Analysis of Data Using Statistical Concepts

This assignment involves analyzing data using appropriate statistical methods. It covers various concepts such as central tendencies, deviations, and dispersion, which help simplify data analysis. Effective knowledge of statistics and its application can resolve numerous problems. The assignment provides a comprehensive understanding of how to analyze data in a simple manner.

STATISTICS FOR
MANAGEMENT

Table of Contents
INTRODUCTION...........................................................................................................................1
ACTIVITY 1....................................................................................................................................1
a) National Statistical Data.....................................................................................................1
b) Graphical representation of national statistical data..........................................................3
c) Differences between CPI, CPIH and RPI Indices..............................................................5
d) Use of collected data form Consumer price Index to determine annual inflation.............5
e) Significance of calculating inflation rate............................................................................6
Activity 2.........................................................................................................................................7
a) O-give curve to determine Median.....................................................................................7
b) Mean and standard deviation for hourly earnings of London area..................................11
c) Comparison of earning of London and Manchester area.................................................13
ACTIVITY 3..................................................................................................................................14
a) Economic Order Quantity (EOQ).....................................................................................14
c) Calculation of inventory policy cost................................................................................15
ACTIVITY 4..................................................................................................................................16
a) Charts and tables on the basis of office of national statistics produce line......................16
b) An O-give curve of cumulative % of staff versus hourly earning...................................18
CONCLUSION..............................................................................................................................20
REFRENCES ................................................................................................................................21

INTRODUCTION
Statistics is considered as one of the mathematical analysis that would be used in
qualifying models representations, for given set of data and actual verifications. It is generally
used to analyse, modified and draw a valid conclusions from data. An organisation or individual
can summarize business data using various methodologies of statistics (Gui and Aslam, 2017).
The report is made to analyse the concept of statistics of management for evaluating economical
data extracted from published National Statistics. These data are further represented in charts and
other forms of graphical method. Furthermore, concept of economic order quantity for inventory
management is also described in present assignment.
ACTIVITY 1
a) National Statistical Data
Consumer Price Indices:
Inflation can be defined as rate of changing price of basic commodities which influence
mostly the interest rate on mortgages, saving and more. These rates generally affects state
pension level as well as benefits of the same too. CPI refers to measure the inflation rate and
purchasing power of national currency (Qiu, Qin and Zhou, 2016). This method expresses
current price of basic goods as per difference in price of same year to previous one. It includes
bread, meat, milk and other essential household products. This will indicate effect of inflation on
current situation of marketplace. In context with CPIH, as per National Statistics, it has
evaluated that Consumer Price Index which includes housing costs of owners refers to most
encompassing measure of inflation. Thus, information provided as per CPI and CPIH helps
organisations as well as individuals in estimating the changing price of economy in future also.
Retail Price Index:
RPI is generally used by governmental bodies for several purposes like amount payable
on index-linked securities, wage negotiation, inflation rates etc. The data which is not included in
CPI such as mortgage interest payments, building insurance, house depreciation and more
included in retail price index (Gikhman and Skorokhod, 2015). It also tracks changes in the cost
of fixed or basic commodities.
1

Statistical data in terms of CPI index
Year Average
2007 104.7
2008 108.48
2009 110.83
2010 114.48
2011 119.61
2012 123.74
2013 126.13
2014 127.97
2015 128.03
2016 128.88
2017 132.3
Statistical data in terms of RPI Index
Year Average
2007 206.55
2008 214.83
2009 213.68
2010 223.56
2011 235.18
2012 242.73
2013 249.96
2014 256.03
2

2015 258.54
2016 263.05
2017 272.48
b) Graphical representation of national statistical data
Graphical representation of Consumer Price Index from year 2007-2017:
Year Average
2007 104.7
2008 108.48
2009 110.83
2010 114.48
2011 119.61
2012 123.74
2013 126.13
2014 127.97
2015 128.03
2016 128.88
2017 132.3
3

Graphical representation of Consumer Price Index from year 2007-2017:
Year Average
2007 206.55
2008 214.83
2009 213.68
2010 223.56
2011 235.18
2012 242.73
2013 249.96
2014 256.03
2015 258.54
4
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
0
20
40
60
80
100
120
140
104.7 108.48 110.83 114.48 119.61 123.74 126.13 127.97 128.03 128.88 132.3
Average

2016 263.05
2017 272.48
c) Differences between CPI, CPIH and RPI Indices
CPI CPIH RPI
Data and information gathered as per
consumer price index forms basis for
inflation as per targeted by
Government (Lu and et. al., 2013).
It excludes mortgage interest
payments and housing costs also.
It is another method like
CPI which is made just to
to measures owner
occupiers' housing costs.
For this purpose, CPIH uses
technique like rental
This method is to calculate
variance in price of basic
products of previous and
current year. Unlike CPI, it
also includes housing costs
like mortgage interest
5
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
0
50
100
150
200
250
300
206.55 214.83 213.68 223.56 235.18 242.73 249.96 256.03 258.54 263.05 272.48
Average

equivalence for measuring
OOH which includes
housing, water, fuels,
electricity and more.
payments and council tax.
It is considered as one of the main
method which helps in deciding the
cost of living and rate of inflation as
well.
Since components
including under OOH are
slightly increased therefore,
CPIH seems to be lower
than or equal to CPI over a
certain period (Groves,
2016).
As compare to CPI or
CPIH, retail price index
measure changes in price
rates on monthly basis.
d) Use of collected data form Consumer price Index to determine annual inflation
The consumer price index as per above mentioned national statistical data, Bureau of
Labour Statistics reported that it has slightly increased to near about 2% (Lam, 2012). An
increase in electricity and gasoline, used cars, trucks and other basic transportation, food items
etc. is majorly affect purchasing power of people. Along with this, consumption of some goods
like new vehicles, indexes for communication and recreation all, also has also declined slightly
from 2016 to 2017.
e) Significance of calculating inflation rate
Measuring inflation rate is considered as most difficult task for statisticians. For this
process, a number of various goods and services which refers to representative of economy will
put together in a basket (Keller, 2015). Further, cost of this basket will then compare with past
data to analyse the inflation rate. For this purpose, mostly statistician use CPI to measure price
changes in goods and services which includes food, gasoline, auto-mobile and more.
6

Activity 2
Hourly pay rates in different regions of UK
a) O-give curve to determine Median
O-give curve refers to statistical tool which is used for measuring the value of median of
a certain data. Under this process, two types of curves are drawn viz. More-than type and Less-
than type, where point of inflexion are termed as median of given data. Basically, this kind of
curve is drawn on cartesian plan of 2-D data where X-origin represents class-interval and Y-
origin shows cumulative frequencies (Jessop, 2016). Concept of both kind of O-give curve can
be elaborated by following example:-
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
7

8
1 2 3 4 5 6
0
5
10
15
20
25
30
35
40
45
50
No. of Leisure central staff
(f)
No. of Leisure central staff
(f)
More than O-give
Cumulative frequency

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
9
1 2 3 4 5 6
0
5
10
15
20
25
30
35
40
45
50
No. of Leisure central staff
(f)
No. of Leisure central staff
(f)
Less than O-give
Cumulative frequency

Median determined in terms of More-than and Less-than type O-give curve:
Therefore, the point where both kinds of O-give curve that are less-than and more-than is
considered as Median. From this process, median for hourly earning for leisure centre staff of
London area is calculated as near about £19.0.
Quartile: A quartile is a statistical term which helps to define or explain a division of
observations into four equal intervals based upon values of data and how they are used to
compare entire set of observations (Walters, 2016). First quartile: It is denoted by Q1 and is termed as median of lower half of any given
data set. This can further be said that 25 % numbers lie below Q1 and 75% lie above it.
 Third quartile: It is symbolically represented by Q3 and is known to be median of upper
half of any given data set. So, this can further be said that 75% numbers fall under Q3
and 25% lie above it.
10
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)
More than O-give
Cumulative frequency
Less than O-give
Cumulative frequency

Inter quartile: Inter quartile or inter quartile range is a statistical measure of variability.
It is based on dividing any given data set into quartiles.
Now Quartiles can be calculated as per:-
Therefore, First Quartile of deviation can be calculated as per:-
Here lower limit (l) = 10, frequency (f) = 23, Class interval (h) = 10 and Total frequency (N/4)
= ∑F/4 = 12.5, cf = 4
Q1 = L + (N/4 – cf)/ f x h
= 10 + (12.5 – 4)/ 23 x 10
= 10 + 85/ 23
= 13.7
While, Third Quartile of deviation can be calculated as per:-
Here l = 20, f = 13, h = 10 and 3N/4 = ¾ of ∑F = 37.5, cf =27
Q3 = L + (3N/4 – cf)/ f x h
= 20 + (37.5 – 27) / 13 x 10
= 20 + 105/13
= 28.07
Therefore, Inter-quartile range can be calculated by measuring the difference among first and
third quartiles, as shown below:-
IQR = Q3 – Q1
= (28.07-13.7)
= 14.0 (approx)
b) Mean and standard deviation for hourly earnings of London area
Central tendency can be defined as process to show entire data into single manner. This
method is given by Professor Bowley which has given various types of techniques to calculate
and analyse large information into simpler form (Hecke, 2012). It includes mean, median, mode,
quartiles, standard deviations and more. Concept of some of these methods can be explained in
following manner:-
Mean: It can be defined as an average of a particular data which can be measured by
dividing sum of observation to total numbers. It is also known as arithmetic mean of data which
11

covers entire observations. Therefore, in present context, this methodology helps in calculating
average of hourly earning for leisure centre staff in London area.
Median: It refers to middle data or second quartile of central tendency which denotes the
midpoint of a frequency distribution (Haimes, 2015). It is calculated by various methods like O-
give curve, frequency distribution method and more.
Standard Deviation: It can be defined as a measure of central tendency which is used to
quantify the amount of dispersions or variations of a set of values.
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
Calculation
Mean = ∑Fx / ∑F
= 1070/50
= 21.4
Standard deviation = √ (∑Fx2 / ∑F) - (∑Fx / ∑F)2
12

= √(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 and London area
Basis of Comparison Manchester area London area
Median £14.00 £19.00
Interquartile Range £7.50 £14.00
Mean £16.50 £21.40
Standard Deviations £7.00 £5.00
Therefore, on comparison of hourly earning of both area of Manchester and London, it
has analysed that
13

ACTIVITY 3
a) Economic Order Quantity (EOQ)
EOQ is the order quantity that determine the total cost and ordering cost. It is considered
as one of the most classical production planning methods which was developed by Ford
W.Harris in 1913. In depth analysis, EOQ method can be altered to find out different
production standard or can be stated as fundamental techniques with large supply series to
calculate variable cost (Bedeian, 2014).
Economic Order Quantity can be calculated by using below mentioned formula :
EOQ = √( 2 x D x Co / Ch)
Where, D =
Demand per year;
Co = Cost per order;
Ch = Cost of holding per unit of inventory
As per present case study,
Demand of t-shirt = 2000;
cost per t-shirt is £5 and
cost of holding=2
Therefore, EOQ = square root of (2 x 2000 x 5)/2
= 100 Units
b) Re Order tee-shirts
It is essential for companies to have a knowledge about dimension of crude and
completed stock which helps in increasing effectiveness of production process (Barrett and et.
al., 2012). In case of loss of control on inventory level of stock, an organisation can face
problems like shortage in cost. Therefore, under such condition, firm will also not in state to
cover revenue as well or meet demand of customers on time.
In context with present case, Ms Jones are required to re-order following number of tee-
shirts as shown in below calculation:-
Re-order level (ROQ) = (Lead time x daily average usage) + safety stock
= (21 x 2)+150
= 192 units
14

Frequency of Re-order = Demand per year / ROQ
= 2000 / 192
= 10.41 or 10 days
c) Calculation of inventory policy cost
It is essential for organisations or individuals to calculate inventory policy cost so that
expenses can be reduced and manage stock also (Andreeva and Kianto, 2012).
Inventory Policy Cost = Purchase cost + Cost per order + Carrying cost
= 10 + 5 + 2
= £17
As inventory covers all kinds of expenses and cost of managing stock therefore, it is obtained as
£17.
d) Current service level to customers
Current Level of service = Demand per week x Availability of t-shirt
= 95% of 40
= 38 units
e) Work out the re-order level to achieve desired service level
Re-order level (ROQ) = (Average usage x Lead time) + additional stock
= (21 x 2) + 150
= 192 units
15

ACTIVITY 4
a) Charts and tables on the basis of office of national statistics produce line
CPI (Consumer Price Index)
Year Average
2007 104.7
2008 108.48
2009 110.83
2010 114.48
2011 119.61
2012 123.74
2013 126.13
2014 127.97
2015 128.03
2016 128.88
2017 132.3
16

Retail price index
Year Average
2007 206.55
2008 214.83
2009 213.68
2010 223.56
2011 235.18
2012 242.73
2013 249.96
2014 256.03
17
1 2 3 4 5 6 7 8 9 10 11
0
500
1000
1500
2000
2500
Year
Average

2015 258.54
2016 263.05
2017 272.48
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
type
Cumulative
frequency
Less than
type
Cumulative
frequency
Below 10 4 8.00% More than 0 50 Less than 10 4
18
1 2 3 4 5 6 7 8 9 10 11
0
500
1000
1500
2000
2500
Year
Average

10 but
under 20
23 46.00% More than
10
46 Less than 20 27
20 but
under 30
13 26.00% More than
20
23 Less than 30 40
30 but
under 40
7 14.00% More than
30
10 Less than 40 47
40 but
under 50
3 6.00% More than
40
3 Less than 50 50
Total 50
19
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)
In percentage form
More than type
Cumulative frequency
Less than type
Cumulative frequency

CONCLUSION
From this assignment it has analysed that to analyse any data in appropriate manner,
mostly organisations use statistical concepts. It provides various methods like central tendencies,
deviations, dispersion and more which helps in analysing data in simple manner. An effective
knowledge of statistics as well as ability for applying such applications can help in resolving
various problems.
20

REFRENCES
Books and Journals
Andreeva, T. and Kianto, A., 2012. Does knowledge management really matter? Linking
knowledge management practices, competitiveness and economic performance. Journal
of knowledge management. 16(4). pp.617-636.
Barrett, K. C and et. al., 2012. IBM SPSS for introductory statistics: Use and interpretation.
Routledge.
Bedeian, A. G., 2014. “More than meets the eye”: A guide to interpreting the descriptive statistics
and correlation matrices reported in management research. Academy of Management
Learning & Education. 13(1). pp.121-135.
Haimes, Y. Y., 2015. Risk modeling, assessment, and management. John Wiley & Sons.
Hecke, T. V., 2012. Power study of anova versus Kruskal-Wallis test. Journal of Statistics and
Management Systems. 15(2-3). pp.241-247.
Jessop, A., 2016. StatsNotes: Some Statistics for Management Problems. World Scientific Books.
Keller, G., 2015. Statistics for Management and Economics, Abbreviated. Cengage Learning.
Lam, A. C., 2012. Women and Japanese management: discrimination and reform. Routledge.
Lu, L and et. al., 2013. A review on the key issues for lithium-ion battery management in electric
vehicles. Journal of power sources. 226. pp.272-288.
Qiu, Z., Qin, J. and Zhou, Y., 2016. Composite Estimating Equation Method for the Accelerated
Failure Time Model with Length‐biased Sampling Data. Scandinavian Journal of
Statistics. 43(2). pp.396-415.
Gui, W. and Aslam, M., 2017. Acceptance sampling plans based on truncated life tests for
weighted exponential distribution. Communications in Statistics-Simulation and
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Groves, R., 2016. Housing and the new welfare state: Perspectives from East Asia and Europe.
Routledge.
Gikhman, I. I. and Skorokhod, A.V., 2015. The theory of stochastic processes I. Springer.
Walters, W. H., 2016. Beyond use statistics: Recall, precision, and relevance in the assessment
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