(Solved) Assignment on Statistics for Management

STATISTICS FOR
MANAGEMENT

Table of Contents
INTRODUCTION...........................................................................................................................3
ACTIVITY 1....................................................................................................................................3
P1Process and nature of business and economic data with different published sources........3
P2 Data form variety of sources using various methods of analysis......................................6
M1 Evaluation of sources other than the NSO with regard to the gender pay gap................9
Activity 2.........................................................................................................................................9
P3 Evaluation of qualitative and quantitative data from a range of examples and appropriate
statistical methods..................................................................................................................9
M2 Differences in statistical application in activity 2..........................................................13
D1 Difference between descriptive, exploratory and confirmatory analysis with examples 13
ACTIVITY 3..................................................................................................................................15
P4 Statistical methods used in business planning, inventory management and capacity
management..........................................................................................................................15
M3 the use of the statistical methods used in activity 3.......................................................16
D2 Recommendation and judgements made in activity 3....................................................16
ACTIVITY 4..................................................................................................................................17
P5 Use of adequate charts and tables to execute the findings for a various variables.........17
M4 Justification regarding graphical representations used in activity 1 and 2....................20
D3 Use of graphical and tabular representations used in 1 and 2 activities.........................20
CONCLUSION..............................................................................................................................20
REFRENCES ................................................................................................................................22

INTRODUCTION
Business statistics can be defined as science of good decisions which make under case of
uncertainty such as financial analysis, auditing operations and production etc. It generally covers
statistical study and descriptive stats for collecting, analysing and interpreting the data. Statistical
analysis helps an organization or individual in representing the data and information in graphical
manner (McPherson and Pincus, 2017). Present report is going to evaluate business and
economic data which is obtained from published sources. For this purpose, various types of
statistical methods are used such as quartiles, correlation coefficient, central tendencies etc.
These methods are also applied in further business planning.
ACTIVITY 1
P1Process and nature of business and economic data with different published sources
Consumer Price Indices: CPI can defined as a comprehensive measure which is used
for estimating price changes in goods and services as per consumption expenditures. In other
words it helps in examining the weighted average of prices of consumer goods like
transportation, medical care and food products (Lu and et. al., 2013). It is calculated by
measuring changing price of each item against consumption then further averaging them.
Inflation period of economy is usually measured by using this concept which calculate rate at
which price of items or services purchased by households either rise or fall. Therefore, it is
widely used as economical indicator through which effectiveness of economical policy of
government can be determined. CPI provided detail information to regulatory bodies,
organisations as well as individuals about changing price of economy. While CPIH refers to

consumer price index in terms of housing and considered as most comprehensive measure of
inflation.
Statistical data in terms of CPI index
Year Jan Feb Mar April May Jun July
2007 103.2 103.7 104.2 104.5 104.8 105 104.4
2008 105.5 106.3 106.7 107.6 108.3 109 109
2009 108.7 109.6 109.8 110.1 110.7 111 110.9
2010 112.4 112.9 113.5 114.2 114.4 114.6 114.3
2011 116.9 117.8 118.1 119.3 119.5 119.4 119.4
2012 121.1 121.8 122.2 122.8 122.3 122.5 123.1
2013 124.4 125.2 125.6 125.9 126.1 125.9 125.8
2014 126.7 127.4 127.7 128.1 128 128.3 127.8
2015 127.1 127.4 127.6 128 128.2 128.2 128
2016 127.4 127.7 128.3 128.3 128.5 128.8 129.2
2017 129.8 130.7 131.2 131.7 132.2 132.2 132.1
Aug Sep Oct Nov Dec Total
104.7 104.8 105.3 105.6 106.2 1256.4
109.7 110.3 110 109.9 109.5 1301.8
111.4 111.5 111.7 112 112.6 1330
114.9 114.9 115.2 115.6 116.8 1373.7
120.1 120.9 121 121.2 121.7 1435.3
123.5 124.4 126.8 126.9 127.5 1484.9
126.4 126.8 126.9 127 127.5 1513.5
128.3 128.4 128.5 128.2 128.2 1535.6

128.4 128.2 128.4 128.3 128.5 1536.3
129.2 129.4 129.5 129.8 130.4 1546.5
132.9 133.2 133.4 133.9 134.3 1587.6
Year Total
2007 1256.4
2008 1301.8
2009 1330
2010 1373.7
2011 1435.3
2012 1484.9
2013 1513.5
2014 1535.6
2015 1536.3
2016 1546.5
2017 1587.6
Retail Price Index:
It provides a list of price of particular goods and services which entail the changing rate
of cost of living changes on monthly basis (Lam, 2012). It also refers as a primary tool for
determining the way people are experiencing fall or rise in price rates. Therefore, it can be
calculated as a weighted average of price of those household goods which are bought by end
customers.
Statistical data in terms of RPI Index
Year Jan Feb Mar April May Jun July

2007 201.3 203.1 204.4 205.4 206.2 207.3 206.1
2008 209.8 211.4 212.1 214 215.1 216.8 216.5
2009 210.1 211.4 211.3 211.5 212.8 213.4 213.4
2010 217.9 219.2 220.7 222.8 223.6 224.1 223.6
2011 229 231.3 232.5 234.4 235.2 235.2 234.7
2012 238 239.9 240.8 242.5 242.4 241.8 242.1
2013 245.8 247.6 248.7 249.5 250 249.7 249.7
2014 252.6 254.2 254.8 255.7 255.9 256.3 256
2015 255.4 256.7 257.1 258 258.5 258.9 258.6
2016 258.8 260 261.1 261.4 262.1 263.1 263.4
2017 265.5 268.4 269.3 270.6 271.7 272.3 272.9
Aug Sep Oct Nov Dec Total
207.3 208 208.9 209.7 210.9 2478.6
217.2 218.4 217.7 216 212.9 2577.9
214.4 215.3 216 216.6 218 2564.2
224.5 225.3 225.8 226.8 228.4 2682.7
236.1 237.9 238 238.5 239.4 2822.2
243 244.2 245.6 245.6 246.8 2912.7
251 251 251 252.1 253.4 2999.5
257 257.6 257.7 257.1 257.5 3072.4
259.8 259.6 259.5 259.8 260.6 3102.5
264.4 264.9 264.8 265.5 267.1 3156.6
274.7 275.1 275.3 275.8 278.1 3269.7

Year Total
2007 2478.6
2008 2577.9
2009 2564.2
2010 2682.7
2011 2822.2
2012 2912.7
2013 2999.5
2014 3072.4
2015 3102.5
2016 3156.6
2017 3269.7
P2 Data form variety of sources using various methods of analysis
Chart of Consumer Price Index from year 2007-2017:

Chart of Retail Price Index from year 2007-2017:
Differences between CPI, CPIH and RPI Indices
1 2 3 4 5 6 7 8 9 10 11
0
500
1000
1500
2000
2500
3000
3500
Year
Total
1 2 3 4 5 6 7 8 9 10 11
0
500
1000
1500
2000
2500
Year
Total

CPI CPIH RPI
It can be defined as a weighted
average value of purchased goods
and services.
It refers to new measure of
price inflation from ONS
(Keller, 2015).
It is used for revalorisation
of taxation or excise duty
and uprating the index-
linked gilts as well.
It measures the consumer price
inflation which is produced to
international standards.
It is based on CPI which
measures housing costs of
goods and services
purchased by final
consumers.
It shows changes in cost of
living.
This method is mostly used by
regulatory bodies to determine
changes in price of particular
products (Melnykov, 2013).
This type of technique is
used ONS (Office for
National Statistics) for
publishing a high range of
indices which is also called
the consumer price index
including housing costs.
It is generally used by
business, government and
economists for measuring
the inflation rate.
Usage of Consumer price Index data for calculating annual inflation
Annual inflation rate can be defined as changes in price of particular products where
regulatory bodies use consumer price index method to calculate the same. This would help
organisations to decide expansion (Jessop, 2016). As per above national statistical data,
consumer value list in the year 2017 has been measured as 1587.6 which is much increased as
per previous year 2016 which is approximate 2% as ascended rate of expansion.
Importance of determining rate of inflation
Inflation can be defined as increase in price level of certain goods and services over a
particular period of time in economy. Whenever price of products are hiked then it directly
impacts on purchasing power of people. This would also impact on demand of items also
therefore, it affects economical condition of country both in negative and positive manner ( Paté‐

Cornell, 2012). Government and public organisations measure inflation rate in order to determine
expansion rate of economy with cost of living index.
M1 Evaluation of sources other than the NSO with regard to the gender pay gap
It has analysed from National Statistics data that organisations of UK provide
employment to male candidates mostly as compared to female. It leads to causes high gender gap
as subjected to Consumer Index Price in this nation. For example- As per survey, it has evaluated
that under textiles group, the gender pay gap is recorded as 88% that shows it pay less
consideration to female working staff then males (Gender pay gap in UK, 2018).
Activity 2
P3 Evaluation of qualitative and quantitative data from a range of examples and appropriate
statistical methods
a) O-give curve to determine Median
O-give curve can be defined as a statistical tool to measure median of a particular data. It
represent data into graphical manner by plotting frequency of data against cumulative
distribution functions (Hecke, 2012). In general, O-give curve can be classified into major parts
Less-Than and More-than. Under less-than type O-give curve, upper limit of class interval is
plotted against corresponding cumulative frequency. While more than type of O-give curve is
used lower class limit. The point where both kinds of curves are meet is considered as median of
the particular data.
More than O-give curve
Hourly earning in
Euro
(Class Interval)
No. of Leisure central
staff
(f)
More than O-give Cumulative frequency
Below 10 4 More than 0 50
10 but under 20 23 More than 10 46
20 but under 30 13 More than 20 23
30 but under 40 7 More than 30 10

40 but under 50 3 More than 40 3
Total 50
Less than O-give Curve
Hourly earning in
Euro
(Class Interval)
No. of Leisure central
staff
(f)
Less than O-give Cumulative frequency
Below 10 4 Less than 10 4
10 but under 20 23 Less than 20 27
20 but under 30 13 Less than 30 40
30 but under 40 7 Less than 40 47
40 but under 50 3 Less than 50 50
Total 50
O-give curve
Below 10
10 but under 20
20 but under 30
30 but under 40
40 but under 50
Total
0
10
20
30
40
50
60
No. of Leisure central staff
(f)
More than O-give
Cumulative frequency
Less than O-give
Cumulative frequency

From the above graphical representation, Median obtained is approximate £19.0 for
hourly earning for leisure centre staff of London area (Zhou and Luo, 2015). While interquartile
range can be obtained as :
Q1 can be defined as first quartile range which is calculated by taking 25% of data. While Q3 is
sated as third quartile range that used 75% of total population. Along with this, Inter-quartile
range can be defined as a quantum of statistical dispersion it is also known as mid spread and
middle 50%. It is first quartile which is subtracted from third quartile. It is mainly a quota of
variability which is based on dividing of a data set into quartiles. Inter-Quartile is basically a
measure where extended values lies.
Q1 = L + (N/4 – cf)/ f X h Here l = 10, f = 23, h = 10 and N/4 = ∑F/4 = 12.5, cf = 4
= 10 + (12.5 – 4)/ 23 x 10
= 10 + 85/ 23
= 13.7
Q3 = L + (3N/4 – cf)/ f X h Here l = 20, f = 13, h = 10 and 3N/4 = ¾ of ∑F = 37.5, cf =27
= 20 + (37.5 – 27) / 13 x 10
= 20 + 105/13
= 28.07
So, Inter-quartile range can be obtained as = Q3 – Q1
= (28.07-13.7)
= 14.0 (approx)
b) Mean and standard deviation for hourly earnings of London area
Mean: It is average of range of quantities or values calculated by adding all data and
after then divide it by total of all numbers. End result is mean or average which is also called
arithmetic mean as well. This is most common measure of mid-point in a set of values . It is use
to derive central tendency of data in a question (Zyphur and Oswald, 2013). This type of
statistical calculation erase accidental errors. This will help to acquire more accurate conclusion.
Mean also helps in interpretation of statistical data.
Median: It is a value that separates higher half from lower half in a given data sample. It
is commonly use to measure properties of set of a data. It is very easy to understand and simple

to calculate. Median can be use as location parameter in large descriptive statistics. To identify
median, an individual arrange observation in a order from small to large value. If odd number is
there in observation, then middle value is median (Bedeian, 2014). Whereas if even number is
there in observation , then average of two middle value is median.
Standard Deviation: It can be calculated as square root of variance. Standard deviation
helps in measuring spread of data about mean value. There are mainly two types of standard
deviations which includes population and sample standard deviation. It is a measure which is use
to compute amount of given variations in a data value sets. Standard deviations of statistical
population, data sets, random variable and probability distribution is square root of their variance
(Haimes, 2015). It is mainly use to measure assurance in a statistical conclusion.
Mean is calculated by taking average of sum of observation as shown below:
Hourly
earning in
Euro
(Class
Interval)
No. of Leisure
central staff
(f)
Middle data
(x) (F*x)
Middle data
(x2) (F*x2)
Below 10 4 5 20 25 100
10 but under
20
23 15 345 225 5175
20 but under
30
13 25 325 625 4225
30 but under
40
7 35 245 1225 8575
40 but under
50
3 45 135 2025 6075
Total 50 1070 24150
Working notes:
Mean = ∑Fx / ∑F

= 1070/50
= 21.4
Standard deviation = √ (∑Fx2 / ∑F) - (∑Fx / ∑F)2
= √(24150/50) – (21.4)2
= √483 – 457.96
= √25.04
= 5. 0 (approx)
Thus, as per above calculation, mean and standard deviation for London area are obtained as
£21.4 and £5.0 respectively.
c) Comparison of earning of London and Manchester area
Hourly earning for leisure centre staff in Manchester area:
Median £14.00
Interquartile Range £7.50
Mean £16.50
Standard Deviations £7.00
Hourly earning for leisure centre staff in London area:
Median £19.00
Interquartile Range £14.00
Mean £21.40
Standard Deviations £5.00
Therefore, on comparing the above data, it has interpreted that hourly earning for leisure
centre staff of London area is more than Manchester area.
M2 Differences in statistical application in activity 2
In activity 2, for calculating median of given data, O-give curve has used while other
variables like quartiles, standard deviations and interquartile range, frequency distribution has
taken. The main difference among both methods is that ogive curve is easy to interpret the result
while frequency distribution method requires a tough calculation. But in terms of accuracy,

frequency distribution gives more accurate and correct data as compared to graphical
representation.
D1 Difference between descriptive, exploratory and confirmatory analysis with examples
Descriptive Exploratory Confirmatory
 It aims at exploring the
situations of a research
in detailed manner.
 It describes functions
and characteristics of
data
 It focuses on giving
insights into and an
understand of issues
faced by investigators
during collection of
data.
 It discovers new ideas
and thoughts.
 It uses traditional
methodology like
significance,
confidence and
inference to evaluate
evidence of data.
 It covers all basis of
gathering, presenting
and testing the
evidence of data.

ACTIVITY 3
P4 Statistical methods used in business planning, inventory management and capacity
management
EOQ refers to optimum quantity of goods that can be bought only at one time for
minimising the annual total cost to order holding items in inventory (Barrett and et. al., 2012).
This method is used by organisations in order to minimise cost of inventory as well as can meet
needs of customers on time.
Economic Order Quantity can be calculated by using below mentioned formula :
EOQ = √(2 x demand x cost per order) / cost of holding per unit of inventory)
EOQ = √( 2 x D x Co / Ch)
Where, D = Demand per year;
Co = Cost per order;
Ch = Cost of holding per unit of inventory
According to present case, Demand of t-shirt is 2000 and cost per t-shirt is £5; cost of holding=2
EOQ = √ (2 x 2000 x 5)/2
= 100 Units
b) Re Order tee-shirts
The EOQ method is generally used to measure re-order point through which
organisations can control inventories as well as can fulfil demand of customers on time
(Andreeva and Kianto, 2012). If any business runs out of its inventory level of stock then it leads
to cause shortage in cost. This would also taken as revenue lost as under this condition, company
cannot become able to fill an order on time. Therefore, as per present scenario, Ms Jones needs
to order tee-shirts in following manner:-
Re-order level (ROQ) = (Lead time x daily average usage) + safety stock
= (28 x 2)+150
= 206 units
Frequency of Re-order = Demand per year / ROQ
= 2000 / 206
= 9.7 or 10 days
c) Calculation of inventory policy cost

Inventory Policy Cost = Purchase cost + Cost per order + Carrying cost
= 10 + 5 + 2
= £17
The inventory cost is £17 because inventory includes all the cost of maintaining stock.
d) Current service level to customers
Current Level of service = Demand per week x Availability of t-shirt
= 40 x 95%
= 38 units
e) Work out the re-order level to achieve desired service level
Re-order level (ROQ) = (Lead time x daily average usage) + safety stock
= (28 x 2) + 150
= 206 units
M3 the use of the statistical methods used in activity 3
In order to manage the inventories and handle stock level properly, it is better to use
Economic order quantity analysis, This costing method helps in analysing the optimum quantity
of orders, re-orders as well as stock levels. Furthermore, purchasing cost, cost per order and
carrying cost is evaluated to analyse inventory policy cost.
D2 Recommendation and judgements made in activity 3
Using economic order quantity, owners of Jenny Jones gets success to manage quality of
inventory and complete order of customers on time. Further, it is recommended to its
management team to ascertain the reorder level structure for avoiding additional overhead
expenses and overcome from shortage of cost as well.

ACTIVITY 4
P5 Use of adequate charts and tables to execute the findings for a various variables
a) Graphical representation of CPI (Consumer Price Index) and RPI (Retail Price Index)
CPI (Consumer Price Index)
Year Total
2007 1256.4
2008 1301.8
2009 1330
2010 1373.7
2011 1435.3
2012 1484.9
2013 1513.5
2014 1535.6
2015 1536.3
2016 1546.5
2017 1587.6

Retail price index
Year Total
2007 2478.6
2008 2577.9
2009 2564.2
2010 2682.7
2011 2822.2
2012 2912.7
2013 2999.5
1 2 3 4 5 6 7 8 9 10 11
0
500
1000
1500
2000
2500
Year
Total

2014 3072.4
2015 3102.5
2016 3156.6
2017 3269.7
b) An O-give curve of cumulative % of staff versus hourly earning
More than O-give curve of cumulative % staff versus hourly earning
Hourly earning
in Euro
(Class Interval)
No. of Leisure
central staff
(f)
In percentage
form
More than O-give Cumulative
frequency
Below 10 4 8.00% More than 0 50
1 2 3 4 5 6 7 8 9 1011
0
500
1000
1500
2000
2500
3000
3500
Year
Total

10 but under 20 23 46.00% More than 10 46
20 but under 30 13 26.00% More than 20 23
30 but under 40 7 14.00% More than 30 10
40 but under 50 3 6.00% More than 40 3
Total 50
Less than O-give curve of cumulative % staff versus hourly earning
Hourly earning
in Euro
(Class Interval)
No. of Leisure
central staff
(f)
In percentage
form
Less than O-give Cumulative
frequency
Below 10 4 8.00% Less than 10 4
10 but under 20 23 46.00% Less than 20 27
20 but under 30 13 26.00% Less than 30 40
30 but under 40 7 14.00% Less than 40 47
40 but under 50 3 6.00% Less than 50 50
Total 50
O-give Curve:

M4 Justification regarding graphical representations used in activity 1 and 2
Bar charts and O-give curve methods of graphical representation are used to represent the
data of Activity 1 and Activity 2. O-give helps in evaluating the median and quartiles of data
while Bar chart is to represent the CPI and RPI data of Statistical National of year 2007 to 2017.
D3 Use of graphical and tabular representations used in 1 and 2 activities
Both tabular and graphical representation of data is essential to summarise the entire data
into single form. Tabular formation is used to represent National Statistics data into quantitative
manner which is helpful for analysing data in more appropriate manner. While O-give curve is
used to analyse the basic difference among hourly earning by staff member of Manchester and
London area.
CONCLUSION
This mentioned report defines the importance of statistics in collecting, measuring,
analysing and interpreting the data. For measuring inflation and deflation period of economy,
governmental bodies or organisations can use number of statistical methods. It includes
consumer price index, retail price index, central tendencies like mean, median, standard
Below 10
10 but under 20
20 but under 30
30 but under 40
40 but under 50
Total
0
5
10
15
20
25
30
35
40
45
50
No. of Leisure central staff
(f)
No. of Leisure central staff
(f)
In percentage form
More than O-give
Cumulative frequency
Less than O-give
Cumulative frequency