Statistics for Management: Evaluating Business Data and Planning

This report, titled "Statistics for Management," presents a detailed analysis of business and economic data using various statistical methods. The report begins with an introduction that highlights the importance of statistics in modern business decision-making. Task 1 evaluates business and economic data from diverse published sources, employing t-distribution to compare mean earnings between men and women in both public and private sectors, and calculating annual growth rates. Task 2 focuses on analyzing and evaluating qualitative and quantitative raw business data, including the use of scatter plots to determine the association between hot drink sales and average temperature, calculating correlation coefficients and coefficients of determination, and determining the line of best fit for sales predictions. The report concludes with an evaluation of the reliability of these predictions and factors that may impact the sales values. The report provides comprehensive insights into data analysis and its applications in business planning for quality, inventory, and capacity management.

STATISTICS FOR
MANAGEMENT

Table of Contents
INTRODUCTION...........................................................................................................................1
TASK 1............................................................................................................................................1
P1. Evaluating the nature and process of business and economic data/ information from a
range of different published sources............................................................................................1
P2. Business Data from variety of sources using different methods of analysis.........................3
TASK 2............................................................................................................................................4
P3. Analysing and evaluating qualitative and quantitative raw business data using appropriate
statistical methods........................................................................................................................4
TASK 3............................................................................................................................................8
P4. Application of a range of statistical methods used in business planning for quality,
inventory and capacity management............................................................................................8
TASK 4..........................................................................................................................................11
P5. Utilisation of appropriate charts/ tables to communicate findings for a number of given
variables.....................................................................................................................................11
CONCLUSION..............................................................................................................................13
REFERENCES..............................................................................................................................14
APPENDICES...............................................................................................................................15

INTRODUCTION
The present business environment demands agility and innovative advents on a rapid
scale. This is only possible when the business managers exploit the advantages of statistics and
employ it towards gaining valuable insights in regards to different areas of various managerial
functions that are pursued by a given business entity. Statistics can be defined as those scientific
tools and techniques which enable the management to explore ideas through summarisation of
large data sets so as to give them a meaningful context (Babu, 2012). This facilitates the practice
of informed decision-making within the organisation. The given report aims to provide a
comprehensive account on evaluation of business and economic data which is secured from
different published sources. Apart from this, appropriate statistical methods have been utilised to
seek enhancement of business planning procedures in regards to quality, inventory and capacity
management along with their communication through suitable charts and tables.
TASK 1
P1. Evaluating the nature and process of business and economic data/ information from a range
of different published sources
In order to determine any sort of conclusion or postulate a business strategy regarding a
particular area of managerial function, an enterprise may collect economic data/ information
from a range of published sources. Usually such a data is of qualitative or quantitative nature
depending upon the requirements that a manager feels, are necessary, for their inclusion for
conducting any sort of analytical procedures on them (Berenson and et.al., 2012). In the context
of given scenario, a study has been taken into consideration which undertakes a random
sampling technique to collect data on men and women who are working full-time in Public as
well as Private Sectors. Here, the sample size consists of 1000 participants each, but data is taken
of eight years only, therefore, to test the hypothesis with (8-1)+(8-1) = 14 degress of freedom,
instead of Normal Disrtibution, it will be better to use t-distribution method as shown below -
(a) Mean Earnings of Men and Women in Public Sector:
Testing Hypothesis:
H1: Earnings of men in the public sector is significantly different to the earnings of
women in the public sector
1

H0: Earnings of men in the public sector is not significantly different to the earnings of
women in the public sector
Mean Earnings within Public Sector(in £s)
Year (A) Men (B) Women (C)
Difference in Income
Earned (B-C)
2009 30638 25224 5414
2010 31264 26113 5151
2011 31380 26470 4910
2012 31816 26663 5153
2013 32541 27338 5203
2014 32878 27705 5173
2015 33685 27900 5785
2016 34011 28053 5958
Mean 32276.63 26933.25
Standard Deviation 1204.144 987.7715
S*S 1449962 975692.5
S*S/n-1 207137.5 139384.6
Average Difference 5343.38
Calculation:
Mean = Sum of observation/No. Of observation
for men, Mean = 258213/8
=32276.625
for women, Mean = 215466/8
= 26933.25
T-distribution,
t = (x1 – x2)/ √[(S1)2/n-1 + (S2)2 /n-1}
2

here, (S1*S1/n-1) + (S2*S2/n-1)
= 207137.5 + 139384.6
= 346522.1
and, x1 – x2 = 5343.375
therefore, value of t = 5343.375 / √346522.2
= 5343.375 / 588.6613
= 9.07, for public sector
From the above table it can be seen that both men and women working in the public sector have
seen substantial rise in their mean earnings between 2009 and 2016. While average income
earned by Men between this stipulated period has rose by 11% (=(£34,011-£30,638)/£30,638),
their female counterparts have experienced an improvement of 11.22%
(=(£28,053-£25,224)/£25,224) within the same time-frame. This indicates that while there has
been a difference of an average of £5,343.38 between the two, their rate of change over the years
has been almost equal. Based on this evaluation, it can be said that their exists a significant
difference between the earnings of men and women operational in the public sector. As a result,
Null Hypothesis (H0) is rejected while Alternative Hypothesis (H1) is accepted.
(b) Mean Earnings of Men and Women in Private Sector:
Testing Hypothesis:
H1: Earnings of men in the private sector is significantly different to the earnings of
women in the private sector
H0: Earnings of men in the private sector is not significantly different to the earnings of
women in the private sector
Mean Earnings within Private Sector(in £s)
Year (A) Men (B) Women (C) Difference in Income Earned (B-C)
2009 27632 19551 8081
2010 27000 19532 7468
2011 27233 19565 7668
3

2012 27705 20313 7392
2013 28201 20698 7503
2014 28442 21017 7425
2015 28881 21403 7478
2016 29679 22251 7428
Mean 28096.53 20541.25
Standard Deviation 834.1923 994.349
S*S 695876.7 988729.9
S*S/n-1 99410.96 141247.1
Average Difference 7555.38
Calculation:
Mean = Sum of observation/No. Of observation
for men, Mean = 224773/8
=28096.53
for women, Mean = 164330/8
= 20541.25
T-distribution,
t = (x1 – x2)/ √[(S1)2/n-1 + (S2)2 /n-1}
here, (S1*S1/n-1) + (S2*S2/n-1)
= 99410.96 + 141247.1
= 240658.1
and, x1 – x2 = 7555.375
therefore, value of t = 7555.375 / √240658.1
= 7555.375 / 490.5692
= 15.40 for private sector
4

From the above table it is clearly evident that men and women working full time in the Private
Sector have seen a considerable rise over the years. Between 2009 and 2016, mean earnings for
men have increased by 7.41% (=(£29,679-£27,632)/£27,632) whereas for women it is attributed
to be 13.81% (=(£22,251-£19,551)/£19,551). Based on these figures it can be said that the
women working in the private sector have been thriving even more than their male counterparts.
Therefore, based on this evaluation, it can be said that their exists a significant difference
between the earnings of men and women operational in the private sector. As a result, Null
Hypothesis (H0) is rejected while Alternative Hypothesis (H1) is accepted.
therefore, t-Distribution curve, with degress of freedom 14 –
a) Since t-distribution critical value is 2.145 and test statistic in public sector is obtained as 9.07,
which is higher than critical value, therefore, null hypothesis is rejected and alterntative
hypothesis will be accepted under this case, so there is asignificant difference between earnings
of both men and women.
b) Test statistics in private sector also obtained as 15.4 which is much higher than critical value
therefore, alternative hypothesis is accepted with rejected the null hypthoesis.
5

P2. Business Data from variety of sources using different methods of analysis
(c) Presenting an Earnings-Time Chart for each group in Table A for the period 2009-2016:
2009 2010 2011 2012 2013 2014 2015 2016
0
5000
10000
15000
20000
25000
30000
35000
40000
30638 31264 31380 31816 32541 32878 33685 34011
25224 26113 26470 26663 27338 27705 27900 28053
27632 27000 27233 27705 28201 28442 28881 29679
19551 19532 19565 20313 20698 21017 21403 22251
Time-Earnings Chart for Public & Private Sector
Men
Public
Sector
Women
Public
Sector
Men
Private
Sector
Women
Private
Sector
Years
Mean Earnings (in £s)
(d) Determination of Annual Growth rate in earnings:
Annual Growth rate can be defined as that increase in value for a particular investment,
portfolio or earnings which is recorded over a period of year (Evans and Lindner, 2012). It is
calculated by using the following formula:
[(Ending Balance-Initial Balance)/(Initial Balance)]*100
This has been calculated and presented for both men and women working in Public as
well as Private Sector in the following table:
Annual Growth Rate
6

Public Sector Private Sector
Year Men Women Men Women
2009 0.00% 0.00% 0.00% 0.00%
2010 2.04% 3.52% -2.29% -0.10%
2011 0.37% 1.37% 0.86% 0.17%
2012 1.39% 0.73% 1.73% 3.82%
2013 2.28% 2.53% 1.79% 1.90%
2014 1.04% 1.34% 0.85% 1.54%
2015 2.45% 0.70% 1.54% 1.84%
2016 0.97% 0.55% 2.76% 3.96%
Based on the above figures, it can be said that public as well private sector's annual
growth for men and women has been highly irregular. Also, it is interesting to that in 2010
Public Sector had a positive and high annual growth rate in comparison to Private Sector which
experienced a downturn in its annual growth rate. Currently, the annual growth rate is highest for
women working in private sector among all the four groups while the least is being experienced
by women in Public Sector.
TASK 2
P3. Analysing and evaluating qualitative and quantitative raw business data using appropriate
statistical methods
(a) Drawing a Scatter Plot to determine association between hot drink sales and average
temperature:
7

12 13 14 15 16 17 18 19 20 21
0
2
4
6
8
10
12
14
16
18
20
15
10
13.5
15
18
14
13
8.5
6
9
Scatter Plot
Hot Drink Sales
(000s)
Average Temperature (in Celsius)
Hot Drink Sales (in 000s)
The above Scatter Plot provides a graphical representation of data attached in the
Appendices Section of this report. X-axis plots data relating to Average Temperature measured
in Celsius degrees whereas the Y-axis plots data relating to Hot Drink Sales measured in
thousands. On the basis of this diagram, it can be ascertained that there is a wide dispersion of
the variables throughout the scatter plot. However, it is also clearly visible that the variables are
moving in an upward direction as the average temperature increases in subsequent weeks,
specifically from week 1 to 10. Thus, a positive association can be determined between the two
factors.
(b) Ascertaining Correlation Coefficient and Coefficient of Determination:
8

12 13 14 15 16 17 18 19 20 21
0
2
4
6
8
10
12
14
16
18
20
15
10
13.5
15
18
14
13
8.5
6
9
f(x) = 1.06222865412446 x − 5.11432706222865
R² = 0.638555145067446
Scatter Plot
Hot Drink
Sales (000s)
Linear (Hot
Drink Sales
(000s))
Average Temperature (in Celsius)
Hot Drink Sales (in 000s)
Based on the trend-lines depicted in the above scatter plot, it can be inferred that both
average temperature and hot drink sales follow same pattern of movement within the 10 week
period, that is, if one rises other rises too and vice versa. Thus, there is a positive correlation
between two factors. Here, the correlation coefficient (R=√R2) of both variables comes out to
be 0.8 which indicates that there exists a strong relationship between hot drink sales and average
temperature (Grossmann and Rinderle-Ma, 2015). On the other hand, the coefficient of
determination (R2) comes out to be 0.64 which indicates that the two variables share a moderate
positive linear relationship.
(c) Determining the line of best fit in order to predict sales from average weekly temperature:
Line of Best fit can be defined as that line which represents the data on a scatter plot in
the most effective manner. In the context of Hero Coffee Shop, the line of best fit is depicted by
a linear trend-line which has been included in the Scatter Diagram illustrated above. The
predicted number of sales, here, is denoted by f(x) with an slope of m=1.06. This means that the
trend line would predict that when the average temperature (x) increases by 1 degree Celsius, the
hot drink sales would be 1.06 higher. Also, the line would cross the y-axis at the point where
average weekly temperature is -5.11.
(d)Prediction of expected sales for weekly temperature when it is:
y= mx+c; where
9

y= function of x
m= slope of the equation
c= intercept
(i) 17.5 degree Celsius:
In this case, the predicted expected sales (in 000s) of Hero Coffee Shop are calculated as under:
y = mx+c
y=1.06x-5.11
y=[(1.06*17.5)-5.11]
y=[(18.55)-(5.11)]
y=13.44 or 13,440 units of hot drinks
(ii)25 degree Celsius:
In this case, the predicted expected sales (in 000s) of Hero Coffee Shop are calculated as under:
y = mx+c
y=1.06x-5.11
y=[(1.06*25)-5.11]
y=[(26.50)-(5.11)]
y=21.39 or 21,390 units of hot drinks
(e) Evaluating the reliability of predictions made in regards to additional factors which may
impact the sales values achieved:
The reliability of predictions made in regards to the expected sales of Hero Coffee Shop's
hot drinks in association with the average weekly temperature is not high. This is due to the fact
that there are other additional factors which may impact the sales values achieved in the Task 2.
P3. Part (d)(i) and (ii) sections of this report. Some of them include the shop's budget, its
efficiency in catering to the customer demand as well as ensuing competition in the external
environment among others (Groebner and et.al., 2013). Thus, it can be concluded that although
there is a considerable amount of impact on hot drink sales due to temperature, accounting it as
the sole reason for making predictions on the sale of such products is not highly reliable.
10

TASK 3
P4. Application of a range of statistical methods used in business planning for quality, inventory
and capacity management
Section A:
Normal Distribution or Bell curves are a type of symmetrical continuous probability
distribution which provides valuable insights regarding the real-valued random variables whose
distributions are unknown (Keller, 2015). As per the given case scenario, the EU regulations
undertake three regulations into account which state the limits regarding the percentage of
content which must be declared on the Olive Oil bottles by the supplier. The z-score for the
company comes out to be:
z= (Variable (X) – Mean (μ))/ Standard Deviation (σ)
As per the given EU regulations:
 Average Content must be at least 200 ml- This regulation has not been violated as the
firm declared content on its olive oil bottle with mean content of 202 ml.
z = (200 ml – 202 ml)/ 2.4
z= -2/2.4 = -0.8.3333
Therefore, the P(x>200) = 1- P(z<0.8333) = 1-0.79673 = 0.20327
 Up to 2.5% of bottles may contain less than 198 ml- If 1000 bottles are to be assumed, 25
bottles out of them may contain 198 ml instead of 200 ml. Thus, the standard deviation,
here, is 2 ml (200-198). The company's z-score will become:
z= (198-202)/2.4 = -4/2.4 = -1.67 = 1- P(z<1.67) = 1- 1.0475 = 0.0475
Probability 0.0475 = 4.75%
therefore, 4.75% of the bottles have less than 198ml. So, EU always accept only up to 2.5%. and,
EU permits 2.5% or less than 198ml but since 4.75% has less than 198ml. Thus, it reflects that
mean is failed.
Normal Distribution curve
11

Up to 0.01% of bottles may contain less than 196 ml- If 1000 bottles are to be assumed, 10
bottles out of them may contain 196 ml instead of 200 ml. Thus, the standard deviation, here, is 4
ml (200-196). The company's z-score will become:
z= (196-202)/2.4 = -6/2.4 = -2.5= 1- P(z<2.5) = 1- 1.0062= 0.0062
Probability 0.0062 = 0.62%
therefore, 0.62% of the bottles have less than 196ml. So, EU always accept only up to 0.01%.
Along with this, EU permits only 0.01% which is to be less than 196ml. That means mean has
failed in this situation also.
Normal Distribution curve
12

Section B:
a) Deliveries currently made each year:
For the purpose of finding number of deliveries made each year, it is ascertained that the
supermarket is open only 360 days (=365-5) each year. It is also important to note that the
delivery of olive oil is made every 12 days (Lee and Peters, 2015). Based on such information,
the relevant calculations have been presented as under:
Particulars £
Number of days in a year (given) 360
Number of deliveries made each year (=360/12) 30
b) Number of bottles of olive oil currently delivered with each delivery:
Particulars £
Annual Demand for Consumption (given) 450000
Number of deliveries made each year (given) 30
Number of bottles currently delivered with each delivery 15000
c) Determination of Economic Order Quantity (EOQ) using appropriate statistical formula:
Economic Order Quantity can be defined as that level of output where the total cost of
inventory is minimal (Lind, Marchal and Wathen, 2012). It is calculated using following
formula:
EOQ = √((2*A*D)/(S*P)); where
A= Annual Demand (in units)
D= Acquisition Cost
S= Storage Cost (% of the cost price)
P= Cost Price
Particulars £
Annual Demand for Consumption (A) 450000 (in units)
Storage Cost (S) 0.25%
13

Delivery Cost (D) 20
Cost Price (P) 2
Economic Order Quantity 60000
d) Application of Total Variable Cost model to determine the current ordering policy:
Total Variable Cost = Purchase Cost + Order Cost + Holding Cost
TVC = £2+ £20 + £0.50
TVC = £22.50 per unit
TVC for meeting annual demand under current ordering policy = £22.50*450000 = £10,125,000
e) Comparing the Total Variable Cost with Cost of changing the amount to EOQ and making
relevant Recommendations on findings:
Total Variable Cost = Purchase Cost + Order Cost + Holding Cost
TVC = [(P*A) + ((A/EOQ)*D) + ((EOQ/2)*S)]
TVC = [(£2*450000)+((450000/6000)*£20)+ ((6000/2)*(0.25*£2))]
TVC = [£9000000+(75000*£20)+(3000*£0.5)]
TVC = [£9000000+£1500000+£1500)]
TVC = £10,501,500
Based on the two findings, it has been analysed that using EOQ, total inventory cost has
been reduced. So, it is recommended that the business needs to change its current policy to EOQ
policy. (Oh, 2014).
TASK 4
P5. Utilisation of appropriate charts/ tables to communicate findings for a number of given
variables
(a) Representation of above data as:(i) Bar Chart:
14

1
2
3
4
5
0 5 10 15 20 25 30 35 40
8
28
37
17
10
6
18
24
9
3
4
20
32
12
12
Number of Bedrooms in houses located in Wimbeldon
Eton Avenue
Church Lane
Green Street
Number of houses
Number of Bedrooms
(ii)Pie Chart:
1
2
3
4
5
Proportion of Houses for houses located in Wimbeldon
Based on number of bedrooms
One bedroom house
Two bedroom house
Three bedroom house
Four bedroom house
Five bedroom house
(b) Discussing the ways to effectively communicate the presentation of relationship between
number of bedrooms and the house price:
It is important to communicate the data results derived through the collected raw
information so as to facilitate an informed decision-making on the part of users of such given
data. Thus, it becomes crucial to understand and implement the correct methodology while
15

communicating information regarding the depiction of relationship, composition, comparison or
distribution in an effective manner (Data Visualisation, 2019). In the given case scenario, the
relationship between number of bedrooms and average price of the house has been determined.
In order to communicate such results, Rosaline is advised to undertake the following steps:
(i) A well-written report providing insights regarding the house-type and related prices; and
(ii) Utilisation of graphical tools such as charts to depict the relationship in an effective
manner.
Based on this, the following information has been depicted in a graphical manner by
using a Line Chart:
Green Street Church Lane Eton Avenue
0
200000
400000
600000
800000
1000000
1200000
600000
700000 750000
700000
850000
1000000
Relationship between House Prices and Number of Bedrooms
Two bedroom
house
Three Bedroom
house
Popular Streets in Wimbeldon
Average Price of Houses (in £)
The above Line Diagram provides a comprehensive insight on the relationship shared
between the Price of the houses and their design, specifically in terms of number of bedrooms.
For instance, it is clearly evident that the Three bedroom houses are much more expensive in
comparison to Two-bedroom homes. Apart from this, based on the price rates, it is clearly
observed that Eton Avenue seems to be the most expensive street in Wimbledon while Green
Street seems to be the cheapest for both Two and Three Bedroom House price rates respectively
(Siegel, 2016).
16

CONCLUSION
From the above report it can be concluded that Statistics from a management perspective
play a crucial role, specifically in terms of the decision-making function. Different statistical
tools and techniques enable the business manager to analyse, interpret and present the data in an
effective manner. This enables the communication of important information derived from
collected raw data sets to various stakeholders across all organisational levels. Thus, helping the
business management to predict profits based on forecasted value of expected sales in an
effective manner.
17

REFERENCES
Books and Journal
Babu, K. V. S. N., 2012. Business intelligence: Concepts, components, techniques and
benefits. Components, Techniques and Benefits (September 22, 2012).
Berenson, M. and et.al., 2012. Basic business statistics: Concepts and applications. Pearson
higher education AU.
Evans, J. R. and Lindner, C. H., 2012. Business analytics: the next frontier for decision
sciences. Decision Line. 43(2). pp.4-6.
Groebner, D. F. and et.al., 2013. Business statistics. Pearson Education UK.
Grossmann, W. and Rinderle-Ma, S., 2015. Fundamentals of Business intelligence. Springer.
Keller, G., 2015. Statistics for Management and Economics, Abbreviated. Cengage Learning.
Lee, N. and Peters, M., 2015. Business statistics using EXCEL and SPSS. Sage.
Lind, D. A., Marchal, W. G. and Wathen, S. A., 2012. Statistical techniques in business &
economics. New York, NY: McGraw-Hill/Irwin,.
Oh, J. H., 2014. Research methods.
Siegel, A., 2016. Practical business statistics. Academic Press.
Online
Data Visualisation. 2019. [Online]. Available Through:
<https://eazybi.com/blog/data_visualization_and_chart_types/>
18

APPENDICES
1. Data provided on Hero Coffee Shop for 10 consecutive weeks:
Hero Coffee Shop
Week Average Temperature (0C) Hot Drink Sales (000s)
1 18.5 15
2 16 10
3 13 13.5
4 19.5 15
5 20 18
6 19 14
7 15.5 13
8 14 8.5
9 12.5 6
10 15 9
Correlation Coefficient 0.80
2. Data relating to the plot of Normal Distribution Curve:
Standard Deviation Z Score
2.4 0.20327
4 0.9332
2 0.02275
3. Data given for determining number of houses in Wimbledon having various number of
bedrooms
Number of Bedrooms Green Street Church Lane Eton Avenue
19