Statistics for Management Solved Assignment - Doc

STATISTICS FOR
MANAGEMENT

Table of Contents
INTRODUCTION...........................................................................................................................1
ACTIVITY 1....................................................................................................................................1
A) Locating data by collecting data from ONS of last ten years for CPI and RPI.....................1
B) Preparation of graph and table for the data displayed............................................................2
C) Highlighting Retail Price Index (RPI) vs Consumer price Index (CPI).................................4
D) Calculating annual inflation by applying CPI........................................................................5
E) Significance of inflation rate..................................................................................................5
ACTIVITY 2....................................................................................................................................6
A) Calculating hourly pay rates of staff......................................................................................6
1. Using an ogive for estimating median hourly earnings and quartiles.....................................6
2. Computing mean and standard deviation for extracting hourly earnings...............................8
B) Making comparison of two different regions in terms of earnings........................................9
ACTIVITY 3..................................................................................................................................10
A) Finding economic order quantity.........................................................................................10
B) Deciding how often tee-shirts need to be ordered................................................................10
C) Calculating inventory policy cost.........................................................................................10
D) Finding current service level to customers..........................................................................10
E) Working out re-order level for the business.........................................................................10
ACTIVITY 4..................................................................................................................................10
A) Producing bar or line charts with reference to RPI and CPI for 2007 to 2017....................10
B) Preparation of ogive chart of cumulative percentage of staff versus hourly earnings.........11
CONCLUSION..............................................................................................................................11
REFERENCES..............................................................................................................................13

INTRODUCTION
Statistical methods are useful for extracting data through incorporating mathematical
equation and output is attained in quantitative format. Appropriate information is provided with
the help of statistics. It is helpful for management of company in order to deal with quality
assurance, operations, production and making financial analysis in business areas. Present report
deals with analysis of RPI and CPI from ONS website for assessing variations. Moreover,
different activities provided by clients in raw data format will be converted into the output by
using appropriate statistical methods. Moreover, computation of EOQ will be made along with
95 % of interval. This will help business to make effective inventory cost policy as it will be
reduced by carrying out EOQ by purchasing optimal quantity of goods.
ACTIVITY 1
A) Locating data by collecting data from ONS of last ten years for CPI and RPI
Retail Price Index
The retail price index as the name suggests effectively is a measure initiated by ONS
(Office for National Statistics) for measuring change in cost of sample which is representative of
retail commodities and services in the best possible manner. This type of index is used for
measuring changes observed in cost of buying “basket” of commodities in terms of inflation
prevailing in the economy (Cavallo, 2017). For the fix period, this index is calculated in effective
manner. The goods or services comprises household goods, petrol, diesel, bus fares and food
products etc. In addition to this, weighing of commodities are related to necessity basis as
housing goods and on the other hand, tobacco comes at lower weight.
Consumer price Index
The Consumer price index is mainly utilised for calculating inflation in the best manner
possible. It is effectively used by national statistical agencies with relation to yearly change in
CPI and is considered as relative measure of inflation. In other words, it is a measure of
alteration observed in price for the commodities and services such as medicine, transportation
and products like grocery items are adequate benchmark for analysing cost of inflation along
with cost of living (Zant, 2018). CPI, hence, is used for assessing purchasing power of customers
whether they stay with current price prevailing in the market or not. Hence, CPI and RPI are
used for assessing inflationary situations in the UK economy.
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Interpretation-
The table made above is constructed for assessing RPI and CPI. The data is taken from
ONS which is statistical agency of UK from period ranging from 2007-2017 consisting of 10
years. It can be evaluated that several fluctuations could be observed in above data base with
reference to purchasing power of UK citizens for past 10 years. The CPI was 2.4 in 2007 which
reached to 3.5 in 2008 and decreased to 2 in next year. Furthermore, figure was 2.5 in 2010,
increased to 3.8 in 2011, 2.6 in 2012. However, it went on reducing to 2.3 in 2013 to 1.5 in 2014,
0.4 in next period. In addition to this, it reached 1 in 2016 and 2.6 in recent year. The Highest
rate of CPI is 3.8 in 2011 and lowest is 0.4 in 2015. While, the highest rate of RPI is 5.2 in 2011
and lowest in 2009 as it reached to -0.5.
B) Preparation of graph and table for the data displayed
Illustration 1: Percentage in RPI
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Illustration 2: Percentage change in CPI
Illustration 3: CPI and RPI indexes
Interpretation-
It can be analysed from the above graphs reflecting percentage changes observed in RPI
and CPI for the past 10 years as data provided from ONS and other reliable sources. It can be
assessed that highest rate of RPI was observed in 2011 as it reached to 5.2 %. However, lowest
rate was in 2009 to -0.5 highlighting lowest RPI rate in the period. On the other hand, CPI is
common measure for calculating inflation was 0.5 % in 2015 as it is reflected in chart prepared
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above. Thus, it can be concluded that RPI of UK has accelerated growth and capability for
attaining better results.
C) Highlighting Retail Price Index (RPI) vs Consumer price Index (CPI)
RPI and CPI are effective methods or techniques for calculating inflation in a better
manner. Basket of goods and services are analysed and as a result, inflation is carried out. CPI is
estimated and average price is extracted out purchasing power of consumers whereas RPI
measures difference in prices of output of retail goods (Cavallo, 2018). Difference can be
analysed in both indexes' is that interest payment for mortgage is excluded in CPI while, RPI
does include the same.
RPI CPI
The population size is small of RPI in
comparison to CPI.
It has large relative large population.
On the other hand, RPI uses arithmetic mean
where number of items' is divided by sum of
their price.
CPI uses geometric mean for assessing
difference current and previous price.
The value of RPI extracted through figures are
higher in comparison to CPI (Schmidt and
et.al., 2017).
It is relatively lower.
RPI includes housing cost, interest payment of
mortgage, road fund license, taxes for council
and building insurance are used for measuring
inflation.
These measures are excluded in calculating
CPI. It includes tuition fees of students,
university accommodation for foreign students.
It can be analysed that differences do exist in both types of indexes. Alterations in price
of goods and services is used as major implication is because of price estimation with
distinguished target customers. Thus, these indexes help to measure inflation from different
perspectives quite effectually.
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D) Calculating annual inflation by applying CPI
Interpretation-
The above table reflects computation of annual inflation with reference to CPI in the best
manner possible. It implies that payment results are inappropriate for decreasing inflation rate in
terms of negative inflation for the period ranging from 2012-2015. This is evident that in 2012,
inflation was -0.32 which reached to -0.12 in next period. Moreover, the figure was -0.35 in 2014
and increased to -0.73 in the financial year 2015. RPI has also faced drastic change over the past
years and sudden change is observed with reference to inflation prevailing in the economy of
UK. If in case, inflation is rising in positive manner, it will not be fruitful for economy. This is
because it will be challenging for the economy on basis of high prices of goods and services
leading to affect per capita income. Moreover, financial stability will be lost leading to have
adverse effect on economy diverted to slower economic growth.
E) Significance of inflation rate
The inflation is required to be computed in order to assess how change in current prices
are occurred with reference to earlier prices of goods and services (Ball, 2017). In simple words,
it is useful as it provides clarity regarding reasons for increment in prices. Elevation in general
price level of items and services are regarded to as inflation. It is essentially required as rise in
prices directly affect the pocket of customers leading to reduce purchasing power of customers
quite effectually. High inflation rate affects economy as divestment starts of following reasons
listed below-
Uncertainties in behaviour-
It can be analysed that rise in inflation and rise in volatility are crucial factors which
creates uncertainties in terms of price and cost in the future. This is the main reason leading to
divestment in economy and decreasing demand of products and services in the economy (Why is
inflation important for the economy?. 2018).
Unsustainable inflationary situations-
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Inappropriate adjustments are made by banks of deflationary fiscal policy and such
inappropriateness leads to increase in interest rate. This will lead to increase in inflationary
situations will lead to create recession in economy.
It can be assessed from the facts that inflation is significant. Moreover, debtors will be
able to know about their efficiency for repayment of loan amount. Borrowings and lending
accelerates and increases level of spending, if inflation is controlled in UK.
ACTIVITY 2
A) Calculating hourly pay rates of staff
1. Using an ogive for estimating median hourly earnings and quartiles
Median-
It is middle most value which is calculated from the data set by dividing it into equal and
separate manner usually arranged in ascending order. In other words, median is the value
obtained by separating higher half from the lower half in effective manner. It is commonly used
method for making separation of data in a better way. Data is arranged from least to greatest and
middle most value is ascertained.
Median Formula: L- Cf-n/ f* I
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= 20 – (40-5) / 50 * 10
= 13
Interpretation-
It can be analysed from the above chart that median and quarterly earnings are computed
with reference to the number of leisure centre staff. Variations are analysed in effective manner
which provides clarity that median and quartile have variations in them. The value arrived by
incorporating formula of mean is 13 which falls within the range of 10-20 team hours. It reflects
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that median is 13 and result of quartile comes to 3. Quartile is another useful statistical technique
that divides data set into four equal part of the data set.
2. Computing mean and standard deviation for extracting hourly earnings
Mean-
It is one of the useful method of calculating average among the data set in effective
manner. In simple words, average of numbers are arrived at by incorporating formula of mean.
The formula of mean is sum of the values being divided by number of values which gives value
of mean. It is also termed as arithmetic mean in statistical language. Primary method is utilised
for calculating average of series for attaining outcome quite effectually.
Mean formula:
= Sum of values / Total numbers
=1070 / 50
= 21.4
It can be interpreted from the above table that mean has been calculated for arriving at
hourly earnings in effective manner. The mean value arrived is 21.4 by taking into account
different variables and mid values such as 5, 15 and 25 which are having similar trend in
effectual manner. Thus, mean is 21.4 attained by sum of values of 1070 and divided by total
number, 50.
Standard deviation-
The standard deviation is termed as quantity of expression by how much the numbers in
the data set differ from that of mean in the same group. In simple words, amount of variation
between data values are arrived in a better manner. This technique has proven to be beneficial for
financial management personnels and portfolio personnels.
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Standard deviation (Formula): √ƸFdx^2/N - (ƸFdx/ N)^2
Fdx = -180
Fdx ^ 2= 32400
N = 50
= √32400 / 50 -(-180/50) ^ 2
= -9.36
The above computation shows that standard deviation is -9.36 and as a result, mean and
standard deviation have high variations. This is evident from the fact that hourly wages of
employees in London are highly dispersed.
B) Making comparison of two different regions in terms of earnings
Interpretation-
It can be analysed from the above computation is that London and Manchester region on
hourly basis which are carried out by applying descriptive statistical methods. It can be analysed
that median of London is 13 and of Manchester is 14 implying clearly that rivalry has become
intense. The standard deviation, interquartile range and mean are calculated for the two regions
showing huge difference among them. Mean of Manchester is 16.5. On the other hand, mean of
London is 13. While, interquartile range of London is 3 and of Manchester is 7.5.
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ACTIVITY 3
A) Finding economic order quantity
Annual demand 30000
Holding cost 10
Fixed cost 5
Formula,
EOQ = 2 DO / C
= 2 * 30000 * 5 / 10
= 173.21
Where annual demand is calculated by, 30 * 20 (selling price) = 600 * 50 weeks in a year =
30000.
B) Deciding how often tee-shirts need to be ordered
As per the EOQ calculated, firm needs to effectively order 173 quantities in order to
satisfy demands in the best manner possible. This will lead to attainment of desired production
by the business and inventory will be handled in a better manner.
C) Calculating inventory policy cost
The inventory policy cost is also called as total cost.
Holding cost + Fixed cost
= 10 + 5
= 15
D) Finding current service level to customers
The current service level can be founded that standard deviation is 15 tee-shirts and
average demand on weekly basis turns out to be 30. Hence, it is required that 173 quantities
should be ordered for reducing inventory costs and fulfilling demand in effective manner.
ROL and service level to customers
ROL = dL + S
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150 = 30 * 4 + S
S = 30
S = z σ d√L
30 = z * 15 * √4
z = 1
Service level approx 84 %.
E) Working out re-order level for the business
Computation of Safety Stock
Maximum daily sales 84.98
Maximum lead time 30
Average daily sales 80
Average lead time 28
(Maximum daily sales * Maximum lead time)
(2) 2549.4
(Average daily sales * Average lead time) (1) 2240
Safety Stock (2-1) 309.4
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ACTIVITY 4
A) Producing bar or line charts with reference to RPI and CPI for 2007 to 2017
Interpretation-
It can be interpreted from the above chart that CPI and RPI are being extracted for last 10
years of time period. Range of CPIH consist of 1 to 3.8, while of RPI have -0.5 to 5.2 range.
These indexes reflect that more number of producers have adequate earnings within retail market
that maximises inflation rate in UK.
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B) Preparation of ogive chart of cumulative percentage of staff versus hourly earnings
Interpretation-
The above ogive chart shows changes occurred in leisure centre staff (cumulative %)
versus hourly earnings that are plotted on the chart. Moreover, frequency polygon on data has
been represented graphically above and below the point determining quarter and middle of data
set in effective manner.
CONCLUSION
Hereby it can be concluded that statistical methods are crucial for making assessment of
business operations in the best manner possible. The report has given outcome with regards to
efficiency of Manager within selected firm for making judicious decision-making for
accelerating business growth with ease. The decision-making tools such as CPI and RPI are
effective for measuring inflation in the UK economy quite effectually. The report also provided
that management will incorporate appropriate statistical technique for measuring production
level and increase productivity up to a high extent. On the other hand, EOQ is also being
calculated which effectively shows how company will be able to minimise total inventory costs
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by purchasing optimal order size which will be beneficial for making inventory policy in
effective manner.
CPI and RPI measures are of much importance for carrying out inflation and scale of it as
it has direct impact on economic growth. RPI measure provide adequate measures and CPI gives
detailed view in terms of variables being entered. Moreover, graphical representation of RPI and
CPI are also done with reference to last 10 years highlighting fluctuations occurred among them
which are easily understandable with the help of graphs made.
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REFERENCES
Books and Journals
Ball, R. J., 2017. Inflation and the Theory of Money. Routledge.
Cavallo, A., 2017. Are online and offline prices similar? evidence from large multi-channel
retailers. American Economic Review. 107(1).pp.283-303.
Cavallo, A., 2018. Scraped data and sticky prices. Review of Economics and Statistics.100(1).
pp.105-119.
Schmidt, O. and eta.l., 2017. The future cost of electrical energy storage based on experience
rates. Nature Energy. 2(8). p.17110.
Zant, W., 2018. Trains, Trade, and Transaction Costs: How Does Domestic Trade by Rail Affect
Market Prices of Malawi Agricultural Commodities?. The World Bank Economic
Review. 32(2). pp.334-356.
ONLINE
Why is inflation important for the economy?. 2018 [Online] Available Through:
<https://learn.stashinvest.com/why-is-inflation-important-for-the-economy>
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