8 2
$8 to less than $9 3
6

Total 39
The above table shows classification of the sample data given with first range describing
how many times an opening price for SFR Limited has fallen between class widths '$0 to less
than $1', '$1 to less than $2' and so on.
This table has then been converted into a Frequency polygon shown below using Excel
for getting a better picture of the behaviour of share opening prices between January 2008 to
December 2017. It can clearly show that the opening prices have frequently fallen, 13 times,
between the class width '$5 to less than $6' and least,1 time, between the class width '$2 to less
than $3' (Haimes, 2015).
$0 to less ...
$1 to less ...
$2 to less ...
$3 to less ...
$4 to less ...
$5 to less ...
$6 to less ...
$7 to less ...
$8 to less ...
0
2
4
6
8
10
12
14
6
1 0
4
2
13
8
2 3
SFR LTD.
(frequency)
Ranges
Frequency (f)
(c) Bar Chart for six listed companies in Material Sector according to market capital
The following table contains collected data on six listed companies of Australian
Securities Exchange (ASX) that have a market capital or total assets exceeding $100 million (in
AUD). These companies are under the purview of having same or similar product offering as
CSR Limited and SFR Limited, that is, materials and constructions (Herrera and Schipp, 2014).
Name of the company ASX Code Market Capitals (in AUD) [in 100 million]
Alumina Limited AWC 66.24
Amcor Limited AMC 153.45
Adelaide Brighton ABC 27.78
7

Ausdrill Limited ASL 8.13
BHP Group Limited BHP 1008.36
Bluescope Steel
Limited BSL 58.6
0 200 400 600 800 1000 1200
66.2364
153.454
27.7811
8.12831
1008.36
58.5986
Bluescope Steel
Limited
BHP Group Limited
Ausdrill Limited
Adelaide Brighton
Amcor Limited
Alumina Limited
Market Capital (in 100 Mil.)
Company
The collected data has been converted into a Bar Chart that shows a horizontal
representation of the market capitals of six companies. One can interpret the bar chart to infer
that BHP Group Limited has the largest Market Capital worth $1008.36 million and Ausdrill
Limited has the least market capital worth $8.13 million (Jiang and Pang, 2011).
(d) Recommendations to invest in CSR Ltd or SFR Ltd. based on fundamental analysis and
expert advice
The CSR Ltd. has shown a falling trend between January 2008 and December 2017 with
its highest opening price being $8.45 in April 20008 and $4.22 in July 2017. This shows that the
stock has been unable to recover its highest opening price in 10 years span moving mostly
between $6 and $7. Apart from this, the stock has experienced frequent splits in the time period
which has greatly reduced its price. However, analysts see it is an optimistic stock to invest for
short term period as it has been increasing slowly in the past two quarters but not for long term.
The SFR Ltd. has shown a consolidated trend between January 2008 and December 2017
with its highest opening price being $8.63in April 20008 and $5.62 in July 2017. However,
8

analysts see it is not an optimistic stock to invest since it has been a consolidated phase for a very
long period (Kyriakarakos and et. al., 2013).
QUESTION 2
(a) Calculation of Mean, Median, first quartile, and third quartile of sold prices for each city
using excel
The collected data shows the calculation of mean, median, first quartile and third quartile
of selling prices of apartments sold in six capital cities of Australia.
Mean has been calculated by taking the average of sale prices of apartments sold in each
city. The average number of apartments sold in Sydney is highest at 1778.11 and lowest in Perth
at 506.83. Median column of this table shows the selling prices of apartments in each city near
which the data values are likely to fall either below or above (Marchington and et. al., 2016).
First quartile shows the middle data value that can be found between Median and the
least selling price of apartment in each city whereas third quartile shows the middle data value
that can be found between Median and the highest selling price of apartment in each city. It can
be seen that the city with highest average has the highest values for Median and quartiles as well
and vice versa.
Capital city Mean Median First Quartile Third Quartile
Sydney (NSW) 2000 1778.11 1810 1227.5 2150
Melbourne (VIC) 3000 733.17 650 600 790
Brisbane (QLD) 4000 572.05 518.5 450.5 643.75
Adelaide (SA) 5000 650.14 605 542 673.25
Perth (WA) 6000 506.83 480 441.25 531.25
Hobart (TAS) 7000 737 730 637 810
(b) Calculation of standard deviation, mean absolute deviation and range for each city using
excel
Standard Deviation for Perth has the lowest number of data values and also
Capital city Standard Mean Maximum Selling Minimum Range for
9

Deviation
Absolute
Deviation Prices ($) Selling Price ($) each city
Sydney
(NSW) 2000 674.21 511.99 3680 940 2740
Melbourne
(VIC) 3000 240.41 160.72 1667 470 1197
Brisbane
(QLD) 4000 173.08 136.64 1010 345 665
Adelaide (SA)
5000 247.83 150.06 1415 360 1055
Perth (WA)
6000 103.29 72.44 815 365 450
Hobart (TAS)
7000 116.83 91.6 893 615 278
c) Box and Whisker Plot for the sold prices of each city
d) Recent trends in apartment prices in Australia
10

This table shows the calculations of normality test for transport, service, distance, age and body
mass index along with confidence interval when the number of hours is more than 10 and less
than 10 hours. For this we have taken mean of each variable as well as the data array to find 90%
confidence intervals through normal distributions using excel.
QUESTION 3
Probability: It is an evaluation of random phenomenon that presents the assumption based
remain associated with analysing the random. Actual outcomes are evaluated on the basis of
changes. It is mainly calculated on the basis of two factors. A theoretical framework and
analysing the frequency of outcomes calculated through this factor. Dice, roulette wheels, cards
and coins are provided with examples (Qiu, Qin and Zhou, 2016).
Australian Labour Market Statistics
Released at 11;30 am (Canberra time) 8 July 2014
Table 6. Employment Type: Employed persons by Sex, Full-time/part-time and
Occupation (ANZSCO), 2013
All data are original series ('000)
Males Females Persons
Occupation
major
group Full-time Part-time Full-time Part-time Full-time Part-time
Managers 909.9 70 385.6 133.4 1295.5 203.4
Professional
s 1043.1 158.2 835.7 526 1878.9 684.2
Technicians
and trade
workers 1344.9 138.7 131.6 109.7 1476.5 248.4
Community
and personal 225.8 129.8 303.7 502 529.5 631.8
11

service
workers
Clerical and
adminstrativ
e workers 354.4 58.3 738.7 510 1093.1 568.3
Sales
workers 232.4 161.3 207.8 471.6 440.2 632.9
Machinery
operators
and drivers 604.4 101.4 52.3 19.2 656.7 120.5
Labourers 464.4 272.7 129.2 247.5 593.6 520.3
Total 5179.4 1090.4 2784.6 2519.4 7964 3609.8
a) Calculation of probability that an employee in Australia
The probability of employee in Australia selected at random is calculated below on the
basis of above table. First of all, chances of getting professional employees form all the eight
occupational groups.
Occupation
major group Chances Probability
Professionals 1 3.125
The above results show that there is one chance of getting professionals form the major
occupation group and probability is calculated on the basis of total chances. While calculating
probability both full time and part time male and female persons are selected as range.
b) Probability of male sale worker employed in Australia
Total number of employees in full and part time is 11574000 employees in Australia and
total number of male members full and part time of sale worker in Australia is 394000
employees’. Chances of getting full time employees is 34%. However, the probability of getting
the sale worker is 1 in terms of male sale worker in Australia.
Chances Probability
Sales
workers
394000/1157000*100
=34% 3.125
12

c) Probability of female employee working in part time of clerical and administrative workers
Total female employee in Australia working as a part-time is 2520000 the chances of
getting female employees that belongs to clerical and administrative worker is calculated as
follows
Chances Probability
Sales
workers
510000/2519400*100
=20.24% 3.125
d) Ratio for total persons in 2013 between Owner managers of incorporated enterprises to Owner
managers of unincorporated enterprises
Male
Full time 2013
Owner managers of incorporated enterprises
Managers 200.5
Professionals 103.2
Technicians and trades workers 109.8
Community and personal
service workers np
Clerical and administrative
workers 17.4
Sales workers np
Machinery operators and
drivers np
Laborers 20.3
Total 502.7
2013
Managers 139.5
Professionals 93.1
Technicians and trades workers 197.4
Community and personal service workers np
Clerical and administrative workers 9.8
Sales workers np
Machinery operators and drivers np
Labourers 50.3
Total 562.6
13

Part-time 2013
Owner managers of incorporated enterprises
Managers 18.3
Professionals 16.4
Technicians and trades workers 9.6
Community and personal service workers np
Clerical and administrative workers 3.7
Sales workers np
Machinery operators and drivers np
Labourers 5.4
Total 60.9
Male
Owner managers of
incorporated
enterprises Full time Part time
Managers 218.8 200.5
Professionals 119.6 103.2
Technicians and trades workers 119.4 109.8
Community and personal service workers np np
Clerical and administrative workers 21.1 17.4
Sales workers 22.2 np
Machinery operators and drivers np np
Labourers 25.7 20.3
Total 563.7 502.7
Female
Full part
Managers 46.2 53.1
Professionals 24.1 40.2
Technicians and trades
workers 3.2 15.1
Community and personal
service workers np np
Clerical and administrative
workers 24.5 14.0
Sales
workers np np
Machinery operators and np np
14

drivers
Labourers 2.9 7.3
Total 117.1 162.4
Owner managers of unincorporated enterprises
Managers 25.2 46.7
Professionals 14.9 59.0
Technicians and trades workers 4.5 20.3
Community and personal service
workers np np
Clerical and administrative workers 47.7 44.9
Sales workers np np
Machinery operators and drivers np np
Labourers 3.1 24.3
Total 101.8 241.4
Calculation of Ratio
Total of Owner managers of
incorporated enterprises
Female 279.6
Male 1066
Total 1345.9
Total Owner managers
of unincorporated
enterprises
Female 343.2
Male 1315
Total 1658.2
Ratio
=1345/1658*100 = .811
b) Professional
QUESTION 4
b)
Hobart
Statistic Jan Feb Mar Apr May Jun Jul Aug
Mean 47.5 39.5 44.6 50.1 47.4 53.7 52.4 53.5
Median 38.5 32 36.9 44.4 37.8 44.2 47.1 46.7
15

Highest
Daily
75.230th 61.09th 88.117th 132.323rd 129.211th 147.37th 63.818th 64.82nd
1916 1996 1946 1960 2018 1954 1922 1976
Statistic Sep Oct Nov Dec
Mean 53 61.1 54.2 56.6
Median 42.5 53.1 49 47.3
Highest Daily 156.215th 65.54th 63.226th 84.6
1957 1906 1957
Tasmania
Statistic Jan Feb Mar Apr May Jun Jul Aug
Mean 47.5 39.5 44.6 50.1 47.4 53.7 52.4 53.5
Median 38.5 32 36.9 44.4 37.8 44.2 47.1 46.7
Highest
Daily
75.230th 61.09th 88.117th 132.323rd 129.211th 147.37th 63.818th 64.82nd
1916 1996 1946 1960 2018 1954 1922 1976
Sep Oct Nov Dec
Mean 47.5 39.5 44.6
Median 38.5 32 36.9
Highest
Daily
75.230th 61.09th 88.117th
1916 1996 1946
16

(a) The above table will follow a Poisson Distribution with following output:
yyear 0.3598901099
yweek 0.0069209637
P(X=0)= (γ^X×e^(-γ))/γ! 0.99
(b) The above table will follow a Poisson Distribution with following output:
mean 0.0893755068
Poisson distribution with mean 0.0893755068
P(no rain) = P(x=0) 0.914
When using a Binomial with 7 trials x>=2 successes
and a probability of 1-0.914 0.00349
QUESTION 5
Transport Distance Service Age
Body Mass
Index
Standard
Deviation 66.95 14.84 4.38 6.48 4.29
Confidence 0.55 0.56 0.15 0.13 0.10
Normality
Test less thanApartment sales have seen highest demand in Sydney in terms of number of apartments
sold at 1778. with least number of apartments sold in Perth between Januar to July 2018. The
maximum selling price in Sydney has been $1667 for 2 bed 2 bath apartments and least at $470
for them. This trend has been growing for Brisbane and Melbourne with least demand in Hobart
for such apartment.

CONCLUSION
From the above project report it has been concluded that statistics is a branch of
mathematics which is used to deal with data analysis, collection, presentations, assessment and
interpretation. It is very beneficial for the managers and accountants as it helps to make strategic
decisions with the help of charts and graphs. It helps to resolve social, conventional and other
business problems. Mean, mode, median, standards deviation, normality test are the main
components of statistics. All these elements are calculated on the basis of current trends and
information. It can also be defined as the science that can be used to to collect, classify and
analyse information that can help to assess future condition of a business entity.
2

REFERENCES
Books and Journals:
Al-Omari, A. I., 2016. Time truncated acceptance sampling plans for Generalized Inverse
Weibull Distribution. Journal of Statistics and Management Systems. 19(1). pp.1-19.
Armstrong, M. and Taylor, S., 2014. Armstrong's handbook of human resource management
practice. Kogan Page Publishers.
Boehm, M. and Thomas, O., 2013. Looking beyond the rim of one's teacup: a multidisciplinary
literature review of Product-Service Systems in Information Systems, Business
Management, and Engineering & Design. Journal of Cleaner Production. 51. pp.245-
260.
Brozović, N. and Schlenker, W., 2011. Optimal management of an ecosystem with an unknown
threshold. Ecological economics. 70(4). pp.627-640.
Embrechts, P. and Hofert, M., 2014. Statistics and quantitative risk management for banking and
insurance. Annual Review of Statistics and Its Application. 1. pp.493-514.
Haimes, Y. Y., 2015. Risk modeling, assessment, and management. John Wiley & Sons.
Herrera, R. and Schipp, B., 2014. Statistics of extreme events in risk management: The impact of
the subprime and global financial crisis on the German stock market. The North
American Journal of Economics and Finance. 29. pp.218-238.
Jiang, H. and Pang, Z., 2011. Network capacity management under competition. Computational
Optimization and Applications. 50(2). pp.287-326.
Kyriakarakos, G. and et. al., 2013. Intelligent demand side energy management system for
autonomous polygeneration microgrids. Applied Energy. 103. pp.39-51.
Marchington, M. and et. al., 2016. Human resource management at work. Kogan Page
Publishers.
Qiu, Z., Qin, J. and Zhou, Y., 2016. Composite Estimating Equation Method for the Accelerated
Failure Time Model with Length‐biased Sampling Data. Scandinavian Journal of
Statistics. 43(2). pp.396-415
Online
Price and research of CSR Limited. 2019. [Online]. Available through:
<https://www.asx.com.au/asx/share-price-research/company/CSR>
Price and research of SFR Limited. 2019. [Online]. Available through:
<https://www.asx.com.au/asx/share-price-research/company/SFR>
3