Quantitative Methods for Business

This report discusses the importance of statistical tools in collecting and analyzing data, and making decisions based on regression coefficients and probability. It also explores the use of standard deviation and mean in quantitative methods for business.

Quantitative Methods for Business

Table of Contents
INTRODUCTION...........................................................................................................................3
QUESTION 2..................................................................................................................................3
a) Explanation of meaning of 4 regression coefficient of data....................................................3
b) Brief explanation regarding decision taken of selection of region..........................................5
c) Calculation of expected running cost......................................................................................5
QUESTION 3..................................................................................................................................6
QUESTION 5..................................................................................................................................8
a) Probability of workers take less than of average time.............................................................9
b) Evaluate whatever income of self-employment in clothing industry is different.................10
c)Decision taken regarding manufacturing process...................................................................10
CONCLUSION..............................................................................................................................10
REFERENCES..............................................................................................................................12

INTRODUCTION
Individuals in order to collect data for the purpose of research use statistics tools.it is
branch of study which useful for individual for solve issue related with social, industrial by
collecting essential information. This report has been formulated to define the requirement and
relevance of statistical tools in order to collect the data, analysis the relation between variables as
well as finding out the occurrence of success or failure of events or project by calculate rate of
probability. This report also showcases use of result of standard deviation and regression in order
to take future decision regarding with running industrial operations.
QUESTION 2
a) Explanation of meaning of 4 regression coefficient of data.
Calculation of regression coefficient of
data
Y= a+bx
X Y
( X-
X) 9Y-Y) (x-x)2 (y-y)2
(x-x) (y-
y)
4 5.3 -4 3.7 16 13.69 14.8
4.6 6.7 -3.4 2.3 11.56 5.29 7.82
5.9 7.5 (2.10 2.5 4.41 6.25 5.25
6.7 8.8 1.3) 0.2 1.69 0.04 0.26
8 8 0 1 0 1 0
8.9 9.1 0.9 0.1 0.81 0.01 0.09
8.9 10.5 0.9 1.5 0.81 2.25 1.35
10.1 10 2.1 1 4.41 1 2.1
10.8 11.7 2.8 2.7 7.84 7.29 7.56
12.1 12.4 4.1 3.4 16.81 11.56 13.94
Sum = 80 90 64.34 48.38 53.17
Mean = 8 9
b1 = Σ [ (xi - x)(yi - y) ] / Σ [ (xi - x)2]
B1 = 53.17/64.34 = 0.82
b0 = y - b1 * x = 9-0.82*8 = 2.44
Distance
Travelled
Running
Costs (x-x) (y-y) (x-x)2 9y-y)2
(x-x) (y-
y)
3.5 6.9 -4.5 -2.1 20.25 4.41 9.45

4.6 7.6 -3.4 -1.4 11.56 1.96 4.76
5.3 7.9 -2.7 -1.1 7.29 1.21 2.97
6 8.3 -2 -0.7 4 0.49 1.4
7.2 8.8 -0.8 -0.2 0.64 0.04 0.16
8.4 9.2 0.4 0.2 0.16 0.04 0.08
10.1 9.6 2.1 0.6) 4.41 0.36 1.26
11.1 10.3 3.1 1.3 9.61 1.69 4.03
11.5 10.1 3.5 1.1 12.25 1.21 3.85
12.3 11.3 4.3 2.3 18.49 5.29 9.86
80 90 0 0 88.66 16.7 37.82
Mean of X series = 8
Mean of Y series = 9
Coefficient regression = 37.82/88.66 = 0.42
9-0.42*8 = 5.64
Regression coefficients: This is a tool which is part of measurement of central tendency,
it is calculated for the purpose of evaluating average changes of variable for particular unit
change in other variable. In order to represent value of coefficient regression slope line has been
drawn. Regression coefficient help in determine relationship between two or more then of 2
variables in which one is depended and other one of independent variable. Coefficient is
calculating by multiplying predictors values (Hazen, Skipper Boone and Hill, 2018).
There are various methods through which individual can able to calculate coefficient
regression however liner regression is one of the most useful and beneficial method as the
calculation is comparatively easy then other method of solving or calculating coefficient of
regression. With the use of calculating of correlations personal able to find out error and the
reason of variations which many lead to determine further business policies and useful in take
effective decisions.
Coefficient regression help in finding out correct value and define positive as well as
negative relationship between variables. Relationship between these variables of Car F and Car
L is positive which means that when the length of travelling distance has been increases then the
cost of travelling or running cost increases automatically. On the basis of that individual able to
take their business decision which will be beneficial for formulation of further investment or
business policies.

b) Brief explanation regarding decision taken of selection of region.
In order to expending new region for the purpose of travelling individual need to choose
to go with Car DF in order to cover up the distance as in order to expand the limit of travelling
the cost of running is comparatively lower then Car L. Thus they decided to select Car F. Which
will help or beneficial for managing the cost of organization for the purpose of running business
operations (Wang and Sun, 2020).
Due to the increment of cost the distance of travelling also increase which may become the
reason that the expected rate is also increase.
c) Calculation of expected running cost.
The expected cost of Car increase from 10 % thus in order to
X
4 5.3 21.2
4.6 6.7 30.82
5.9 7.5 44.25
6.7 8.8 58.96
8 8 64
8.9 9.1 80.99
8.9 10.5 93.45
10.1 10 101
10.8 11.7 126.36
12.1 12.4 133.92
Sum = 80 90 755
Distance Travelled
3.5 6.9 24.15
4.6 7.6 34.96

Distance Travelled
5.3 7.9 49.8
6 8.3 63.36
7.2 8.8 59.04
8.4 9.2 77.28
10.1 9.6 96.96
11.1 10.3 114.33
11.5 10.1 116.15
12.3 11.3 139
80 90 773
If the cost of these miles is more then of 10 % then the value of these car will be increase
for 755 to 830.5 which means that they need to spend more money in order to cover up cost.
However due to increment in cost facilities of these cars and distance of travelling also includes.
QUESTION 3
a) Computation of probability
The term probability defines as tool of measurement of expected future outcomes in
quantitative terms. With the calculation of probability individual able to find result
regarding success or failure of particular business outcomes. On the basis of finding
outcomes of probability personal able to formulate their policies and take decision
regarding control the risk of failure. On the basis of calculating probability success rate of
particular project has been evaluating (Liu, Liu and Zhu, 2020).
Probability useful in determine the rate of success as well as find out the
relevance of these area through which individual able to find to the rate of variations. On
the basis of finding out result of probability personal able to determine the accurate rate
and value of their success of probability rate. Probability is useful in define the accurate
result of future outcomes. On the basis of finding those result, manager able to recognize
the value of their project as well as probability of calculating event. On the basis of that

they formulate their future business policies through which they can able to attain their
goals. As well as the rate of success of project is also increase and they take decision for
control risk of failure of business project.
The result of probability comes between 0 to 1. This tool helps in evaluating frequency of
arrival of particular event or activities. Researchers take decision on the basis of find out the rate
of success. Higher rate of probability defines or represent more chance of completion of project
without any error or risk of failure. Following are the formula which useful in determine
probability of particular event:
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
Probability of Charis to solve problem is calculated = 1/6 =
Probability of solving issue by Albert = 1/8
John’s probability to solve issue = 1/3
P(Cc)
⋅P(Ac)
⋅P(Jc)
Charlie able to solve this issue = 1440/6 = 240
Thus the rate of not solving this issue by Charlie = 1440-240 = 1200
From the remaining 1200 times of solving problem, Albert will able to solve the issue,
1200/8 = 150 times, thus the probability of not solving problem by Albert = 1050 times.
From remaining 1050 times to success of solving of issue of probability john solve the issue
= 1050 /3 = 350 times and their probability of not solving this issue = 700 times, 1050/350.
Thus probability of not solving problem by 3 of them = 700/ 1440 = 0.486 (Zhao Ding, Gao,
Zhao Tang, Han, Yao. and Huang,2018).
b) Probability of solving problem by at least one of them
In case of solving problem of probability by at least one of them need calculate
permutation and combination. Chances of solving issue by John will be determined is
350/1440 it is the rate at which only John is able to solve the problem not remaining the
other one.
Charlie is not able to solve the solution of problem but Albert able to solve issue 150
times and those 150 times John have the chance to solve the issue 150/3 = 50 times. The

probability of at least one solve the issue where Albert able to solve problem is 100/1440
times.
Charlie has the ability to solve issue 240 times. From those 240 times the rate or chances
of solving issue of Albert was calculating at 240/8 = 30 times. And their chance of not
finding solution was calculating or measured at 210 times. Which means that probability
of solving issue of Charlie was calculated at 140/1440 times as John able to solve this
issue from 210/3 = 70 times and on the other side the rate of not solving the case was
determine at 140 times (Wang and Li, 2017).
Thus the rate of solving there issue of at least one of them was valued at 590 times/ 1440
which means the probability was measured0.41 %.
c) Probability of solving problem by only one of them
From the above calculation the rate of probability of solving issue of one of them was
determined. Which is 0.59 %.
B)
1) Probability of one green and other white ball
4C2 + 3C2 = (4 * 3)/2 + 3 * 2 = 6 + 6 = 12
Total Probability of two balls = 14C2 = (14 * 13) /2 = 91
Probability of One is green and the other is white: 12 / 91
2) Probability of picked up same colour ball
They are of same colour: 4C1 + 3C1 = 4 + 3 = 7
Total Probability of two balls = 14C2 = (14 * 13) /2 = 91
Probability of same colour: 7 / 91
QUESTION 5
Standard deviation and mean both are the part of tools of central tendency. Mean is use to
represent the overall value of specific data. On the other side standard deviation is used to
calculate dispersion of mean of variable data series. With the use of calculation of relationship
between mean and standard deviation individual able to determine or measure value of variations
of specific data series. Lower value of standard deviation showcase that the value of nearby to
the mean. Standard deviation is square root of variance. With the valuation of both values
industrialist able to take decision regarding possibility of return and future aspect of their

business. Researchers use standard deviation for evaluate the positive as well as negative
relationship of outcomes. Through which they can able to take decision on the basis of finding
out result. Which will be beneficial for organization (Mekonnen Mazurek. and Putz, 2016).
a) Probability of workers take less than of average time.
X is considering time in order to choose clerical worker for official work. He sends letter
of recommendation to other people
X is considering as distribution,
Value of mean of random sample = 10.5 minute
Value of standard deviation = 3 minute
Number of workers = 50
With the calculation of value of Z the probability of workers to spend less time and done
their work within less than of average time period can be calculated.
Z is use for determine the value of distance of mean of particular area. It is also defining as
standard score. Value or score of Z consider or show positive relation if the value is above
the value of mean and its showcase negative relation if the value of standard deviation is
below then mean.
With the use of calculation of it personal able to calculate the probability of measuring
different score of normal distribution.
Z = Data point – mean /Standard deviation /
9.5 – 10.5 / 3/ 50 = -2.35
p value=0.0094
So, P(X<9.5)=P(Z<−2.35)=0.0094
Thus the probability of taken average time by workers is 0.094 %.
With the use of theses information, it is considering that theses calculation useful for
finding out result as well as formulate and evaluate relationship between different variables. On
the basis of that errors can be found out and theses are useful and measure the correct and
relevant information (Miao, Xie, Yang, Karki, Tai and Chen, 2016).

b) Evaluate whatever income of self-employment in clothing industry is different
Mean and standard deviation use in define the relationship as well as variations between
two variables. These tools useful in determine the variation and significant differences
between various outcomes.
In this case value of mean is calculated was 15000 and the value of standard deviation was
determined at 975, on the other side value of mean in clothing industry was calculated at
14500 and its requirement was determining at 169, the value of standard deviation in this
case= 9.82. On the basis of that it concluded that income of workers work as self-
employment in clothing industry is different as compare to clothing industry as the rate of
variation is comparatively high, which showcase that value of different (Zha. Liu and
Liang, 2019).
c)Decision taken regarding manufacturing process.
In order to determine the probability of 1 % of significance of new procedure is better than
their old one, distribution of sampling mean has been calculated. With their use of
distribution theorem, individual able to find out their result and probability of data series.
For this purpose, mean and standard deviation is use for calculation purpose.
Value of new process of calculating standard deviation is much higher as compare with old
one. Thus the level and rate of significance is much higher then the old procedure, which
showcase that new procedure is more beneficial for manufacturing organization as compare
to the other one. This decision is based on the basis of measure the relationship value of
events and by calculating formulate of finding sampling errors (Blanch Walter and Enge
2018).
CONCLUSION
From the above analysis it has been identified that with the use of different tools of
statistics individual able to determine the relationship between two or more then of two variables
as well as the use these tools of central tendency in order to take future business decision on the
basis of calculate probability of success or failure of occurrence of events. With the use of

calculation of values of standard deviation and regression individual able to formulate future
polices and take decision for run their industries, organization or any sector of business.

REFERENCES
Books and journals
Hazen, B. T., Skipper, J. B., Boone, C. A. and Hill, R. R., 2018. Back in business: Operations
research in support of big data analytics for operations and supply chain
management. Annals of Operations Research. 270(1). pp.201-211.
Wang, K. and Sun, X., 2020. Efficient parameter estimation and variable selection in partial
linear varying coefficient quantile regression model with longitudinal data. Statistical
Papers. 61(3). pp.967-995.
Liu, Y., Liu, J. and Zhu, C., 2020. Low-rank tensor train coefficient array estimation for tensor-
on-tensor regression. IEEE transactions on neural networks and learning
systems. 31(12).pp.5402-5411.
Zhao, S., Ding, G., Gao, Y., Zhao, X., Tang, Y., Han, J., Yao, H. and Huang, Q., 2018. Discrete
probability distribution prediction of image emotions with shared sparse learning. IEEE
Transactions on Affective Computing. 11(4). pp.574-587.
Wang, F. and Li, H., 2017. Towards reliability evaluation involving correlated multivariates
under incomplete probability information: A reconstructed joint probability distribution
for isoprobabilistic transformation. Structural Safety. 69. pp.1-10.
Mekonnen, B.A., Mazurek, K .A. and Putz, G., 2016. Incorporating landscape depression
heterogeneity into the Soil and Water Assessment Tool (SWAT) using a probability
distribution. Hydrological Processes. 30(13). pp.2373-2389.
Miao, S., Xie, K., Yang, H., Karki, R., Tai, H. M. and Chen, T., 2016. A mixture kernel density
model for wind speed probability distribution estimation. Energy Conversion and
Management. 126. pp.1066-1083.
Zhao, Z., Liu, H. and Liang, B., 2019. Probability distribution of the compression capacity of
welded hollow spherical joints with randomly located corrosion. Thin-Walled
Structures.137. pp.167-176.
Blanch, J., Walter, T. and Enge, P., 2018. Gaussian bounds of sample distributions for integrity
analysis. IEEE Transactions on Aerospace and Electronic Systems, 55(4), pp.1806-
1815.

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