Statistics for Management: Client Data Analysis and Report (2024)

This report presents a comprehensive statistical analysis for management, encompassing various datasets and statistical techniques. It begins with an analysis of national statistics, focusing on consumer and retail price indices from 2007 to 2017, presenting the data in tables, charts, and graphs to illustrate trends and differences. The report then delves into the determination of hourly pay rates for a client in different UK regions, calculating median hourly earnings, quartiles, mean, and standard deviation. Further analysis involves comparing leisure center staff data from Manchester and London. The study also includes a paired T-test to analyze the difference between new and old systems for processing insurance claims, along with a discussion on the general conditions for the test. The report concludes with a summary of the differences between indices and a presentation of Ogive curves. The report aims to provide insights into data interpretation and statistical methods relevant for management decision-making.

Statistics for
Management

Table of Contents
INTRODUCTION...........................................................................................................................1
ACTIVITY 1....................................................................................................................................1
a Collection of data from National statistics related with price indices.....................................1
b Representing the changes in indices from 2007 to 2017 in form of tables, charts and graphs
.....................................................................................................................................................2
c Presenting the differenced between above indices..................................................................3
d Presentation of data annual inflation with the data collected above......................................3
e. Presenting the importance on why knowledge of rate of indices is essential.........................4
ACTIVITY 2 ...................................................................................................................................4
1. Determination of hourly pay rates for Client B in Different regions of UK...........................4
A(i). Presenting median hourly earnings and thee quartiles by using ogive estimates.............4
A(ii) Calculation of the mean and standard deviation for hourly earning.................................6
b. Identical survey of leisure central staff in Manchestar and London and its comparison ......7
ACTIVITY 3....................................................................................................................................7
1. Analysis the difference between new and old system for client E regarding processing
better insurance claim.................................................................................................................7
a. Determination of paired T-teat at 5% of significant level......................................................8
b. Presenting the general condition for a paired T-test...............................................................8
ACTIVITY 4....................................................................................................................................9
a. Presentation of the differences between indices form the data collected from office of
national statistics.........................................................................................................................9
b. Presentation of Ogive for cumulative % of staff versus hourly earnings............................10
CONCLUSION..............................................................................................................................10
REFERENCES..............................................................................................................................11

INTRODUCTION
The business operations of an organisation are controlled and operated by the
management of the firm. Various tools and techniques are used by the managers to evaluated
performance of the entity in terms financial and non financial terms. With use and application of
statistical tools the performance are analyzed and along with this the forthcoming threats and
opportunist are also determined so that timely actions can be taken to overcome or handle the
situation. In the present report interpretation and evaluation of different data related with various
clients is carried out which is collected through reliable resources. Data from National statistics
is also gathered and along with this, statistical tools such a mean, median and mode, quartile and
standard deviation are calculated. Data is presented in way of pictures and graphs that aids in
determination of changes in variables.
ACTIVITY 1
a Collection of data from National statistics related with price indices
In the present activity data from National statistical website is collected from consumer
price index and Retail price index for a period of 10 years. With collection of data and analysis
of the current and past position is carried out.
Year CPIH RPI
2007 2.4 4.3
2008 3.5 4.0
2009 2.0 -0.5
2010 2.5 4.6
2011 3.8 5.2
2012 2.6 3.2
2013 2.3 3.0
2014 1.5 2.4
2015 0.4 1.0
2016 1.0 1.8
2017 2.6 3.6
Consumer price index:
The consumer price index is a measure that examines the changes in price level of market
basket of consumer goods and services (Consumer price inflation, 2018). This is computed by
taking price changes for each item in the basket of goods and then averaging them. Same
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procedure is carried out for services as well. The CPI are asses the price changes with cost of
living of the consumers.
Retail price index:
The retail price index is one of the two measure to of consumer price inflation. This index
analyses changes in the cost of fixed basket of goods over a given period. In another words it can
be explained as a measure to compute changes in the cost of a representative sample of retail
goods.
Interpretation:
The above table represent the annual data of consumer price and retail price index from
the period 2007 to 2017 (Retail Price Index, 2018). The CPI index have seen many fluctuations
with up and down. The lowest CPI was in year 2015 with 0.4 and highest was in year 2011 at
3.8. This reflects that CPI outcomes are reflating between scale of 1-4%.
On the other hand RPI have also seen sudden fluctuation with reaching of negative at 0.5
in year 2009 from 4 in the previous years. With this it can be interpreted that RPI outcomes are
reflating in between scale of -0.5 to 5.5%.
b Representing the changes in indices from 2007 to 2017 in form of tables, charts and graphs
Interpretation:
The above diagram is the graphical representation of consumer price index and retail
price index in the context of UK which reflects the fluctuation in both price indexes. From
period 2007 to 2011 both have seen major fluctuation and they do not related with each other
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proportionally. From year 2012 the changes in both prices indexes were same as it can be sen in
the graph then both liners graphs are moving in sames direction in same manner. However, it can
be stated that as compared between both RPI have better percentage. In this context it can be
interpreted that retail price index of UK is more crucial as it gives appropriate and significant
outcomes.
c Presenting the differenced between above indices
The consumer price index reflates the changes in the price level of market basket of the
goods and services offered to consumers (Baak and et.al., 2015. This examine the percentage
changes in the prices of given consumer goods with considering each good separately and then
averaging the to get the outcome of level of price change in a year. On the other hand the retail
price index is one of the measure to calculate the CPI. With the interpretation of both the
inflation and changes in price of the consumers goods in a year can be articulated. The CPI have
changes with times but the fluctuation in RPI are more significant and sudden with experiencing
a negative index in year 2009. On comparing both indices it is determined that between these
two RPI have high level of returns.
d Presentation of data annual inflation with the data collected above
Year CPIH Inflation rate
2007 2.4 0
2008 3.5 46%
2009 2.0 -43%
2010 2.5 25%
2011 3.8 52%
2012 2.6 -32%
2013 2.3 -12%
2014 1.5 -35%
2015 0.4 -73%
2016 1.0 150%
2017 2.6 160%
Interpretation: the above table represents the inflation rate in UK economy with the use
of Consumer price index. In the table it can bee seen that in 20008 the rate was at good pace in
next year had a sudden fall and reached to -43%. for next tow yet the rate of inflation was goods
but to performed badly for years 2012-2015. For a period of 4 sprayers the rate was negative. In
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year 2016 and 2017 the inflation rate have grown by immanence level with 150 and 160%
respectively.
e. Presenting the importance on why knowledge of rate of indices is essential
For a nation it is important to determined the inflation rate, at it assists the statistical and
financial authority and economists of the country to evaluation the financial position and the
status and development level of national economy (Heeringa, West and Berglund, 2017). The
inflation rates are determined with consumer price index as it analyses the change in the prices in
market basket of consumer goods and services. The calculation of CPI depends on RPI, so
articulation of both are important for national economy.
ACTIVITY 2
1. Determination of hourly pay rates for Client B in Different regions of UK
A(i). Presenting median hourly earnings and thee quartiles by using ogive estimates
This activity is related with the determination of difference between hourly earnings of
the professional from different parts of regions. For this different statistical tools and measures
are used and applied which are median and quartile.
Median:
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
13
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Median can be defined as middles number in the range or sequence of number. This tool
is used to determine the difference between lowest and highest value in the scale (statistical
mean, median, mode and range, 2018). To determined median vales all the values in data are
organized in a specific order such as by size, number. The value in the middles is the median
value.
Interpretation: from thee above table it can be interpreted that median value for
employees relative with their hourly wages is calculated as 13. The range of wages per hour is
set with a difference of 10 as 0-10, 10-20 and so on.
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 3
Quartile 2 3
Quartile 3 3
Quartile: this can be stated as division of data into three parts as lower, middles and
upper quartiles. It is calculated as division of data into equal intervals which is based upon the
values and comparison is carried out for whole set of data.
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Interpretation: from the above table of quartile calculation it can be seen that there is on
difference between all three quartiles, all are giving same results. With this it can be stated that
there no significant difference between all observations.
A(ii) Calculation of the mean and standard deviation for hourly earning
Following tables represent the calculation of standard deviation and Mean values from
the same data which is used in previous questions.
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
Mean ƸFX 1070 £ 21.40
ƸF 50
Mean value: the mean vales of a variable data can be interpreted as the average of the
sum of all the outcomes in the data (Carande-Kulis and et.al., 2015). This is calculated with
summing up all the outcomes of variable and dividing it by the number of variables.
Interpretation: from the above label representing the calculation of mean values it can
be interpreted that mean value for variable have comes out to be 21.40. For executing the
calculation the mid values of the variables have been taken as 5,15,25, 35 and so on, which have
been determined as multiples of 5. The total sun of all the variables is interpreted as 1070 and
the total number units of variable is determined as 50 which gives a mean value of 21.40.
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 32400
Standard deviation √ƸFdx^2/N - (ƸFdx/ N)^2
√32400/ 50 -(-180/50)^2
12.96
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25.45584412
£ 12.50
Standard deviation: this is a statistical tool which measures the dispersion of a data
relative to it mean value. This is valuated as square root of the variance between the data point
relative to the mean.
Interpretation: In the above table the standard deviation is calculated for the mean vales
of CF relative to the hourly earnings. This represent the deviation or different between hourly
earning and number of employees in the London staff. The standard deviation is calculated as
12.5 which states the fact that the deviation of hourly earnings relative to the employees in
Landon region.
b. Identical survey of leisure central staff in Manchestar and London and its comparison
Particulars Manchester (£) London (£)
Median 14 13
Interquartile range 7.5 3
Mean 16.5 13
Standard deviation 7 12.5
Interpretation:
From the above table it can be interpreted The median value of Manchester is 14 and for
London it is 13 with a difference of 1. The mean values are 16.5 and 13 for Manchester and
London respectively and the difference in has values have increased (Tsou and Huang, 2018).
The interquartile range for Manchester is high at 7.5 as compared to London at 3. On the other
had the standard deviation is high for London at 2.5 when compared with Manchester at 7.
ACTIVITY 3
1. Analysis the difference between new and old system for client E regarding processing better
insurance claim
Hypothesis:
Null Hypothesis: No statistical significant difference between the mean value of new and old
system.
Alternative Hypothesis: there is statistical significant difference between mean value of new
and old system.
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a. Determination of paired T-teat at 5% of significant level
t-Test: Paired Two Sample for Means
Old system New system
Mean 56.01 54.95
Variance 126.761 146.925
Observations 10 10
Pearson Correlation 0.959425792
Hypothesized Mean Difference 0
df 9
t Stat 0.975056517
P(T<=t) one-tail 0.177504908
t Critical one-tail 1.833112933
P(T<=t) two-tail 0.355009816
t Critical two-tail 2.262157163
Interpretation:
From the above table it can be interpreted that T-test analysis have been used to
determination of outcome of old and new system. The one tail relation between old and new is
determined as 0.177 and for two tails it is 0.35. A result between -1 to +1 reflect moderate
relationship between two variables. Both one and two tail relation are between -1 to 1 and with
this it can be articulated that both have a null hypothesis and there is a statistical significant
relation between old and new system.
b. Presenting the general condition for a paired T-test
T-Test: Paired Two Sample for Means
Old system New system
Mean 56.01 54.95
Variance 126.761 146.925
Observations 10 10
Pearson Correlation 0.95942579
Hypothesized Mean Difference 0
df 9
t Stat 0.97505652
P(T<=t) one-tail 0.17750491
t Critical one-tail 2.82143793
P(T<=t) two-tail 0.35500982
t Critical two-tail 3.24983554
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Interpretation:
From the above table it can be determined that one tail outcome at p tail for new and old
system comes out to as 0.177 on the other hand for Two hand tail it comes out at 0.35 (Gibbons,
2015). the value is less than 0.75 which reflates the fact of strong presence of null hypothesis
and both the variables are moving in different direction. The outcomes between new and old
system are moderate.
ACTIVITY 4
a. Presentation of the differences between indices form the data collected from office of national
statistics
Interpretation
The above bar graph is a graphical representation percentage change in he both indices
that is consumer price and retail price index for a period of 10 years from 2007 to 2017. RPI
have a greater outcomes in percentage from as compared to CPI in all 10 years (Harrell, 2015).
This represents the fact that the manufactures in the market are gaining a command over earning
in the market place and also this have an significant effect on inflation initiation.
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b. Presentation of Ogive for cumulative % of staff versus hourly earnings
Interpretation
The above diagram is a graphical representation in from of Ogive chart for staff and their
hourly earnings. This interprets the difference between frequency value and CF values of data
base (Lau and Tang 2018). Form the above Ogive chart it can be articulated that for the range of
1-10 the outcomes and increment levels are same but with 10-20 range the CF value started to
fall and frequency values are rising constantly from further range of 20-30 and so on.
CONCLUSION
From the above report it can be articulated that for signification and accurate analysis of
various data of the organisation, application and implementation of statistical tools and measure
has been required essentially. The inflation of the economy have a significant effect of consumer
price and retail price index. Further it can be articulated that statistical tools used for analysis of
data as mean, median, mode, standard deviation and quartiles. All this tools together aids the
organisation in an effective and significant analysis of the data with single and double variable,
which assists the management in decision making process and help in determination future plans
of action.
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