Statistics for Management: Statistical Analysis of UK Economic Data

This report presents a comprehensive statistical analysis of UK economic data. It begins with an examination of consumer and retail price indices from 2007 to 2017, exploring fluctuations and differences, and their implications for inflation. The report uses graphical representations to illustrate these trends. Further analysis includes hourly pay rates across different UK regions, utilizing ogive charts to display median and quartile values, followed by calculations of mean and standard deviation. The report also delves into hypothesis testing, employing a paired T-test to assess the significance of differences between new and old systems for processing insurance claims, and constructing confidence intervals. The evaluation of statistical methods, graphical presentations, and tabular analyses are also discussed. The report includes critical evaluations of data sources and statistical methods used throughout the analysis, offering recommendations and conclusions based on the findings.

Statistics for Management

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
ACTIVITY 1...................................................................................................................................1
A. Colleting the information relevant with Consumer price indices and Retail price index from
Office of National Statistics.........................................................................................................1
B. Pictorial presentation of the data changing from 2007 to 2017..............................................3
C. Ascertaining the differences between such variables.............................................................3
D. Implicating the use of Consumer price index in analysing the annual inflation rate..............4
E. Giving the reasons based on importance of analysing rate of inflation..................................5
M1 Critical evaluation of the sources other than Office national statistics with regard to
Gender pay gap............................................................................................................................6
ACTIVITY 2...................................................................................................................................6
1. Client B analysing the hourly pay rates in different UK regions............................................6
A. Presentation of ogive chart which states the details of median and quartiles of data set.......6
2. Calculating the standard deviation and mean value of hourly earnings:.................................8
B. Comparing the hourly earnings of Manchester and London region:.....................................9
M2 Evaluation of the data which have been used by considering the various methods statistics
...................................................................................................................................................10
D1 Analysing the differences between the descriptive, exploratory and confirmatory analysis
...................................................................................................................................................10
ACTIVITY 3.................................................................................................................................10
1. Client E Analysing the significance differences between the new and old system for
processing better insurance claims............................................................................................10
A. Determining a paired T-test at the 5% of significance level:...............................................11
B. Stating a fully usual condition for a paired T test:................................................................12
C. Constructing a 99% confidence interval for analysing mean differences in the new system
...................................................................................................................................................12
M3 Evaluation of the statistical methods used in above activity...............................................14
D2 Explanation to the recommendation made in above activity...............................................14
ACTIVITY 4.................................................................................................................................15

A. Presenting the differences between Indices from Office of national statistics from 2007 to
2017...........................................................................................................................................15
B. Ogive chart of staff vs hourly earnings.................................................................................15
M4 Justification on the choice of graphical presentation..........................................................16
D3 Evaluation of the graphical presentation and tabular analysis.............................................16
CONCLUSION..............................................................................................................................16
REFERENCES..............................................................................................................................17

INTRODUCTION
To analyse the outcomes and make judgement relevant with the business obstacles there will
be requirement of making appropriate changes in the operational analysis. In the present report
there will be analysis and discussion based on various data base gathered through reliable
sources. There will be analysis of annual inflation rate which will be gathered from consumer
price indices from Office of National Statistics. Moreover, there will be identification of various
statistical elements which were analysed on the basis of measuring the mean, median, quartiles
and standard deviation. Along with this, there will be analysis over the hypothesis defining the
significant differences between the new and old system. In addition, there will be pictorial
presentation of various data base which helps in articulating the changes in the variables.
ACTIVITY 1
A. Colleting the information relevant with Consumer price indices and Retail price index from
Office of National Statistics
To determine the changes incurred in the consumer price index for the period of 10 years
they have been collection of data set from Office of National Statistics which will be helpful in
presenting the appropriate analysis over issues. Along with this, there have been collection of
data of retail price index of same time duration (CPIH ANNUAL RATE, 2018). Therefore, these
are the details which reflect the trade power and purchasing power of buyers in UK economy.
1

Interpretation: On the basis of above listed table which represent the annual data of
consumer price index and retail price index for the year 2007 to 2017. However, the
proportionate outcomes have been gathered which ascertain that there have been huge
fluctuations in the data base. The consumer price index which is reflecting the outcome between
1% to 4% of scale. Conversely, RPI have reflecting the drastic changes in the outcomes. It has
negative result in 2009 of -0.5%. Thus, it had reflected the outcomes in between -0.5% to 5%.
2

B. Pictorial presentation of the data changing from 2007 to 2017.
Interpretation: On the basis of above listed graphical presentation of consumers price
index and retail price index in UK statistics which reflects the proportionate fluctuations.
However, in the initial phase there have been huge fluctuations a in the outcomes which not
reflecting the appropriate details and outcomes based on the data base. Thus, RPI have
comparatively more proper and appropriate percentage which represents the higher percentage
results than the CPIH. In respect with such outcomes it can be said that, Retail price index of UK
economy is comparatively strong as it is capable of bringing appropriate outcomes.
C. Ascertaining the differences between such variables
To analyse the differences between the Consumer price index and retail price index which
generally used in analysing the inflation rate of economy (Krackhardt, Schwab and Starbuck,
2017). Therefore, in the both the indexes there have bene use of basket for goods which
determines the accurate inflation rate. CPI have been projected in taking mean value of prices of
economic output which were bought by buyers while retail price index has been measured on the
basis of variation in the prices of the producer economic outputs. As per considering the above
listed outcomes and analysis on the data base which represent that the CPI index is
comparatively stable and reflecting the outcomes in between 1% to 4% while RPI is drastically
changing over the period. RPI have more than the expected outcomes as per considering the
3

challenges and changes in the business (Naidu and Sanford, 2017). On the other side, RPI have
higher returns or proportionate outcomes than compared to CPI. It determines that the producer
in the society are receiving adequate profitability which will bring them better operational
analysis.
D. Implicating the use of Consumer price index in analysing the annual inflation rate
Interpretation: On the basis of above listed table on which it can be said that, there have
been determination of inflation rate through Consumer price index. However, it has reflected that
there have been rise in the level of inflation as compared with the past periods. Thus, it indicates
that UK’s economy has been addressed to have the improper consumer price index. Thus, the
level of economy output and payments are not satisfactory in terms of reducing the inflation
rates. In 2012, 2013, 2014 and 2015 there have been negative inflation which are a favourable
market condition for the economy as the firm has appropriate outcomes. On the other side, in
2016 and 2017 there has been drastic changes in the inflation rate. Thus, the positive change in
inflation is challenging to the economy as there will be rise in the prices of various commodities
which will affect the per capita income as well as brings instability in financial condition of
nation.
4

E. Giving the reasons based on importance of analysing rate of inflation
On a national point of view, it is necessary to have proper ascertainment and analysis
over the inflation rates. Thus, it will help economists in analysing the economic condition and
they can produce a smart plan to overcome such crisis. On the other side, there have been various
importance of the inflation rate in the economy (Yu, He and Zhou, 2018). It insists that the rise
in the inflation rate which will impacts on uplifting the prices of commodities. To meet the
necessary requirement a consumer will spend more on such commodity which will help the
economy to have higher monetary circulation. Thus, there will be increment in the level of
money supply as government will have higher funds collection or reserves for the future
development.
Moreover, the rise in the inflation rate have negative impacts on the per capita income or
the GDP rate in an economy. People will start spending more on commodities which will affect
their savings therefore, there will be no money left in the banks (Huang and et.al., 2018).
Additionally, it will again invite the Global financial crisis. So, it is necessary to have
appropriate analysis over the inflation rate fluctuation which will help the economists in planning
the policies and designing rules which will help them in governing the operational tasks.
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M1 Critical evaluation of the sources other than Office national statistics with regard to Gender
pay gap
Interpretation: on the basis of current analysis over the gap between the gender pay gap in
UK where it can be said that, there is differences in the earning capacity and types of
employment. There are large number of part time job doers on which full time employees are
comparatively less. The gaps between such segmentation determines that people are more
comfortable in doing part time jobs. It ensures the appropriate level of employment in the part
time jobs which helps in balancing the GDP level as well as employment stability in UK.
ACTIVITY 2
1. Client B analysing the hourly pay rates in different UK regions
A. Presentation of ogive chart which states the details of median and quartiles of data set
To analyse the differences between the hourly earnings of the professionals at various
location there have been use of various statistical tools. The descriptive analysis of the data base
is comprised of analysing the median and quartile such as:
Median:
This a technique of identifying the difference among the variable of lower and higher
scale. Therefore, this value is equally or more than the value which will fall above. Along with
this, it is also known as middle value of the database which will be adequate in analysing the
outcomes and making appropriate operational analysis.
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Hourly Earnings CI 0 to 10 10 to 20 20 to 30 30 to 40 40 to 50
No. of leisure centre staff (F) 4 23 13 7 3
R frequency 4.00 % 23.00 % 13.00 % 7.00 % 3.00 %
CF 4 27 40 47 50
CRF 4.00 % 27.00 % 40.00 % 47.00 % 50.00 %
Hourly Earnings CI
No. of leisure canter staff
(F) CF
0 to 10 4 4
10 to 20 23 27
20 to 30 13 40
30 to 40 7 47
40 to 50 3 50
Median L+ Cf-n/ f* i
20+(40-5/ 50) * 10
27
Hourly Earnings CI No. of leisure centre staff (F)
0 to 10 4
10 to 20 23
20 to 30 13
30 to 40 7
40 to 50 3
Quartile 1 20.5
Quartile 2 21.40
Quartile 3 26
7

Interpretation: On the basis of above listed measurement for median and quartile analysis
on which the value has been derived through implicating various techniques. The median value
of the outcome has been analysed as 13 which falls between 10 to 20 hour working team.
Therefore, the mid value is 13. On the other side, there have been analysing over the quartile of
the frequency table which represent the same outcomes for all 3 quartiles such as 20.5, 21.40 and
26.
2. Calculating the standard deviation and mean value of hourly earnings:
On the basis of same variables there will be ascertainment of the mean value and standard
deviation. Therefore, it has been analysed as:
Mean value:
This determines the average of the data base which is will be based on analysing all outcomes
(Shingari, Kumar and Khetan, 2017). To analyse the mean value of the hourly earnings of the
London region employees which are as follows:
Hourly Earnings CI 0 to 10
10 to
20
20 to
30
30 to
40
40 to
50
Tota
l
No. of leisure centre staff
(F) 4 23 13 7 3 50
Mid value (X) 5 15 25 35 45 125
FX 20 345 325 245 135 1070
Mean ƸFX 1070
£
21.40
ƸF 50
8

Interpretation: On the basis of above listed analysis there have ascertainment and
analysis over the data base and variables which will be representing the adequate outcomes.
However, to analyse the mean value there have been use of mid value of the variables based on
scale such as 5, 15, 25 and so on that have been multiplied with the frequency. Therefore, to
analyse the average of the data base there have been use of sum FX which will be divided by
sum of frequency. Thus, it has present the mean value as 21.40 which represent that there are
average number of leisure centre staff is 21.40.
Standard deviation:
This analysis provides information regarding the quantity of expressing the group
differences from a mean value to the group (Amidon and et.al., 2018). However, there have been
analysis over the data base such as:
Hourly Earnings CI 0 to 10
10 to
20
20 to
30
30 to
40
40 to
50 Total
No. of leisure centre staff
(F) 4 23 13 7 3 50
Mid value (X) 5 15 25 35 45 125
FX 20 345 325 245 135 1070
DX= X-A -20 -10 0 10 20
FDX -80 -230 0 70 60 -180
FDX^2 6400 52900 0 4900 3600
3240
0
Standard deviation √ƸFdx^2/N - (ƸFdx/ N)^2
√32400/ 50 -(-180/50)^2
12.96
25.45584412
£10.15
Interpretation: In relation with the above listed analysis there have been ascertainment of
standard deviation of the outcomes. Considering the various variables and several measurements
which have represented the outcomes as 10.15. Thus, there are 10.15 is the difference between
the group or the hourly wages of London region employees.
B. Comparing the hourly earnings of Manchester and London region:
Particulars Manchester (£) London (£)
Median 14 27
Interquartile range 7.5 5
9