Statistics Assignment: Analysis of Financial and Market Data

This statistics assignment provides a comprehensive analysis of various statistical concepts and techniques. The assignment begins with descriptive statistics, including stem-and-leaf displays, histograms, and bar charts, applied to financial data like stock prices. It then delves into market recommendations based on financial ratios such as P/E and dividend yield. The assignment also covers probability calculations, including conditional probability and the probability of events occurring. Further, it explores the calculation of mean, median, and standard deviation, along with the creation of box and whisker plots. The document analyzes new vehicle sales data across different states and time periods. The assignment also includes detailed probability calculations using normal and binomial distributions, and the application of Z-scores. Finally, it addresses random sampling techniques and provides relevant statistical output, offering a complete overview of statistical methods and their practical applications.

STATISTICS

TABLE OF CONTENTS
QUESTION 1...................................................................................................................................1
(a) Stem-and-Leaf Display of Westpac banking corporation.................................................2
(b) Histogram for NAB and WBC..........................................................................................4
(C). Bar charts of six listed companies...................................................................................4
(d) Market recommendation...................................................................................................5
QUESTION 2...................................................................................................................................6
(a) and (b) Calculation of mean, median and standard deviation...........................................6
c) Box and whisker plot for new vehicle sales for each year.................................................6
(D.) number of new vehicles sales of each state, and the trends in new vehicles sales in
different Australian states.......................................................................................................7
Question 3........................................................................................................................................1
A. What is the probability that randomly selected household lives in Victoria?...................1
B. What is the probability that randomly selected household lives in Tasmania and has
internet access in 2010-11?....................................................................................................1
C. What is the probability that randomly selected household lives in New South Wales and
has internet access in 2012-13?..............................................................................................1
D. What is the probability that randomly selected household has access to internet in 2010-11
or 2012-13?.............................................................................................................................1
Question 4........................................................................................................................................3
A) What value does the upper 5% of the time exceed?..........................................................3
B) What is the probability that the air temperature will be less than 21 degree Celsius?......3
C) probability calculation.......................................................................................................3
Question 5........................................................................................................................................4
A) Binomial distribution.........................................................................................................4
B) Binomial distribution with Z score....................................................................................4
C) Random sampling..............................................................................................................4

QUESTION 1
Quarterly prices
Date Price (NAB) Price (WBC)
Jan-09 17.995 15.462
Apr-09 19.611 18.982
Jul-09 23.128 21.444
Oct-09 28.376 26.07
Jan-10 25.067 23.589
Apr-10 26.617 26.891
Jul-10 23.889 23.718
Oct-10 24.202 22.442
Jan-11 23.442 22.729
Apr-11 25.742 24.558
Jul-11 22.814 20.188
Oct-11 24.43 22.067
Jan-12 22.672 20.91
Apr-12 23.984 22.472
Jul-12 23.746 22.936
Oct-12 24.516 25.22
Jan-13 26.009 27.721
Apr-13 32.321 33.416
Jul-13 29.687 30.631
Oct-13 33.566 34.002
Jan-14 31.608 30.7
Apr-14 33.556 34.927
Jul-14 33.575 34.42
Oct-14 33.262 34.589
Jan-15 33.87 34.27
Apr-15 34.954 36.26
Jul-15 33.525 34.668
Oct-15 29.071 31.38
1

Jan-16 26.67 30.85
Apr-16 27.19 31.05
Jul-16 26.54 31.09
Oct-16 28 30.47
Jan-17 30.33 31.71
Apr-17 34 35.06
Jul-17 29.95 31.82
Oct-17 32.66 32.99
(a) Stem-and-Leaf Display of Westpac banking corporation
Leaf
unit: 10
1 5 9
2 0 1 1 2 2 2 3 3 4 4 5 5 6 7 8
3
0 1 1 1 1 1 1 2 2 3 3 4 4 4 5 5
5 5 6
n 36
mean
28.1028
3
median 30.5505
std. dev.
5.64847
9
minimum 15.462
maximu
m 36.26
Stem-and-Leaf Display
NAB
Leaf
unit: 10
1 8
2
0 3 3 3 3 4 4 4 4 4 5 5 6 6 7 7 7 7
8 8 9
2

3 0 0 0 2 2 3 3 4 4 4 4 4 4 5
n 36
mean
27.7937
5
median 26.93
std. dev.
4.53568
3
minimum 17.995
maximu
m 34.954
Stem and leaf display of NAB (left) and WBC (Right)
N 36
mean 28.10283
median 30.5505
std. dev. 5.648479
minimum 15.462
maximum 36.26
Stem-and-Leaf Display
Leaf
unit: 10
1 5 9
2 0 1 1 2 2 2 3 3 4 4 5 5 6 7 8
3
0 1 1 1 1 1 1 2 2 3 3 4 4 4 5 5
5 5 6
3

(b) Histogram for NAB and WBC
(C). Bar charts of six listed companies
Company Name
Market
capital
Ascent Resource 6.85
ActivEX 35.45
Adelaide Brighton 3.29
Admiralty Resources 17.31
ALCHEMY RESOURCES 6.61
Alara Resources 12.58
4

(d) Market recommendation
NAB
P/E Ratio of NAB is 11.8 and Dividend yield ratio is 8.1
From the above data it can be interpreted that Price /earnings ratio that shows the
willingness of the investor to pay the amount in order to receive one dollar of that company’s
earnings. Higher the P/E ratio the higher is the anticipated growth of the investors in future.
Moreover, It can interpreted that Dividend yield ratio that shows the amount of dividend the
company pay’s to its shareholders or investors. The dividend yield ratio of NAB is 8.1.
Trend ratio and Debt / equity ratio
Westpac Banking Corporation
P/E ratio and dividend yield ratio
Trend ratio and debt / equity ratio
5

It is recommended to the investor that it should invest in NAB as it is paying higher
dividend and it provide earnings ratio is also equal to the WBC. Moreover, the information
gathered about the company shows that it have less debt as compared to WBC. Also, it is
beneficial for the investor to invest their money in NAB as it will give them more returns.
QUESTION 2
(a) and (b) Calculation of mean, median and standard deviation
State NSW VIC QLD SA WA TAS NT ACT
Mean
33130.
3
27187.
9
19418.
8 5978.2 8352.8 1647.1 894.7 1543.4
Standard
deviation 3874.4 2913.6 2762.8 705.5 889.3 286.5 182.8 21.1
Minimum 28392 22426 16870 5174 7580 1298 626 1509
Maximum 43449 34262 27270 7613 10749 2074 1240 1573
Quartile 1
31395.
75 25973
17984.
75 5390 7810 1371.5 789.5 1527
Median 32750
27080.
5 18722 5968.5 8085 1629 865.5 1546
Quartile 3 33830
27978.
5
19599.
25
6310.2
5
8682.2
5
1906.7
5 982.5
1560.7
5
c) Box and whisker plot for new vehicle sales for each year
State NSW VIC QLD SA WA TAS NT AC
T
Mean 33130.3 27187.
9 19418.8 5978.2 8352.8 1647.1 894.7 154
3.4
Standar
d
deviatio
n
3874.4 2913.6 2762.8 705.5 889.3 286.5 182.8 21.
1
Minimu
m 28392 22426 16870 5174 7580 1298 626 150
9
Maximu
m 43449 34262 27270 7613 10749 2074 1240 157
3
6

Quartile
1
31395.7
5 25973 17984.7
5 5390 7810 1371.5 789.5 152
7
Median 32750 27080.
5 18722 5968.5 8085 1629 865.5 154
6
Quartile
3 33830 27978.
5
19599.2
5
6310.2
5
8682.2
5
1906.7
5 982.5
156
0.7
5
(D.) number of new vehicles sales of each state, and the trends in new vehicles sales in different
Australian states.
Month NSW
Jan-2016 28392
Feb-2016 32633
Mar-2016 35963
Apr-2016 29391
7

May-2016 32867
Jun-2016 43449
Jul-2016 30219
Aug-2016 31788
Sep-2016 34424
Oct-2016 31850
Nov-2016 32955
Dec-2016 33632
Jan-2017
4047296.50
000046
Feb-2017
4647042.11
188864
Mar-2017
5117957.67
132925
8
Jan-2016
Feb-2016
Mar-2016
Apr-2016
May-2016
Jun-2016
Jul-2016
Aug-2016
Sep-2016
Oct-2016
Nov-2016
Dec-2016
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
50000
f(x) = 141.416083916084 x + 32211.0454545455
State NSW
Linear (State NSW)

Month VIC
Jan-2016 22426
Feb-2016 26782
Mar-2016 27716
Apr-2016 23963
May-2016 26125
Jun-2016 34262
Jul-2016 25517
Aug-2016 27096
Sep-2016 28766
Oct-2016 27546
Nov-2016 28991
Dec-2016 27065
Jan-2017
6917891.79
253974
Feb-2017
8256722.10
023184
Mar-2017
8543789.93
939264
Apr-2017
7390293.57
925296
9

Month QLD
Jan-2016 17193
Feb-2016 18711
Mar-2016 21470
Apr-2016 17753
May-2016 19565
Jun-2016 27270
Jul-2016 18445
Aug-2016 18062
Sep-2016 19702
Oct-2016 16870
Nov-2016 18733
Dec-2016 19252
10
1 2 3 4 5 6 7 8 9 10 11 12 13
0
5000
10000
15000
20000
25000
30000
35000
40000 f(x) = 307.353146853147 x + 25190.1212121212
month Jan-2016 Feb-2016
Mar-2016 Apr-2016 May-2016
Jun-2016 Jul-2016 Aug-2016
Sep-2016 Oct-2016 Nov-2016
Dec-2016 VIC
Linear ( month Jan-2016 Feb-
2016 Mar-2016 Apr-2016 May-
2016 Jun-2016 Jul-2016 Aug-
2016 Sep-2016 Oct-2016 Nov-
2016 Dec-2016 VIC)