Business Statistics and Data Analysis

The provided document discusses various business statistics models and methods utilized by companies to inform operational management. The Economic Order Quantity (EOQ) model is used by Jenny Jones to manage her inventory of popular tee-shirts, ensuring 95% customer satisfaction. Additionally, the report showcases how secondary data from published sources, literature, and articles are employed to gather information and draw conclusions. It also highlights changes in indices like CPI and RPI from the Office of National Statistics website, illustrating the importance of data-driven decision-making.

STATISTICS FOR
MANAGEMENT

Table of Contents
INTRODUCTION...........................................................................................................................1
ACTIVITY 1....................................................................................................................................1
(a) Determining whether earnings of men are different from women in public sector...............1
(b) Determining whether earnings of men are different from women in private sector.............2
(c) Earnings-Time Chart Plot for each Sector:............................................................................3
(d) Annual Growth Rate and its computation:............................................................................5
ACTIVITY 2 ...................................................................................................................................8
(i) Calculating Median and Quartiles through Ogive..................................................................9
(ii) Ascertaining the measures of Central Tendency and Dispersion........................................11
(c) Comparing the statistical measures for two branches of Leisure Centre.............................12
ACTIVITY 3 .................................................................................................................................13
(a) Economic order Quantity ....................................................................................................13
(b) Number of Orders to be placed...........................................................................................14
(d) Current Service Level to Customers....................................................................................14
(e) Re-order levels that fulfil desired service levels..................................................................14
ACTIVITY 4 .................................................................................................................................15
(a) Line and/or Bar Charts for data indicating changes in CPI, CPIH and RPI from 2007 to
2017...........................................................................................................................................15
(b)Producing Ogive for Cumulative Percentage of Staff versus Hourly Earnings ..................17
CONCLUSION..............................................................................................................................17
REFERENCES..............................................................................................................................19

INTRODUCTION
Statistics help management in undertaking projects by making accurate decisions in terms
of production and quality based on the acquired knowledge about customer tastes and
preferences. This theoretical framework includes investigation, interpretation, protection and
demonstration of collected data (Cawthorn and Mariani, 2017). It helps in measuring the
performance of management as well as stimulate innovation by providing a foundation for
research and development activities in the organisation. This report entails a detailed evaluation
of statistical tools and techniques in relation to Hypothesis testing, central measures of tendency,
dispersion and variability. Furthermore, the report includes interpretation of data collected,
analysed and presented under each task.
ACTIVITY 1
The concept of hypothesis testing relates to the affirmation of assumptions in regards to a
certain set of data set derived from a population indicating whether such data hold true or not.
For this purpose, two opposing hypotheses are made viz. Null hypothesis (H0) and Alternative
Hypothesis (H1). The Null Hypothesis can be defined as an asserting statement which says that
there is no difference between sample statistic and population parameters. On the other hand,
Alternative Hypothesis one which opposes this assertion (General and Welfare, 2013). While
conducting a statistical test, null hypothesis is taken into account or is tested. If this hypothesis
does not hold true, it is rejected whereas alternative hypothesis is accepted and vice versa.
Hypothesis testing helps in deriving important conclusions or inferences through the
measurement of deviations in sample data from population parameters. Thus, it is one of the
most widely accepted forms of statistical methods undertaken by businesses so as to enable an
informed decision-making on their part.
In the context of scenario mentioned in the case study, following analysis of different
situations have been imparted using hypothesis testing:
Public Sector:
(a) Determining whether earnings of men are different from women in public sector
Under this scenario, the following hypothesis are taken under investigation:
H0: Earnings of men is not significantly different from that of women employed in Public Sector.
H1: Earnings of men is significantly different from that of women employed in Public Sector.
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In order to determine whether the assertions hold true or not, Null Hypotheses (H0) has been
tested and results have been analysed as under:
Total Gap (%) from 2009 to 2016: 10.62% (Adding the figures in fifth column)
Given above is a tabular representation of sample data collected showcasing the mean
earnings in '£' of full time employees' annual pay by sex in United Kingdom for the period 2009
to 2016. This table also indicates the difference between the mean earnings between both men
and women in each year spanning for a period of 8 years (2009 to 2016). In addition to this, there
has been an analysis given regarding the changes in gender pay-gap.
On a closer look, one can ascertain that the lowest difference between male and female
amounts to 4910 in 2011. Also, 2013 is the year when wages between the two genders did not
have a significant change in their difference. This gap further reduced to £5,173 in 2014.
However in 2015, highest gap between the pays of both genders was recorded with more than
11% increase. Also, the total gap from 2009 to 2016 is 10.62% which is quite high, thus,
rejecting the Null Hypotheses (H0) and accepting Alternative Hypotheses (H1) (Groebner and
et.al., 2013). From the above figure, one can say that the earnings of men are significantly
different from that of women.
(b) Determining whether earnings of men are different from women in private sector
Under this scenario, the following hypothesis are taken under investigation:
H0: Earnings of men is not significantly different from that of women employed in Private
Sector.
H1: Earnings of men is significantly different from that of women employed in Private Sector.
In order to determine whether the assertions hold true or not, Null Hypotheses has been tested
and results have been analysed as under:
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Total Gap (%) from 2009 to 2016: -8% (Adding the figures in fifth column)
Given above is a tabular representation of sample data collected showcasing the mean
earnings in '£' of full time employees' annual pay by sex in United Kingdom for the period 2009
to 2016. This table also indicates the difference between the mean earnings between both men
and women in each year spanning for a period of 8 years (2009 to 2016) and employed in Private
Sector. In addition to this, there has been an analysis given regarding the changes in gender pay-
gap.
On a closer look, one can ascertain that the lowest difference between male and female is
recorded in 2014 when the gap was at £7,425. Also, 2015 is the year when wages between the
two genders did not have a significant change in their difference. This gap further reduced to
£7,428 in 2016. However in 2010, highest reduction in gap between the pays of both genders
was recorded with more than 7.5% decrease. Also, the total gap from 2009 to 2016 is an adverse
8% which indicates a positive image as their has been an overall reduction in the pay-gap over
the years. This is also evidenced in the 'Gap' column of the table when, initially, the pay gap
amounted to £8,081 whereas it had decreased to £7,428 in 2016. Thus, rejecting the Alternative
Hypotheses (H1) and accepting Null Hypotheses (H1). From the above figure, one can say that
the earnings of men are not significantly different from that of women.
(c) Earnings-Time Chart Plot for each Sector: Public Sector:
 Annual Mean Earnings for Men from 2009 to 2016:
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 Annual Mean Earnings for Women from 2009 to 2016:
 Private Sector:
 Annual Mean Earnings for Men from 2009 to 2016:
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 Annual Mean Earnings for Women from 2009 to 2016:
(d) Annual Growth Rate and its computation:
The concept of Annual Growth Rate denotes to the percentage change of a particular
variable which is associated to a specific period of time. If the annual growth rate of a company
is increasing continuously than there are more chances that investors will attract and invest in the
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business of organisation. It can be terms of income or earnings and it shows that financial
position of corporation is strong and it is earning good profit.
Annual Growth Rate (%) = [(Value1- Value0)/(Value0)]*100 where,
Value1 = Measurement in Current Year
Value0 = Measurement in Previous Year
Public Sector:
 Annual Mean Earnings for Men:
As per the earnings-time chart, the following changes have been recorded in regards to
the annual growth rate in mean earnings of males employed in the Public Sector. As per this
table, there has been a positive trend recorded, however, the rate at which this trend occurs is
inconsistent. For instance, the growth rate has been fluctuating between 0.37% and 0.25% for the
particular time period. However, there has been almost an alternate increase followed by a
decrease indicating that any change in previous year is nullified with a decrease in growth of pay
in subsequent year.
 Annual Mean Earnings for Women:
For female workforce employed in this sector, there has been a considerable series of
peak and low experienced in terms of wages earned by them. However, this sector also has been
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experiencing a positive trend similar to that of its male counterparts. One can also see that every
third year there has been a growth close to the rate of 0.70%. Also, every second year between
2010 and 2016, the sector experienced a growth close to 1.34%. This indicates that the sector
tends to follow a certain pattern of rise and fall in a given time-period (Jennings, Nagel and
Mansfield, 2016).
Private Sector:
 Annual Mean Earnings for Men:
For male workforce employed in Private sector, there has been a considerable series of
peaks and low experienced in terms of wages earned by them. However, this sector also has been
highly volatile with an inconsistent increase or decrease in the wage growth on an annual basis.
For instance, the sector experienced a 2.29% decline in the year 2010. As pay is a dependent
variable that is prone to be influenced by a number of economic factors. One can also see that
between 2012 and 2013, the sector underwent a stagnancy point with almost no increase in the
mean earnings for both the years closing at the minimum rate of 1.73%. On the other hand, the
highest growth recorded in the mean earnings amounts to 2.76% for the year 2016. This indicates
that the sector may experience a slight decline or not much of a rise in the pay for the year 2017.
 Annual Mean Earnings for Women:
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For female workforce employed in Private sector, this sector also has been highly
volatile with an conflicting display of increase and decrease in the wage growth on an annual
basis. The sector recorded a 3.82% rise in the year 2012 whereas an adverse decline in wages
was observed in 2010 with a rate of 0.10%. One can also see that between 2013 and 2015, the
sector underwent a stagnancy point with almost no increase in the mean earnings for both the
years closing at the minimum rate of 1.54%. The highest growth recorded in the mean earnings
amounts to 2.76% for the year 2016. This indicates that the sector may experience a slight
decline or not much of a rise in the pay for the year 2017.
ACTIVITY 2
Additive Frequency: 'Additive' or 'Cumulative' Frequency refers to the subsequent summation
of frequencies for each class interval given in a sample or data set. These given table indicates
the cumulative frequency that has been ascertained by adding the individual frequency figures
for each class interval, given under 'No. of Leisure Centre Staff', starting from £0 to £10 and
ending on £40 to £50 (Hollnagel, 2018). It is worthy to note that the cumulative frequency figure
for last interval will always be equivalent to the total number of leisure centre staff working in
the London Branch.
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From this table, the cumulative or additive frequencies can be plotted on a graph known
as 'Ogive'. This is shown below:
The above graph indicates a curvilinear relationship between the upper class boundaries
or intervals and the cumulative frequencies (Miller and et.al., 2016). An ogive helps in making
sure that researcher has not left out any relevant data while constructing the sample from
population parameters.
(i) Calculating Median and Quartiles through Ogive
Median is a central tendency measure in statistics which is employed to ascertain the
number of values that fall below or above this central point for a given dataset. On the other hand
Quartile provides the range under which variables fall. This divides the data set into three areas
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viz. 25%, 50% and 75%. These are known as First Quartile, Median and Third Quartile
respectively. The difference between First and Third Quartile is known as Inter-quartile Range.
In order to ascertain these statistical values from Ogive, a “Less than Ogive” and “More
than Ogive” are formulated and plotted on a graph (Salperwyck and Lemaire, 2013). The point
of intersection between the two indicates the central point or Median Value. These have been
presented below:
It can be observed from the above tables that in “More than Ogive”, lower class
boundaries are taken as the starting point and vice versa. By combining the plots of these two
following value of Median can be ascertained:
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The point of intersection for “More than Ogive” and “Less than Ogive”, median value
comes at 25.5 belonging to 20 but under 30 class interval. Whereas Quartiles can be calculated as
follows:
First Quartile = (25% of (n+1)) = (0.25* (£50+1)) = £12.75
Third Quartile = (75% of (n+1)) = (0.75* (£50+1)) = £38.25
Inter-Quartile Range = Q3- Q1 = (£38.25 - £12.75) = £25.5
(ii) Ascertaining the measures of Central Tendency and Dispersion
In the context of given case scenario, the measures of central tendency and dispersion
relate to mean and standard deviation. Mean is the average value returned for a sample data
whereas standard deviation is the amount of deviation present among the variables from the
mean value (Siegel and et.al., 2012).
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Mean has been calculated by using the following formula:
Mean = ∑fx / ∑f where,
∑fx = Summation of (frequency * central point of intervals)
∑f = Summation of frequency
For the current scenario, the calculations for mean ensue as under:
Mean = ∑fx / ∑f = 1070/50 = £21.4
On the other hand, standard deviation is calculated as follows:
Standard deviation = √ (∑fx2 / ∑f) - (∑fx / ∑f)2 where,
∑fx2 = Summation of Squared (frequency * central point of intervals)
∑f = Summation of frequency
(∑fx / ∑f)2 = Squared Mean
Standard deviation = √ (∑Fx2 / ∑F) - (∑Fx / ∑F)2 = √[(28050/50) – (21.4)2 ]= √[561 – 457.96]
= √103.04 = 10.15
(c) Comparing the statistical measures for two branches of Leisure Centre
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Analysing the results for two leisure centres situated in London and Manchester on the
basis of Median, Mean, Standard Deviation and Inter-Quartile Range, following inferences are
drawn:
 The median values at £25.5 and £14 respectively indicate that London staff is paid more
hourly wages as compared to its counterpart. This has resulted in a higher average hourly
income earned by the London staff.
 Manchester has a lower level of dispersion present in comparison to London.
 The inter-quartile range of London is higher showing more accurate and useful data as
compared to its Manchester counterpart.
ACTIVITY 3
(a) Economic order Quantity
It denotes the optimal quantity of stock, an organisation should order each time so that
ordering & holding inventory cost can be reduce. It is helpful for the company to find an
appropriate order size at which ordering and holding cost associated to raw material or stock can
be minimize. It is very important for an organisation to know how much units it should ordered
so that it does not have to bear the cost of excess inventory (Tam and Clarke, 2015). This
concept is beneficial for manufacturing campaniles. With the help of formula it can be
calculated:
EOQ = √2*D*Co/Ch
Jenny Jones' requires implementation of a fresh inventory policy that would enable her to
sell tee-shirts' 95% of the time regarding customer visits. The following basic information can be
narrated in a tabular format:
Economic Order Quantity = √ [(2*Annual Demand* Delivery Cost)/ Holding Cost]
= √ [(2*1500 tee-shirts*£5)/£2]
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= 86.6 or 87 tee-shirts
(b) Number of Orders to be placed
Number of Orders required to be placed = [(Annual Demand / Economic order Quantity)]
= 1500 tee-shirts/ 87 = 17.24 or 17 orders.
(c) Computing Inventory Policy Cost
It is the cost of holding goods in stock and it presents as a percentage of the total value of
stock which involves capital, shrinkage costs, taxation, depreciation, warehousing etc (Willer
and Lernoud, 2017). Inventory policy cost has classified into ordering cost and holding cost.
Hence, Jenny Jones needs to expend £173.21 in order to implement her new policy.
(d) Current Service Level to Customers
Current Level of service = Weekly Demand * Availability of tee-shirt
= 30*95%
= 28.5 units
(e) Re-order levels that fulfil desired service levels
Re-order level (ROQ) = (Lead time*daily average usage)+safety stock
= (28*2)+150
= 206 units
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ACTIVITY 4
(a) Line and/or Bar Charts for data indicating changes in CPI, CPIH and RPI from 2007 to 2017
CPIH: CPIH or Consumer Price Index Housing is a conventional measure that includes implicit
housing costs (World Health Organization, 2013). As they are a type of inflation rate, their effect
has already been captured in the CPI line chart, no separate chart has been produced.
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(b)Producing Ogive for Cumulative Percentage of Staff versus Hourly Earnings
CONCLUSION
From the above report, it can be concluded that in order to make effective as well as
accurate decisions in regards to managing their operations different methodologies are utilized
by business entities of varying size and nature. For instance, Jenny Jones has been able to
employ the model of Economic Order Quantity (EOQ) to develop a inventory policy which helps
in catering to 95% of its customers visiting her shop for purchasing her highly popular line of
tee-shirts. The report also backgrounds the manner in which secondary data such as information
derived from published sources, literary works as well as articles is used to collect data and draw
inferences in order to reach definite conclusions. This included accumulation of data in regards
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to changes in indices such as CPI and RPI from Office of National Statistics Website, from
which charts were drawn for inferring purpose so as to reach a concrete conclusion.
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REFERENCES
Books and Journal
Cawthorn, D. M. and Mariani, S., 2017. Global trade statistics lack granularity to inform
traceability and management of diverse and high-value fishes. Scientific reports. 7(1).
p.12852.
General, S. and Welfare, C. S., 2013. Central statistics office.
Groebner, D.F., and et.al., 2013. Business statistics. Pearson Education UK.
Hollnagel, E., 2018. Safety-I and safety-II: the past and future of safety management. CRC Press.
Jennings, J., Nagel, J. C. and Mansfield, J. W., 2016. Federal workforce statistics sources: OPM
and OMB. Congressional Research Service (published December 7).
Miller, K. D., and et.al., 2016. Cancer treatment and survivorship statistics, 2016. CA: a cancer
journal for clinicians. 66(4). pp.271-289.
Salperwyck, C. and Lemaire, V., 2013. August. Incremental Decision Tree based on order
statistics. In The 2013 International Joint Conference on Neural Networks (IJCNN)(pp.
1-8). IEEE.
Siegel, R., and et.al., 2012. Cancer treatment and survivorship statistics, 2012. CA: a cancer
journal for clinicians. 62(4). pp.220-241.
Tam, S. M. and Clarke, F., 2015. Big data, official statistics and some initiatives by the
Australian Bureau of Statistics. International Statistical Review. 83(3). pp.436-448.
Willer, H. and Lernoud, J., 2017. The world of organic agriculture. Statistics and emerging
trends 2017 (pp. 1-336). Research Institute of Organic Agriculture FiBL and IFOAM-
Organics International.
World Health Organization, 2013. Strengthening civil registration and vital statistics for births,
deaths and causes of death: resource kit.
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