UGB108 Quantitative Methods for Business: Alternative Assessment

This assignment solution for UGB108 Quantitative Methods for Business provides a comprehensive analysis of various statistical tools and techniques. The solution begins with an analysis of computer disc access times, calculating the mean and standard deviation to interpret data variability. It then delves into different sampling methods, including simple random, quota, cluster, and systematic sampling, explaining their relevance and providing examples. The solution further explores probability calculations, determining the likelihood of events occurring. Finally, it addresses correlation analysis using Spearman's rank correlation coefficient to assess whether consumers receive value for their money. The solution also includes calculations of Person's correlation between employees weeks of experience and number of rejections. The assignment covers key concepts in quantitative methods, offering a practical application of statistical principles to business scenarios.

Quantitative methods for business alternative

Table of Contents
INTRODUCTION...........................................................................................................................1
QUESTION 1...................................................................................................................................1
A) Analysis of time required to access computer disc system.....................................................1
QUESTION 3...................................................................................................................................5
A)Calculation of probability........................................................................................................5
QUESTION 4...................................................................................................................................6
A) Computation of Spearman’s rank correlation coefficient to determine whether consumer
gets value of money or not...........................................................................................................6
CONCLUSION................................................................................................................................9

INTRODUCTION
Statistical is branch of study which useful for collect, organize, analysis and interpret
data collected from various source. This branch is useful for solve issue of industrial, social or
socialistic problem in effective manner. There will be many tools used for collection and
interpretation of data. This report has been formulated to define some specific quantitative tools
which help in analysis and collect data by solving questions . Speciality measure value of mean,
standard deviation use of sampling, and relevance of probability and method which useful to
define correlation between variable. All theses information is provides in systematic manner.
QUESTION 1
A) Analysis of time required to access computer disc system.
Access time
in milestone
Frequency Mid value Fm x= m-X fx fx2
30-35 17 32.5 552.5 -11.91 -202.47 40995
35-40 24 37.5 900 -6.91 -165.84 27556
40-45 19 42.5 807.5 -1.91 -36.29 1317
45-50 28 47.5 1330 3.09 86.52 7569
50-55 19 52.5 997.5 8.09 153.71 23716
55-60 13 57.2 743.6 12.79 166.27 27646
N = 120 Efm = 5330 2 128800
X =
5330/120 =
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44.41
Standard
deviation=
128800/120
= 32.76
Here X = mean= frequency
m = mid value
Computation of mean = X = 5330/120 = 44.41
Computation of standard deviation= Standard deviation= 128800/120 = 32.76
Interpretation: Mean is essential part of statistical as it will useful for represent data or
size of set. It is define as average value of particular set of data which represent the overall data.
Thus research calculate mean through which they can easily interpret specific data. There will be
various methods through which researcher can calculated mean. In this case mean of overall
series was 44.41 which means that computer access need average of 44 time for access and run
their program.
Standard deviation is a tool to measure central dispersion. This tool is useful to evaluate
level of variability in particular set of data. On the basis of calculation of standard deviation
researcher able to find out rate of variability of different variable use for the purpose of research.
This is useful in the calculation of correlation thus standard deviation also beneficial for defining
relation between two variable. In this case value of standard deviation was calculated at 32.76
which means that magnitude among value of mean and standard deviation is high. This tool is
also useful to determiner level of risk thus most of research apply this tool during the time of
their research project.
Explanation of relevance of different types of sampling methods.
Sampling: This tool is used for collection of data for research purpose. Sample is define
characteristic of particular group. It is selection or choices of particular group which represent
the whole set of population. In general it is hard for researcher to find out or collect data of each
unit specially in case of formulate report on population of measure demographic factors impacts.
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In case where large data is required for select sampling is used by researcher which can help in
consumer time as well as cost and make easy for researcher to formulate heir report and provides
accurate result to their hypothesises.
There will be many types of method are used through which they can easily calculate and
select sample size which represent group.
 Simple random sampling: This is consider as part of probability sampling. In which
research can choose any person on randomly basis. In this probability of choose for
sample size of each or every individual is equal as their will be no case or chances of
favouritism ,it is easiest method of sampling which useful for deciding and choosing
particular grump for sampling purpose. In this type of sampling method researcher can
easily find way and they can also analysis each section of their research purpose however
in their will be some limitation of this methods.
It is not possible that random sampling may given information regarding every characteristic of
particular size of their sample especially in case of large size of business dealing it is hard to
definiens and financing all the torts in specific sample of size , thus in case of scientific research ,
they research not use this type of sample method to collect their sample for the purpose of
research.
Example: In school summer activity camp is organized by management department, in which
they organize supports program for their students. For playing football they can choose any of
students from who is present at the time of organizing event. Probability of selection of 11
player from 500 students is equal. For the purpose of selection of random student they can use
various methods by picking chits from bowl or any other ways.
It is one of the easiest method as researcher not need to focus on particular group and chances of
discrimination issue is nil, every employee or group get equal chance.
 Quota sampling: There will be two types of methods which researcher use for selection
of their sample size. One is probability and other one is no probability sample method. In
this sample is taken on the basis of selection of standards. Sample is formulated which
have specific qualities. Researcher select those group or size of sample which is
beneficial for their project and through which they can complete their research report'
objective. Sample size are decided and their attributes are selected on the basis of
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particular or specific objectives. Theses type of sample method is generally used in case
of exploratory as well as hypothesises research .
Example: If an organization want to find out which department of their various branches is
perform well on the basis of that they select sales department as it generate more revenue to
manage this department help in generate more benefits and revenue.
 Cluster sampling: In this method researcher use different style for select their sample
data. Researcher on the basis of their specific criteria divided population or any set of
data in various sections which represent different parts or trots of their research data.
Cluster can be divided according to geographical or demographical elements. In most of
reports research use demographic factors for the purpose of their research. Different
sections help in making and selection of cluster sampling easy. It showcase different
characteristics of each group on the basis of size, location, religion, gender etc. It is
useful and relevant method of sampling by applying tools of this sampling researcher
able to get accurate and reliable result as by applying this tools of sampling organization
able to collect and choose which source of sampling which is included all the traits of
their various size of sample and which one is beneficial ans useful for the purpose of
research. This will help in getting better result . Which useful for finding best result.
However their will also some limitations regarding this method thus while using this
method of collecting sample researcher need to focus on limitations also.
Example: If UK government wants to formulate a research report which give them information
regarding number of immigrants labour or employee line in England then they decide their
cluster or sample size on the basis of location. Through which they can easily interpret
immigrants number live in London, Manchester, Liverpool, and other area of UK.
 Systematic sampling: In this type method of sampling researchers select their sample on
interval basis. They select personas from group of population on random basis. In this
method research choose their size of sample from initial of their research and then choose
different size of samples of personas on interval basis. The time period require for gap is
select on the basis of objective and time required to complete the research. On the basis
of that research decide the time gap after that they select particular size of sampling.
Example: In case if manager decide to select 100 of employees to represent their
organization a international level. Then they select 10th number of employee of each element of
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their 1000 of employees. For select number of people by using this m,method of sampling ,
researcher use specific formula which define below:
Total number of employee/ Sample size =1000/ 100 = 10
a cumulative frequency distribution table
Data series Frequency Cumulative frequency
0-5 2 2
5.-.10 3 5
10..-15.. 4 9
15..-20... 7 16
20....-25.. 20 36
25..-30.. 11 47
30...-35... 3 50
QUESTION 3
A)Calculation of probability
The term probability is used to measure the occurrence of happening specific event. In
general probability of occurring specific event is come between 0 to 1 and. Researcher on the
basis of arising of frequency able to find out the arrival of occurrence of specific event. Higher
probability showcase more chances of success of particular event. This methods is also part of
quantitative measurement of statical tool which use by researcher for finding probability result of
their hypothesis scenario.
Probability of particular event can be calculated on the basis of applying this formula =
P (A) = Number of Favourable outcomes/ Total number of favourable outcomes
a) Probability of non of them solve problem
Probability of Chris to solve problem = 1/6
Probability of Albert solve issue = 1/8
Probability of John solve problem = 1/3
5

P(Cc)⋅P(Ac)⋅P(Jc) = 1440 / 6 = 240 time, Chris not able to solve the problem = 1440-
240 = 1200 .
Albert able to solve this problem = 1200/8 = 150 times, the probability of not solving
problem = 1200 – 150 = 1050 times.
John solve issue = 1050/3 = 700 times, which means that probability of not solving issue of
John = 1050-700 = 250. Probability of not solving problem = 700/1440 = 0.486 times.
b) probability of at least one of them solve problem
probability of solving the problem at least one = 350+100+140 = 590 = 590/1440 = 0.41 %.
c) probability of only one of them solve the problem
P(C)⋅P(Ac)⋅P(Jc)+P(A)⋅P(Cc)⋅P(Jc)+P(J)⋅P(Ac)⋅P(Cc) = 0.58 %
Probability of picked random balls=
One green and other white = 1/5*1/9+ 1/4*1/5 = 0.11
ci) Probability of same colour = 3/5*2*5+4/9+5/9 = 047
QUESTION 4
A) Computation of Spearman’s rank correlation coefficient to determine whether consumer gets
value of money or not.
Calculation of correlations
Spearman’s rank correlation coefficient,
Brand Price/Litre Quality
ranking
Quality
ranking
Differenc
e between
ranks (d)
d²
T 1.92 2 1 1 1
U 1.58 6 3 3 9
V 1.35 7 2 5 25
W 1.6 4 7 -3 9
X 2.05 3 5 -2 4
Y 1.39 5 4 1 1
6

Z 1.77 1 6 -5 25
Total 74
R = 1 – (6 total of difference variation's square/ n³ – n = 74/336 = 0.22
Calculation of
Person's
correlation
between
employees
weeks of
experience(x)
and number
of rejections
(Y)
X Y X2 Y 2 XY
4 21 16 441 84
5 22 25 484 110
7 15 49 225 105
9 18 81 324 162
10 14 100 196 140
11 14 121 196 154
12 11 144 121 132
14 13 196 169 182
72 128 732 2156 985
Number of
frequency*xy
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Calculation of
Person's
correlation
between
employees
weeks of
experience(x)
and number
of rejections
(Y)
– Total of x*
total of y /
8*985-
72*128/
8*732- (72)2*
8*2156-(732)2
- 1336 / 672
- 518576
25.92*720 =
18663 =
0.071
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CONCLUSION
From the above analysis it has been concluded that personal by qualitative tools can able
to collect and interpret data in effective way. There will be various methods which help in
selection of data by using sample size and researcher through calculate value of mean and
standard deviation can evaluate specific term which represent the overall data. They also use
probability which help in measure chances of successful of particular project and with the
calculation of correlation and coefficient method research or any business organization able to
find out relation between two or more then of two variables all these information help in
formulating effective research report which useful in finding solution of basis problems.
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