Statistics for Management Report

This report examines the role of statistics in management decision-making. It analyzes inflation trends using CPI, CPIH, and RPI, and explores inventory management techniques like EOQ and reorder level. The report provides practical examples and calculations to illustrate the concepts.

Statistics for Management

Table of Contents
INTRODUCTION...........................................................................................................................3
Activity: 1........................................................................................................................................3
Activity 2.........................................................................................................................................9
Activity 3.......................................................................................................................................12
Activity 4.......................................................................................................................................13
CONCLUSION..............................................................................................................................18
REFERENCES..............................................................................................................................19

INTRODUCTION
Statistics for management is used by managers in order to formulate strategic decisions
that may help organisation to attain long term sustainability. It is very important for the mangers
top make appropriate decision so that their company can achieve all its predetermined goals. It is
essential for the businesses to formulate effective strategies so that all the problems that may
occur in future can be dealt appropriately (Groumpos, 2015). Success of business entities
depends upon the management of operations and other activities that are performed by its
employees. Statistics for management help to identify market conditions so that improvements
can be made in the products or services that are offered to the customers. It helps to forecast the
material requirements that are needed for the production process. This report covers various
topics like evaluation of business and its strategies, economic information and data, raw data of
business by using different statistical methods, application of all those methods in planning etc.
communication of the findings by using appropriate charts and tables have also been discussed
under this report.
Activity: 1
(a): Use of office national statistics
CONSUMER PRICE INDEX (CPI) is a term which measures inflation of consumer
prices which means calculation of change in price for consumer goods and services in market
basket it is also called HARMONISED INDEX OF CONSUMER PRICES(HICP).
(I)
CPI is a statistical form of measuring changes that are continuously going on in market
in relation to market price of consumer goods by taking different samples of various products on
periodically basis and this also shows share of a product in total consumer expenditure and also
which products leads to highest inflation.
Use of CPI is done to calculate real value of wages, salary, pension as there is inflation in
goods and services then income needs to be changed accordingly by taking this index as a base
for such changes (Asante and Armstrong, 2012).
CPIH refers to “consumer Price Inflation including owner’s occupiers' Housing Cost”. It
is same as Consumer Price Inflation but this also includes changes in housing rent. It does not
include changes in value of house property as by its name it seems to be. Ownership of home is

widespread which a large part of population still leaves in rental apartments and that cost on an
average to them at 10% of their earnings which makes it necessary to include housing rent to
calculate inflation rate which helps in calculation of real pay.
(ii):
RETAIL PRICE INDEX(RPI) measures change in cost of represented sample of
consumer goods and services. It is first calculated in 1947 and in year 1975 highest annual
inflation was recorded according to RPI as 26.9%. In 2009 it was first time when RPI was
recorded as negative as in that year reduction in cost of goods and services. RPI already consider
housing rent inflation which gives more correct information regarding inflation (Inflation and
price indices, 2018).
b) Indices from 2007 to 2017
CPI
Year Jan Feb Mar April May Jun July
2007 103.2 103.7 104.2 104.5 104.8 105 104.4
2008 105.5 106.3 106.7 107.6 108.3 109 109
2009 108.7 109.6 109.8 110.1 110.7 111 110.9
2010 112.4 112.9 113.5 114.2 114.4 114.6 114.3
2011 116.9 117.8 118.1 119.3 119.5 119.4 119.4
2012 121.1 121.8 122.2 122.8 122.3 122.5 123.1
2013 124.4 125.2 125.6 125.9 126.1 125.9 125.8
2014 126.7 127.4 127.7 128.1 128 128.3 127.8
2015 127.1 127.4 127.6 128 128.2 128.2 128
2016 127.4 127.7 128.3 128.3 128.5 128.8 129.2
2017 129.8 130.7 131.2 131.7 132.2 132.2 132.1
Aug Sep Oct Nov Dec Total
104.7 104.8 105.3 105.6 106.2 1256.4
109.7 110.3 110 109.9 109.5 1301.8
111.4 111.5 111.7 112 112.6 1330
114.9 114.9 115.2 115.6 116.8 1373.7
120.1 120.9 121 121.2 121.7 1435.3

123.5 124.4 126.8 126.9 127.5 1484.9
126.4 126.8 126.9 127 127.5 1513.5
128.3 128.4 128.5 128.2 128.2 1535.6
128.4 128.2 128.4 128.3 128.5 1536.3
129.2 129.4 129.5 129.8 130.4 1546.5
132.9 133.2 133.4 133.9 134.3 1587.6
Year Total
2007 1256.4
2008 1301.8
2009 1330
2010 1373.7
2011 1435.3
2012 1484.9
2013 1513.5
2014 1535.6
2015 1536.3
2016 1546.5
2017 1587.6

CPI
Year Jan Feb Mar April May Jun July
2007 201.3 203.1 204.4 205.4 206.2 207.3 206.1
2008 209.8 211.4 212.1 214 215.1 216.8 216.5
2009 210.1 211.4 211.3 211.5 212.8 213.4 213.4
2010 217.9 219.2 220.7 222.8 223.6 224.1 223.6
2011 229 231.3 232.5 234.4 235.2 235.2 234.7
2012 238 239.9 240.8 242.5 242.4 241.8 242.1
2013 245.8 247.6 248.7 249.5 250 249.7 249.7
2014 252.6 254.2 254.8 255.7 255.9 256.3 256
2015 255.4 256.7 257.1 258 258.5 258.9 258.6
2016 258.8 260 261.1 261.4 262.1 263.1 263.4
2017 265.5 268.4 269.3 270.6 271.7 272.3 272.9
Aug Sep Oct Nov Dec Total
207.3 208 208.9 209.7 210.9 2478.6

217.2 218.4 217.7 216 212.9 2577.9
214.4 215.3 216 216.6 218 2564.2
224.5 225.3 225.8 226.8 228.4 2682.7
236.1 237.9 238 238.5 239.4 2822.2
243 244.2 245.6 245.6 246.8 2912.7
251 251 251 252.1 253.4 2999.5
257 257.6 257.7 257.1 257.5 3072.4
259.8 259.6 259.5 259.8 260.6 3102.5
264.4 264.9 264.8 265.5 267.1 3156.6
274.7 275.1 275.3 275.8 278.1 3269.7
RPI Index
Year Total
2007 2478.6
2008 2577.9
2009 2564.2
2010 2682.7
2011 2822.2
2012 2912.7
2013 2999.5
2014 3072.4
2015 3102.5
2016 3156.6
2017 3269.7

2478.6
2577.9 2564.2
2682.7
2822.2 2912.7 2999.5 3072.4 3102.5 3156.6
3269.7
RPI
(c): Difference between CPI and RPI
CPI and RPI both measures inflation for changes in price for consumer goods on a
market base but there is a little difference between both is that RPI also includes cost of housing
which CPI do not consider and this makes RPI a better base to make further calculation as it will
provide more accurate results regarding inflation. When it comes to calculations RPI is
calculated by arithmetic i.e., price of each product is added and they are simply divided by
number of products whereas CPI is calculated geometric mean. It is calculated by multiplying
price of each product then taking nth root of them, value of 'n' is number of products considered.
It can be seen that geometric mean shows better reflection of change in consumers spending
pattern in relation to change in price of products (Lin and et. al., 2011).
When CPI and RPI will be calculated then difference of approximately 1 % will always
be seen as CPI would be higher than RPI by 1% and this is called Formula Effect.
(d): Calculation of annual inflation rate
Measuring inflation is a very difficult task as it requires huge amount of data CPI
measures price change form respective of purchaser. For calculation of CPI various samples are

taken from consumer goods that shows change in price in a year and inflation of that period is
calculated.
Inflation is always calculating between two periods like month, quarter, years. Amount of
current years calculated data will be reduced by its base year then result of this is divided by base
year information then multiplied by 100.
EXAMPLE- INDEX OF PREVIOUS YEAR 100
INDEX OF CURRENT YEAR 145
INFLATION = (145-100/100) *100
=45%
(e): Reason regarding importance of inflation
INFLATION can mean either increase in price or increase in money supply. Inflation
means increase in price is higher then set benchmarks which puts a economy in a very uncertain
situation as this will increase price of some necessary goods high and capacity to afford them
will reduce then demand for more pay as salary and wages by employees will be done.
Inflation is increasing day by day and main reason to know rate of inflation is calculating
amount that must be increased in pay so, when price of a product got up then affordable capacity
can also be increased. Higher inflation leads to reduction in value of money and investors will
find no real return on their money. Inflation has a great impact on economic development as
higher inflation discourage investment because of uncertainty in returns as low inflation provides
stability and encourage investments. Also higher inflation rate makes economy less competitive
as higher priced goods loses their sale in international market which reduces exports and leads
financial loss to country by less foreign exchange. In case inflation is higher than its benchmark
then real wages are low and this leads low standard of living because income is low as compare
to expenses. Significance of inflation is that it makes value of currency less as same amount of
money will give you less purchase (Ichinose and Yamamoto, 2011).
Activity 2
Hourly
Earning
No. of
leisure
centre staff
Cumulative
Frequency
(x) Class

Boundaries
0-9 0-9.5 4 4
10-19 9.5-19.5 23 27
20-29 19.5-29.5 13 40
30-39 29.5-39.5 7 47
40-49 39.5-49.5 3 50
N = 50
N 50
2 2
= 25
Hence
median
class is
10-19 i.e. 9.5-19.5
The upper quartile corresponds to the 75th percentile i.e. 75% of the total frequency.
75% of the total
frequency
75%*50
= 37.5
The lower quartile corresponds to the 25th percentile i.e. 25% of the total frequency
25% of the total
frequency
25%*50
= 12.5
The interquartile range = upper quartile – lower
quartile
37.5-12.5
= 25
Hourly
Earning
No. of
leisure
centre staff Mid-point
f x fx
0-9 4 4.5 18
10-19 23 14.5 333.5
20-29 13 24.5 318.5

30-39 7 34.5 241.5
40-49 3 44.5 133.5
50 1045
mean(x)=sum(fx)/total(f)=1045/50=20.9
f x X-x (X-x)2 f*(X-x)2
0-9 4 4.5 -16.4 268.96 1075.84
10-19 23 14.5 -6.4 40.96 942.08
20-29 13 24.5 3.6 12.96 168.48
30-39 7 34.5 13.6 184.96 1294.72
40-49 3 44.5 23.6 556.96 1670.88
50 5152
Standard .
d 103.04 10.15
Median 14 19.5
Interquartil
e 7.5 25
Mean 16.5 20.9
Standard
deviation 7 10.15
(B) .
Mean – In the case of statistics, arithmetic mean is a tool which helps in ascertaining the
average of various variables having different vales. This tool is based on quantitative data which
has numbers. This tool enables to calculate average by dividing the total of all values by the
number of values. This tool is the most common and best technique of analysing statistical data
in order to calculate further deviations such as standard deviation.
Mode – This is a statistical term which helps in ascertaining frequency of repeating the
numbers which can help in organising data to determine results from the huge data. It is a

measure of central tendency of counting the frequency of each result. The basic aim of this tool
is to ascertain the highest number of occurrences. mean is the average value of the data.
Median – This is a technique of ascertaining mod point of a data of numbers. In order to
determine mid value all, the numbers of a sequence must be arranged first from lowest to
highest. In order to calculate the median, middle pair is determined first and then added together
so that it can be divided by two. This tool is often used to skew the average of the values. median
describes that if it is higher than the mean value then most of the data in the series will be above
the average.
STANDARD DEVIATION: - it defines the variability or flexibility in given data series.
INTERQUARTILE RANGE: - By considering the value of median the data spread is measured
with the help of interquartile range (Gollier, 2011).
On the basis of above explanation, the statistical data of two given areas can be compared
and interpretation as follows:
On the basis of mean it can be measured that the hourly earnings of the staffs in London area
are higher than the staffs in Manchester area. on the basis of standard deviation, the uncertainty
and variability was high in London area's staff earning than the Manchester area. on the basis of
median, the most of staffs in London area earned hourly income above the average income.
Apart from that, in another one the staffs were not getting above the average (Boehm and
Thomas, 2013). On the basis of interquartile range, the hourly incomes speared to more close to
the average in London are but much far away in Manchester areas. And for quantitative
significance level the various tests can be applied like, t-test, anova test, etc.
Activity 3
(a) Economic Order Quantity (EOQ): It is that order quantity which a company is required
to maintain as its stock so that the inventory cost can be minimized. It has elements such as
annual consumption, ordering cost and carrying cost. The aim of using this method is to
reduce the cost associated with placing an order.
 EOQ = √2AO/C
Where, A= Annual consumption;
O = Ordering Cost;
C = Carrying Cost
 EOQ = √2*2000*5/2

= 100 Units
(b) Re-order Level: It is a level at which company should replenish its order as soon as the re-
order period arrives. It takes into accounts the time of replenishment and time of receipt at the
store.
A company also likes to keep safety stock so that it can carry out its activities without
any difficulty.
 Re-order level (ROQ) = (Lead time*daily average usage) +safety stock
= (28*2) +150
= 206 units
 Frequency of Re-order = Annual consumption/ ROQ
= 2000/206 = 9.7 or 10 days
(c) Inventory Policy Cost: A company is requiring to maintain the minimum level of stock and
many costs are incurred for maintaining that stock, so the cost associated with ordering,
receiving and maintaining the stock (Kyriakarakos and et. al., 2013).
 Inventory Policy Cost = Purchase cost + Ordering cost + Carrying cost
= 10 + 5 + 2
= £17
 The inventory cost is £17 because inventory includes all the cost of maintaining stock.
(d) Current Level of service = Weekly Demand * Availability of t-shirt
= 40*95%
= 38 units
(e) Re-order level to achieve desired service level:
Re-order level (ROQ) = (Lead time*daily average usage) +safety stock
= (28*2) +150
= 206 units
The current level of service provided is 95% and the desired level is 100%. The company
will be able to reach the desired level by ordering 206 units (Wheeler, Shaw and Barr, 2013).
Activity 4
(a):

CONSUMER PRICE INDEX: It is a remedy to estimate the inflation changes in the
consumer prices of a particular country. Another name of Consumer Price Index (CPI) is
Harmonised Index of Consumer Prices (HICP).
Year Annual Change
2017 2.70% 2.00%
2016 0.70% 0.70%
2015 0.00% -1.50%
2014 1.50% -1.10%
2013 2.60% -0.20%
2012 2.80% -1.70%
2011 4.50% 1.20%
2010 3.30% 1.10%
2009 2.20% -1.40%
2008 3.60% 1.30%
2007 2.30% 0.00%
29/06/1905
30/06/1905
01/07/1905
02/07/1905
03/07/1905
04/07/1905
05/07/1905
06/07/1905
07/07/1905
08/07/1905
09/07/1905
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
0.02
0.025
2.00%
0.70%
-1.50%-1.10%-0.20%-1.70%
1.20%
1.10%
-1.40%
1.30%
0.00% Change
Table 1. Consumer Price Index
Source: Self-generated

INTERPRETAION: The graph indicates the changes in the CPI from 2007 to 2017.
From the year 2007 to 2011 the fluctuations were very high. In that span of time the inflation rate
was negative for a year i.e. 2009. After 2009, the rate was going upward steadily till 2011. From
the year 2012 to 2015 the inflation was downward. After maintaining a pace going downward the
inflation was again on the rise in the year 2016 and 2017 due to air fares, fall in prices of goods
like toys and games (Jiang and Pang, 2011).
CPIH: It is a measure of CPI by which the owner occupiers' housing costs are calculated.
Such costs attribute to one’s costs of owning, maintaining and living in the own house. There are
many other cost associated with owing a house such as repayment of housing loan, commission
to a housing agent, insurance etc. For ascertaining the total cost of all the house owners this
method of calculation is used (Murphy, Myors and Wolach, 2014).
Year % change
2007 2.40%
2008 3.50%
2009 2.00%
2010 2.50%
2011 3.80%
2012 2.60%
2013 2.30%
2014 1.50%
2015 0.40%
2016 1.00%
2017 2.60%
Table 2. CPIH indices
Source: Self-generated

1 2 3 4 5 6 7 8 9 10 11
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Change
Interpretation: The CPIH graph indicates that the movement of prices of owning and
maintaining the houses by owners is steady from the year 2007 to 2010. In the year 2011, it
reached at the highest of the CPIH for 10 years whereas the year 2015 recorded the lowest in
CPIH index indicating downward movement and fall in the standard of living (Brozović and
Schlenker, 2011).
RPI: This measure is used to calculate the changes in the cost of the products and
services sold and provided respectively in the UK market. The cost includes cost of living of the
families consuming the products and services. The basis of calculation is the consumption by the
family and the RPI increases with increase in the overall consumption.
Year Change
2017 3.60%
2016 1.80%
2015 1.00%
2014 2.40%
2013 3.00%
2012 3.20%
2011 5.20%

2010 4.60%
2009 -0.50%
2008 4.00%
2007 4.30%
1 2 3 4 5 6 7 8 9 10 11
-1.00%
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
Table 2. Retail Price Index
Source: Self-generated
Interpretation: RPI indicates an upward movement in the retail prices from the year 2007 to
2014. The upward movement states that the consumption was increasing every year till 2014.
The consumption of the overall household goods and services declined in the year 2015 causing
the RPI fall downward. The decline in the retail prices were negative in the year 2015. In the
2016 and 2017 the trend was steady and upward resulting in stability in retail prices (Beyer and
Dye, 2012).
(b)
Hourly earnings Class Boundaries
Number of leisure
staff Cumulative Frequency
0 – 09 0 – 9.5 4 4
10 – 19 9.5 – 19.5 23 27
20 – 29 19.5 – 29.5 13 40
30 – 39 29.5 – 39.5 7 47