(PDF) Statistics for management | Assignment Sample

STATISTICS FOR
MANAGEMENT

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................1
ACTIVITY 1....................................................................................................................................1
A. Locating CPI, CPIH with reference to Office of National Statistics......................................1
B. Representing charts, table and graph for reflecting indices of year 2007 to 2017..................2
C. Retail price Index vs Consumer Price Index...........................................................................3
D. Extracting annual inflation with use of Consumer Price Index..............................................4
E. Reason about importance of inflation rate...............................................................................4
ACTIVITY 2....................................................................................................................................5
A.1 Ogive for estimating median and quartile of hourly earnings..............................................5
A.2 Standard deviation and mean for hourly earnings................................................................6
......................................................................................................................................................7
B. Comparing London and Manchester's earning........................................................................8
ACTIVITY 3....................................................................................................................................8
A. Carrying paired t test with 5% significance level...................................................................8
B. Usual conditions for paired t test.............................................................................................9
C. Constructing 99% confidence interval....................................................................................9
ACTIVITY 4..................................................................................................................................11
A. Indicating charts with CPI, CPIH and RPI from year 2007 to 2017.....................................11
B. Ogive for cumulative % of staff vs hourly earnings.............................................................12
CONCLUSION..............................................................................................................................12
REFERENCES..............................................................................................................................13

INTRODUCTION
Statistics are replicated as numerical statements of facts with reference to any department
of enquiry which is placed in relation to other. It refers to body of methodology and technique
which is developed for presentation, collection and analysis of quantitative data with application
of these data in context of decision making. There will be application different statistical tools
through management with context of showing outcome and aim of financial analysis, quality
assurance along with different operations of business areas. The present report will give brief
discussion about activities which are required for resolving research and business planning
issues. It will reflect CPI and RPI on basis of Office of National statistics website with tabular
and graphical format as well. Furthermore, it will show variations in these indices with method
of calculating annual inflation with its importance. This report will show proper analysis and
evaluation of hourly pay rates in different regions of UK with appropriate statistics such as mean,
median, quartile and standard deviation. In the similar aspect, it will be investigating mean with t
test at 5% significance and represent ogive chart for indices and staff% vs hourly earnings.
ACTIVITY 1
A. Locating CPI, CPIH with reference to Office of National Statistics
(CPI) Consumer Price Index: It is measure of average alteration over time in payment
of prices through urban consumers for market basket of consumer services and goods. It
accounts rising and falling prices as it is used as inflation measure with effectiveness of
economic policy of government. It provides businesses, citizens and government as idea related
to price alterations in economy as guide for taking informed decisions (O’Neill, Ralph and
Smith, 2017).
(RPI) Retail Price Index: It is also and particular measure of inflation which is
published through office of National Statistics as it reflects alteration in cost of representative
sample about retail services and goods. It considers items like housing, bus fares, household
goods and petrol as it weighs highly to food and housing and tobacco like products are lower
weighting.
CPIH: These indices considers owner occupier's housing cost and considers as lead
measure about inflation. It is replicated as comprehensive measure of UK and comprises owner
occupier's housing costs along with council tax as well. It uses approach referred as rental
equivalence for measuring OOH.
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Year 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
CPI 2.3 3.6 2.2 3.3 4.5 2.8 2.6 1.5 0 0.7 2.7
CPIH 2.4 3.5 2 2.5 3.8 2.6 2.3 1.5 0.4 1 2.6
RPI 4.3 4 -0.5 4.6 5.2 3.2 3 2.4 1 1.8 3.6
Interpretation: The above table is showing multiple indices of consecutive 10 years from
2007 to 2017. It has been observed that in year 2015 it was having 0 inflation as it shows
multiple fluctuations which was highest in year 2011 as 4.5. It perhaps as the best method for
gauging inflation amount in economy of UK. In the similar aspect, CPIH has been traced which
has considered owner's occupier's housing cost with range of 0.4 to 3.8 but on contrary, RPI has
abnormal changes with -0.5 in 2009 and sudden raise of 4.6 in 2010 as from year 2007 to 2017 it
decreased from 4.3 to 3.6 respectively. It is showing consumer purchasing power with trade of
United Kingdom.
B. Representing charts, table and graph for reflecting indices of year 2007 to 2017
Interpretation: The above graph is showing graphical format for indices with percentage
change from year 2007 to 2017. All indices have various fluctuations as there trend is approx
similar but in RPI there is drastic change from year 2009 to 2010 as it was negative and suddenly
it raised to 4.6 and started raising but it decreased till 2015 and raised till 2017 (James, 2018).
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Individual trend of each indice is plotted above and in UK, appropriate growth and stability with
motive for getting outcome in continuous aspect. Henceforth, it has been determined that clear
percentage is described in RPI whereas CPI is not able to give proper analysis and CPIH is
similar for other index and attained lowest in every year with growth in 2015 and 2016.
C. Retail price Index vs Consumer Price Index
Particular Retail Price Index Consumer Price Index
Originated In 1956, it was originated in Unite
Kingdom.
In 1996, it was originated in European
Union.
Objective For monitoring cost of living with
context of government planning with
context of various arrangements.
The Euro countries are compared for
compliance with treaty of Maastricht.
Exclusions Life insurance, Income tax, national
insurance and charges of pensions
Council tax, house prices, building
insurance, holiday spending abroad,
ground rent, Income tax and national
insurance
Considerati
ons
Spending related to abroad on holiday Tuition fees of foreign students and
Forex commission with perspective of
tourists.
Averaging
data
Combination of ratio of average along
with relatives or arithmetic mean
It applies geometric mean and some
normal ratio with perspective of
average.
Weighing
data
The living cost of ONS and food
survey.
The household monetary consumption
expenditure with its component of
multiple national accounts.
Population The wealthy and pensioners are
excluded with state benefits.
Every residents of United Kingdom.
Application
to index
Government debt payments as they pay
with negotiations and pensions for
Public service pensions, benefits and tax
credits
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private sector (Zhao and et.al., 2018).
CPIH is similar to CPI as it will attempt for adding measure on basis of owner occupiers'
housing costs and H stands for housing as it is used estimating this cost and aggregated to CPI
for creating CPIH. Hence, this method is used for extracting OOH as Rental Equivalence and it
will not measure some specific things like house prices, water rates etc.
D. Extracting annual inflation with use of Consumer Price Index
Year 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
CPI 2.3 3.6 2.2 3.3 4.5 2.8 2.6 1.5 0 0.7 2.7
Annua
l
Inflati
on 0 0.57 -0.39 0.5 0.36 -0.38 -0.07 -0.42 -1 0 2.86
Particulars Formula
Inflation Rate (CPI 2 – CPI 1)/ CPI 1
CPI 1 Consumer rice index of 1st period
CPI 2 Consumer price index of 2nd period
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E. Reason about importance of inflation rate
Inflation is elaborated as increase in level of general price as it is price of various goods
and services related to apparel, housing, transportation, fuel and food should be raised in order
for incurring inflation in overall economy. The data through rate of CPI and RPI are used in
multiple ways through businesses and government and has very vital role for setting economic
policy. The main reason is that bank of England will be using inflation for setting interest rates.
In case committee of monetary policy of banks has CPI inflation in increasing manner along with
rate of interest with trial of subdue it. On the contrary, inflation will be likely to decrease with
similar percentage as it might cut interest rates as well. This is the main reason that inflation is
considered as crucial factor for identifying rate of bank charges with context of mortgages and
rate offers for savings of accounts (Importance of Inflation for Industry, 2016). In the similar
aspect, it will impact on income of some people as any description about index linked rise in line
with perspective of inflation as measured from RPI and CPI.
ACTIVITY 2
A.1 Ogive for estimating median and quartile of hourly earnings
The difference has been analysed among hourly earnings of its professionals at multiple
locations so in this context, different statistical tools has been applied. There is presence of
descriptive analysis of data base which consists of analysing quartile and median like:
Median
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The median could be calculated with application of formula as L + Cf – n / f * I as in numerical
format it is 20 + (40 – 5 / 50) * 10 and its final outcome is 27.
Quartile 1: 20.5
Quartile 2: 21.40
Quartile 3: 26
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Interpretation: The above analysis has extracted median and quartile with reference to
ogive chart where its median is 27 which come in 20 to 30 hour working team as it is its mid
value. While analysing quartile, there is extraction of quartile which has been articulated as 20.5,
21.40 and 26. This is statistical term which helps in giving description with multiple provisions
on its observations in different interval as Q1, Q2 and Q3.
A.2 Standard deviation and mean for hourly earnings
Mean value:
Interpretation: The above table is extracting mean value of hourly earnings with
different range and their mid value is pertained with gap of 10 such as 5, 15, 25 and like this till
45 as its aggregate is 125. There is multiplication of frequency and middle value whose sum is
1070. With application of these amount in formula, its mean is 21.40 (Liu and et.al., 2018).
Standard deviation:
It is referred as measure of dispersion with specific data set which is extracted from
mean. This analysis will be giving information on basis of quantity which is directly reflecting
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group variations through mean value of group. On the contrary, there is appropriate analysis of
this data base is provided below:
Interpretation: The formula for calculating standard deviation is √ƸFdx^2/N - (ƸFdx/
N)^2 which is √32400/ 50 -(-180/50)^2 and extraction as 10.15. There is consideration of
different variables and numerous measurements with variation among hourly wages and
employees of London.
B. Comparing London and Manchester's earning
Particulars Median Interquartile range Mean Standard deviation
London (£) 27 5 21.4 10.15
Manchester (£) 14 7.5 16.5 7
Interpretation: The above data is representing comparison among two regions of UK as
London and Manchester with application of Interquartile range, median, standard deviation and
mean. The median of both region such as London has 27 and Manchester as 14 where London is
leading and interquartile range has very fewer variations. The IQ range of London is 5 and
Manchester as 16.5. In the similar aspect, the mean is 21.4 and 16.5 respectively through which
standard deviation is extracted as it shows that London has high risk movements as compared to
Manchester (Guo and et.al., 2018).
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ACTIVITY 3
Setting hypothesis:
Null hypothesis: No significant variation among mean value of new and old system.
Alternative hypothesis: Significant difference in mean value of new and old system.
A. Carrying paired t test with 5% significance level
Regression Statistics
Multiple R 0.959
R Square 0.920
Adjusted R Square 0.911
Standard Error 3.367
Observations 10
Annova table
df SS MS F Significance F
Regression 1 1050.15 1050.15 92.63 0.000011
Residual 8 90.70 11.34
Total 9 1140.85
Coefficients
Standard
Error t Stat P-value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept 7.04 5.20 1.35 0.21 -4.95 19.03 -4.95 19.03
New
system 0.89 0.09 9.62 0.00 0.68 1.10 0.68 1.10
B. Usual conditions for paired t test
Interpretation: The above table is deriving t test with two sample means with 5%
significance level or 95% confidence interval. The criteria for selecting alternative or null
hypothesis on basis of p value as if p value is more than 0.05 then null hypothesis is accepted and
vice versa. In the above criteria, its value is derived as 0.000011 which is less than 0.05 so
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alternative hypothesis is accepted. It could be interpreted as that there is significant difference in
mean value of new and old system (Musa and Mahmud, 2018).
C. Constructing 99% confidence interval
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Coeffi
cients
Stand
ard
Error t Stat P-value Lower 95% Upper 95%
Lower
99.0%
Upper
99.0%
Intercept 7.04 5.20 1.35 0.21 -4.95 19.03 -10.40 24.48
New
system 0.89 0.09 9.62 0.00 0.68 1.10 0.58 1.20
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Interpretation: The above outcome is t test with 99% confidence interval as it has
analysed via operations according to operations. There is result with deriving about p value with
specified criteria in above test. Here, significance value is less than 0.05 then alternative
hypothesis is accepted where it could be interpreted that there is presence of significance
difference in old and new system (Sun and et.al., 2018).
ACTIVITY 4
A. Indicating charts with CPI, CPIH and RPI from year 2007 to 2017
Interpretation: The above bar chart is showing percentage change of CPI, CPIH and RPI
over past 10 years as 2007 to 2017. Henceforth, RPI has presence of high percentage outcome as
it directly insist about number of producer which are directly retaining sufficient earning in
market and this will directly impact on raising inflation.
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B. Ogive for cumulative % of staff vs hourly earnings
Interpretation: The above graph is reflecting ogive chart of hourly earnings and
cumulative % staff with presence of various differences and plot value has considered
cumulative. Furthermore, there is reflection of frequency polygon along with data value on
particular point and it has determined middle and quarter of specific data set.
CONCLUSION
From the above report it had been concluded that, statistics plays important role in
business as they are very crucial for measuring different parameters. It had shown analysis of
database in accurate aspect with implication of numerous statistical tool. In the similar aspect, it
had been articulated that, using descriptive statistics which comprises mean, median, standard
deviation and quartile of data base shows appropriate analysis. Further, it had shown that
inflation could be measure with retail price index and consumer price index to be appropriate and
sufficient to bring proper ascertainment of data set.
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