Statistics for Management: Data Analysis and Growth Rate Calculation

This report provides a comprehensive analysis of statistical methods relevant to management, encompassing hypothesis testing, data analysis, and inventory management techniques. The report begins with hypothesis testing on mean earnings in public and private sectors, comparing male and female workforces, and calculating annual growth rates. It then delves into analyzing raw business data using statistical methods such as Ogive, calculating mean and standard deviation, and comparing earnings between regions. Furthermore, the report covers economic order quantity calculations and inventory policy cost determination. Finally, the report includes the creation of line/bar charts showcasing changes in CPI, CPIH, and RPI, along with the creation of Ogive using provided data, offering a complete overview of statistical applications in a business context.

STATISTICS FOR
MANAGEMENT

Table of Contents
INTRODUCTION...........................................................................................................................1
TASK 1............................................................................................................................................1
(a) Testing Hypothesis for mean earnings in public sector.........................................................1
(b) Testing Hypothesis for mean earnings in private sector.......................................................3
(c) Producing Earnings-Time Chart for each group....................................................................4
In case of Male Workforce of Public Sector:..............................................................................4
In case of Female Workforce of Public Sector:..........................................................................4
In case of Male Workforce of Private Sector:.............................................................................5
In case of Female Workforce of Private Sector:.........................................................................5
(d) Determination of Annual Growth Rate for each segment.....................................................6
TASK 2............................................................................................................................................7
(a) Analysing raw business data using a number of statistical methods:....................................7
(i) Using Ogive to estimate Median and Quartiles for Leisure Centre Staff, London ...............8
(ii) Calculation of Mean and Standard Deviation for hourly earnings......................................10
(b) Comparison of earnings between two regions.....................................................................10
TASK 3..........................................................................................................................................11
(a) Calculating Economic Order Quantity................................................................................11
(b) Calculating Frequency of Orders.........................................................................................12
(c) Ascertaining Inventory Policy Cost.....................................................................................13
TASK 4 .........................................................................................................................................14
(a) Producing Line/Bar Charts for showcasing changes in CPI, CPIH and RPI:.....................14
(b) Creating Ogive using table 1...............................................................................................15
REFERENCES..............................................................................................................................17
APPENDICES...............................................................................................................................18

INTRODUCTION
Statistics is an important part of decision-making done by management. It helps in
creation of various policies and plans that are helpful in achieving the goals and objectives of the
business. Various methods of analysis are formulated on the basis of statistical techniques used
to convert raw data into cooked or meaningful information (Al-Omari, 2016). This report aims to
provide an in-depth knowledge in regards to data collection, ogive, central tendency, dispersion
and variability. Also, it shows how graphical representation of the data is helpful in spotting
trends and patterns in regards to different variables. In addition to this, recommendations
regarding findings are also provided along with each section.
TASK 1
A hypothesis is a proposed statement for a particular phenomenon. Generally, this
statement or explanation is created on the basis of data collected previously and conclusions
drawn thereof. In statistics, this type of method is used in order to check or verify the substance
of a proposed statement. This means that using statistical tools and techniques such as measures
of central tendency, variability and dispersion, the researcher is able to justify whether their
proposed statement held true in regards to a phenomenon or not. This process is known as
'Hypothesis Testing'.
Under this scenario, two events are created by the researcher. One that holds true is called
H0 or H 'naught'. On the other hand, the event considered as 'false' is called 'H1'. It is important to
note that the statements proposed by the researcher must be 'testable' acknowledging the current
situation. Also, these must be 'achievable' and 'verifiable' through the employment of statistical
and analytical tools and methods (Anderson and et.al., 2012).
(a) Testing Hypothesis for mean earnings in public sector
In the given case scenario, a study was conducted that included random sampling of 1000
participants for both women and men. The assumptions used to conduct the statistical techniques
over this study included that the mean annual gross earnings followed a normal distribution. The
study aimed to compare the earnings of men and women. From the given case scenario, the
following hypothesis can be derived:
Statement: Earnings of men is not substantially significant to that of women in Public
Sector.
1

H0: Statement is true.
H1: Statement is false.
Year Public Sector
Men (£) Women (£) Gap (in £) Gap (%)
2009 30638 25224 5414
2010 31264 26113 5151 -4.86
2011 31380 26470 4910 -4.68
2012 31816 26663 5153 4.95
2013 32541 27338 5203 0.97
2014 32878 27705 5173 -0.58
2015 33685 27900 5785 11.83
2016 34011 28053 5958 2.99
In order to analyse the significance of aforementioned hypothesis, mean earnings of men
and women paid for the public sector has been extracted from the results of a study. The above
given table shows the annual mean earnings (in £) calculated from samples' data for the period of
2009 to 2016. As can be observed, the earnings for men are not equivalent to that of women. In
order to facilitate simplified understanding of the table, another two columns have been added.
The 'Gap' Column gives the difference between the yearly mean earnings of male and female for
each period spanning between 2009 and 2016. The next column, 'Gap (in percent)', represents the
year-on-year change in the pay gap for both the genders.
As per these calculations, it can be observed that the minimum pay gap between men and
women's earnings is £4,910 recorded for 2011. Furthermore, the maximum pay gap experienced
by Public Sector is recorded in 2016 at £5,958. It is important to note that there has been a
decline in pay gap from 2009 to 2014. In 2009, the gap between the earnings of male and female
was at £5,414 which went down to £5,173 by 2014. Also, the percentage gap decreased between
this period by roughly 4% to 5%.This shows that there have been improvements in the payment
patterns of Public Sector towards women demographic as the rise in their earnings has been
much more monumental than that of their male counterparts. If one looks at 2014 to 2013
earnings for women, they received an increment of almost £1,000 each year. Whereas the male
workforce for the same time-period had a total growth of £1,000. Hence, one can say that the rise
2

in income of women has been the sole or direct factor driving the gender pay gap on the
downside.
From above observations and calculations, it can inferred that the overall gender pay gap
in the Public Sector has been on the rising side in the recent years. Therefore, our hypothesis
does not hold true. It can be observed from the most recent pay made to men is almost £6,000 or
21.23% higher than that paid to women resulting in acceptance of H1 and rejection of H0.
(b) Testing Hypothesis for mean earnings in private sector
In the given case scenario, a study was conducted that included random sampling of 1000
participants for both women and men. The assumptions used to conduct the statistical techniques
over this study included that the mean annual gross earnings followed a normal distribution. The
study aimed to compare the earnings of men and women of Private Sector. Following this
scenario from above, the hypothesis derived is given as under:
Statement: Earnings of men is not substantially significant to that of women in Private
Sector.
H0: Statement is true.
H1: Statement is false.
Year Private Sector
Men (£) Women (£) Gap (£) Gap (%)
2009 27632 19551 8081
2010 27000 19532 7468 -7.59
2011 27233 19565 7668 2.68
2012 27705 20313 7392 -3.6
2013 28201 20698 7503 1.5
2014 28442 21017 7425 -1.03
2015 28881 21403 7478 0.71
2016 29679 22251 7428 -0.67
Total 224773 164330
In the above table, the annual gap between male and female workforce has been
calculated by subtracting the wages paid to women from that of men. Similarly, the year-on-year
gap percentage has been calculated to account the changes in pay gap from 2010 to 2016. There
has been a considerable decrease in the gap from 2009 to 2016. This sector experienced the
3

lowest pay gap in 2012 recorded at £7,392. It is noteworthy that both Men and Women have
experienced an almost same increase in their annual gross earnings from one year to another. The
highest change in pay-gap occurred between 2010 and 2011 where the gap reduced by 7.59%. In
addition to this, the sector also experienced a recent decline of mere 0.67%. However, there has
been an increase in the gap of 2016 earnings of men and women. Taking this into account, it can
be inferred that hypothesis ( H1) holds true, that is, there is a significant earning gap (£7428 or
33.38%) between male and female workforce employed in the private sector.
(c) Producing Earnings-Time Chart for each group
 In case of Male Workforce of Public Sector:
2009 2010 2011 2012 2013 2014 2015 2016
28000
29000
30000
31000
32000
33000
34000
35000
30638
31264 31380
31816
32541 32878
33685 34011
Earnings
Time
Earnings
 In case of Female Workforce of Public Sector:
4

2009 2010 2011 2012 2013 2014 2015 2016
23500
24000
24500
25000
25500
26000
26500
27000
27500
28000
28500
25224
26113
26470 26663
27338
27705 27900 28053
Earnings
Time
Earnings
 In case of Male Workforce of Private Sector:
01/07/1905
02/07/1905
03/07/1905
04/07/1905
05/07/1905
06/07/1905
07/07/1905
08/07/1905
25500
26000
26500
27000
27500
28000
28500
29000
29500
30000
27632
27000 27233
27705
28201 28442
28881
29679
Earnings
Time
Earnings
 In case of Female Workforce of Private Sector:
5

2009 2010 2011 2012 2013 2014 2015 2016
18000
18500
19000
19500
20000
20500
21000
21500
22000
22500
19551 19532 19565
20313
20698
21017
21403
22251
Earnings
Time
Earnings
(d) Determination of Annual Growth Rate for each segment
Annual Growth Rate is the rate at which a variable increases from one period to another
period (Armstrong and Taylor, 2014). In the context of given case scenario, the annual growth
rate for each demographic of Public as well as Private Sector has been calculated by the
following formula:
Annual Growth Rate = [(Current year – Previous Year) / (Previous Year)]*100
The following cases have been formed based on Table A for both Private and Public
Sector:
 For Male Workforce of Public Sector:
Year Public Sector
Men (£) Annual Growth Rate (%)
2009 30638
2010 31264 2.04%
2011 31380 0.37%
2012 31816 1.39%
2013 32541 2.28%
2014 32878 1.04%
2015 33685 2.45%
6

2016 34011 0.97%
 For Female Workforce of Public Sector:
Year Public Sector
Women (£) Annual Growth Rate (%)
2009 25224
2010 26113 3.52%
2011 26470 1.37%
2012 26663 0.73%
2013 27338 2.53%
2014 27705 1.34%
2015 27900 0.70%
 For Male Workforce of Private Sector:
Year Private Sector
Men (£) Annual Growth Rate (%)
2009 27632 0.00%
2010 27000 -2.29%
2011 27233 0.86%
2012 27705 1.73%
2013 28201 1.79%
2014 28442 0.85%
2015 28881 1.54%
2016 29679 2.76%
 For Female Workforce of Private Sector:
Year Private Sector
Earnings Annual Growth Rate (%)
2009 19551
2010 19532 -0.10%
2011 19565 0.17%
7

2012 20313 3.82%
2013 20698 1.90%
2014 21017 1.54%
2015 21403 1.84%
2016 22251 3.96%
TASK 2
(a) Analysing raw business data using a number of statistical methods:
In Statistics, raw data includes those figures or information that has not beet processed
yet or converted into something more meaningful. This business data may be segregated into
divisions based on the objectives it aims to achieve and utilized as information for many research
and development purpose including population and sample. Population is referred to as a vast
pool of data from which a sample is drawn . It may include group of people, objects or units of
measure. On the other hand, a sample is a smaller group of data reflecting all the characteristics
of population it is drawn from. To achieve this, many researchers take help of data analysis or
statistical methods to convert mass data into an insight.
Under Data Analysis, a research may conduct either a quantitative analysis or a
qualitative analysis. Even though both aim to serve the same purpose, Quantitative Analysis
targets quantification of data whereas qualitative analysis targets the underlying reasons such as
motivation factors and psychology of the consumer to gain an in-depth understanding from the
collected data (Bedeian, 2014). In the context of Leisure Centre Staff of London, a quantitative
analysis has been carried out to derive meaningful inferences from the data collected.
(i) Using Ogive to estimate Median and Quartiles for Leisure Centre Staff, London
An Ogive or Cumulative histogram, is a graphical representation of Cumulative
Frequencies used to ascertain number of data points which lie below or above a certain value
present in the data set. The Cumulative Frequency, here, is the addition of each frequency with
that of next class interval (Boehm and Thomas, 2013). It is important to note that the Cumulative
Frequency for the last interval would always be equal to the sum of all data values present in the
data set. The following table shows the calculations regarding cumulative frequency for the
purpose of generating Ogive:
8

Hourly Earnings (£) Hourly Earnings (£)
No. of Leisure Centre
Staff
Cumulative
Frequency
0-10 5 4 4
10-20 15 23 27
20-30 25 13 40
30-40 35 7 47
40-50 45 3 50
Total 50
As per the table given above, information regarding a survey of 50 leisure centre staff
members in London has revealed that the hourly earnings made by them range between £10 to
£50. For facilitating better understanding, the given class limits have been converted into a
singular unit by calculating average of each class interval (Brozović and Schlenker, 2011). This
has been done by taking the adding upper and lower-class limits and dividing the total by 2.
Therefore, for Hourly Earnings falling between £0 to £10, the average will be £5 (=(0+10)/2).
The cumulative frequency of first class interval will be 4 as its the first unit present in the table.
For calculating cumulative frequency for second class intervals and so on, the preceding
frequency has been added to the current frequency giving a total of 27 (=4+23). This process has
been repeated for all the given intervals. Note here, the total of number of leisure centre staff is
equal to the last cumulative frequency for £40 to £50 class interval.
9

0 10 20 30 40
0
10
20
30
40
50
60
4
27
40
47 50
Ogive
Cumulative
Frequency
Upper Class Boundaries
Cumulative Frequency
The above graph depicts an Ogive for the hourly ratings earned by the Leisure Centre
Staff present in the London area. Here, the X-Axis shows the Upper Class Boundaries from the
previous table from £0 to £50 whereas the Y-Axis shows the Cumulative Frequency calculated in
the previous table. This diagram shows the accumulation occurring in the data set. Here, the
difference between two data points plotted on the Ogive renders the frequency. Also, there is a
steep increase in the data points, thus, indicating that as the number of hours increases, the
earnings made by the staff also go increasing. Just by observing the above image, one can
estimate the Median as well as the Class interval in which it falls.
Median is referred to as the middle value of a given data set segregating higher data
values from the lower ones. It is one of the most widely used measures of central tendency after
mean and mode. With the help of an ogive, median value can be ascertained by equally
separating the values presented in the graph. As per the Ogive, the median class would likely to
fall at £20 to £30 interval for hourly earnings. Also, the cumulative frequency would be near to
50% of 50 staff members. This gives a rough idea that the Median is likely to be 25 falling under
£20 to £30 class interval.
As far as quartiles are concerned, they are the intercept points which further separate the
given data set into two main areas viz. 25% and 75%. Therefore, a quartile intercepting the graph
at 25% level is known as First Quartile whereas when the area is separated at 75% level, it is
known as Third Quartile. Note that Median is also known as Second Quartile with a 50% level of
10

area interception. From the above Ogive, the first quartile can be estimated near 25% of hourly
earnings between £10 to £50 that comes to £12.50. On the other hand, 75% of the hourly
earnings for same range gives a third quartile value of £37.50. In order to double check these
values, the following calculations were carried out:
Median (50%) = (2*(50+1)/4) £25.5
Quartile (25%) = (1*(50+1)/4) £12.75
Quartile (75%) =(3*(50+1)/4) £38.25
(ii) Calculation of Mean and Standard Deviation for hourly earnings
Hourly
Earnings
Hourly
Earnings
(x)
No. of
Leisure
Centre Staff
(f)
Total Hourly
Earnings of
Staff
(f)*(x)
Squared
Hourly
Earnings
(x2)
Number of Staff *
Squared hourly
earnings
(f)*(x2)
0-10 5 4 20 25 100
10-20 15 23 345 225 5175
20-30 25 13 325 625 8125
30-40 35 7 245 1225 8575
40-50 45 3 135 2025 6075
Total 50 1070 28050
Mean = Total Hourly Earnings of Staff/ Number of Staff = 1070/50 = £21.4
Standard Deviation = [(28050/50) – (21.4)]^ 0.5 = £10.15
Mean relates to the average of data values for a given sample. In the context of given
scenario, the Mean Hourly Earnings for the London Staff is £21.4. This means that the 50 staff
members earn a £21.4 hourly wage on an average basis. On the other hand, the standard
deviation for the above table comes to £10.15 (Haimes, 2015). Since this measure of dispersion
is not located nearby the mean, central tendency measure, it can be concluded that there is
deviation of values from the central point of given data set.
11

(b) Comparison of earnings between two regions
London Manchester
Median £25.5 £14
Mean £21.4 £16.5
Standard Deviation £10.15 £7
Inter-Quartile Range £25.5 £7.5
By taking into consideration two surveys conducted for the leisure centre staff of London
and Manchester Area, it can be observed that the average hourly earnings of Manchester rank
higher than that of London. However, the Manchester centre lacks in other measures as
compared to that of London (Herrera and Schipp, 2014). Looking at the Median, it can be said
that there is a higher gap between the two for London as compared to Manchester indicating that
the average hourly earnings are closely held to the data set's middle value. The inter-quartile
range for London Centre is higher as compared to the other signalling that the number of data
sets falling within this range is high and lesser number of outliers are present in it as opposed to
Manchester Centre.
TASK 3
Economic Order Quantity or EOQ, is that level of quantity for a given product where the
related ordering and carrying cost are minimal. It is one of the most widely used tool to ascertain
volume and frequency of orders across organisations. Ordering Cost is the cost incurred when
inventory is purchased from the suppliers. This cost tends to decline as the volume of order
increases resulting in economies of scale (Kyriakarakos and et.al., 2013). On the other hand,
Carrying Cost or the holding Cost is the one which is incurred for storing the bought inventory in
warehouses until they are consumed for production of final goods. It is important to note that the
larger the volume of inventory, the higher carrying cost is. This tool also helps in determining the
most effective inventory policy an organisation must implement to avoid running out of stock.
(a) Calculating Economic Order Quantity
Economic Order Quantity is calculated by using following formula:
EOQ= [(2*Annual Consumption* Ordering Cost)/ Carrying Cost]^0.5
12

Here, Annual Consumption is the total number of units consumed or demanded by
customers regarding a particular product (Marchington and et.al., 2016). Order Cost tends to
differ for purchased items and manufacturers as the former would include those costs that are
incurred when purchasing or placing a requisition order while the latter would include the time
incurred to initiate the work order including scheduling and inspection time.
In the given scenario, Jenny Jones wants to develop a new inventory policy that would
enable her customers to purchase tee-shirt 95% of the time they asked. The following related
information has been given regarding the tee-shirt:
Number of Weeks Shop is open 50
Average Weekly demand (shirts) 30
Annual Demand for shirts (= 30*50) 1500
Delivery Cost (£) 5
Cost of Tee (£) 10
Holding Cost (£) (= 0.20*£10) 2
From the above table, Economic Order Quantity for Ms. Jones' Shop can be derived as
follows:
EOQ = [(2*Annual Demand* Delivery Cost)/ Holding Cost]^0.5
= [(2*1500*5)/ 2]^0.5
= [15000/2]^0.5
= [7500]^0.5
= 86.60 or 87 units.
This means that at 87 units of tee-shirts, Ms. Jones is able to minimize her ordering as
well as carrying cost to achieve economies of scale as well as revenues (Jiang and Pang, 2011).
Thus, Jenny must order at least 87 units of tee-shirts from its suppliers that in order to minimize
its total inventory cost, annually.
(b) Calculating Frequency of Orders
After determining the quantity that Jenny to order for developing an effective inventory
policy, it is imperative to also calculate how often would she need to place such orders. This can
be found out by dividing annual demand by the economic order quantity for the tee-shirts.
13

Thus,
Number of Orders required to be placed = 1500 tee-shirts/ 87 = 17.24 or 17 orders.
This indicates that, Ms. Jones would require to place 17 orders annually to minimize
ordering as well as carrying costs incurred by her.
(c) Ascertaining Inventory Policy Cost
For the given case scenario, Jenny owns a store which is open for 50 weeks in a year.
One of her tee-shirts is popular among customers who only visit her shop to make purchase of
that product. Jenny has been facing a difficult time dealing with holding an adequate amount of
stock for everyone, especially between placement and receipt of an order (Qiu, Qin and Zhou,
2016). This has led to her losing customers to other competing stores located in the shopping
centre. For this purpose, she needs to minimize her ordering and carrying costs for prevention of
losses as well as maintenance of competitive advantage.
In order to calculate Inventory Policy Cost, she would need to consider three main costs
viz. Cost of Product, Annual Ordering Cost and Annual Carrying Cost. Inventory Policy Cost or
Total Cost is the minimum outlay incurred for implementation of policy. She would have to
expend a minimum of following ordering, purchase and carrying costs:
Delivery Cost (£) 5
Cost of Tee (£) 10
Holding Cost (£) (= 0.20*£10) 2
Economic Order Quantity (tee-shirts) 87
Total Annual Holding Cost = [(87 units/ 2)* 2] (A) £87
Total Annual Ordering Cost = [(1500/87)*5] (B) £86.21
Total Annual Inventory Cost [(C) = (A) + (B)] £173.21
Hence, the total inventory cost per annum for the business is £173.21. This means that if
Ms. Jenny wants to implement an inventory policy where her desired service level is 95% along
with a minimum purchasing and holding costs, then, she would need to incur a minimum outlay
of £173.21.
(d) Current Service Level to Customers:
Desired Probability to purchase the tee-shirts 95.00%
14

Selling Price per tee-shirt (£) 20
Standard Deviation 15
Safety Stock 150 Shirts
Current Level of service = Weekly Demand * Availability of t-shirt
= 30*95%
= 28.5 units
e) Work out the re-order level to achieve desired service levels
Re-order level (ROQ) = (Lead time*daily average usage)+safety stock
= (28*2)+150
= 206 units
TASK 4
(a) Producing Line/Bar Charts for showcasing changes in CPI, CPIH and RPI:
 Consumer Price Index (CPI) (Consumer Price Index. 2019)
Year CPI Change in CPI (year-on-year)
2007 1256.4
2008 1301.8 3.61%
2009 1330 2.17%
2010 1373.7 3.29%
2011 1435.3 4.48%
2012 1484.9 3.46%
2013 1513.5 1.93%
2014 1535.6 1.46%
2015 1536.3 0.05%
2016 1546.5 0.66%
15

2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Change in CPI
Year
Change in CPI
alAlalalAlal
 Retail Price Index: (Retail Price Index. 2019)
Year RPI Change in RPI
2007 2478.6
2008 2577.9 4.0062938756
2009 2564.2 -0.5314403196
2010 2682.7 4.6213243897
2011 2822.2 5.1999850896
2012 2912.7 3.2067181631
2013 2999.5 2.9800528719
2014 3072.4 2.4304050675
2015 3102.5 0.9796901445
2016 3156.6 1.7437550363
2017 3269.7 3.5829690173
16

2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
-1
0
1
2
3
4
5
6
Change in RPI
Year
Change in RPI
(b) Creating Ogive using table 1
Hourly Earnings (£) No. of Leisure Centre Staff
Cumulative
Frequency
Less than 10 4 4
Less than 20 23 27
Less than 30 13 40
Less than 40 7 47
Less than 50 3 50
Total 50
17

0 10 20 30 40
0
10
20
30
40
50
60
4
27
40
47 50
Ogive
Cumulative
Frequency
Upper Class Boundaries
Cumulative Frequency
18