(Solution) Statistics for Management : PDF

Statistics for Management

Table of Contents

INTRODUCTION
Statistics is mathematical tool for evaluation of situations and to take effective decisions
on the basis of evaluation. These data are helpful to face and overcome the future unpredictable
situations. The stats are analysed for achieving pre determined purpose of business. It is tool and
process of gathering, presenting, analysing and interpretation of data. With the help of past stats
company forecast the future sales. It enables a business to make qualitative as well as
quantitative decision in the business. The statistics is a tool which is used by businesses,
government and individuals in order to determine various elements like inflation, deflation and
Consumer Price Index etc. The present report explain evaluation of business and economic data.
The raw business data is very crucial for business which is being explained in this report. The
statistical method methods plays an important role in business planning, this is also explained in
this report. There are different chart has also been prepared in order to express findings.
LO 1
Analysis of business and economic data
Data is related with figure and facts which enables an individual or organisation to draw a
valuable outcome. Data is single pieces of recorded information which is used for evaluation in
business. This is raw information and with the help of data the statistics are prepared. The data
can be qualitative and quantitative also (Beyer and Dye, 2012). As qualitative data is contained
with information about characteristics and qualities. The information related with quality can not
be measure in numbers. This includes style of person and eye colour etc. It can be observed by
the observation and interactions etc. While second one is quantitative data is kind of type of data
which deals with quantitative information. This type of data is analysed and than used this for
forecast.
A & B. Different price index
Consumer Price Index:
This index measures the price changes in some definitive collection of goods and services
purchased by customers in an effort to measure inflation. Simply this measures the change in the
regular goods and services which is consumed by consumers. The regular goods and services
like household goods, groceries, transportation, medical etc. With the help of this it gauge the
cost of living and inflation (Brozović and Schlenker, 2011). The CPI is used by economists,
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institutions, government and big business houses. The economist use CPI to calculate price
change in bread, milk and other necessary goods to see whether is there any change in
purchasing power or not. As based on this finding economist advise on expansionary and
contraction fiscal policy to correct the changes in prices. The consumer price index is an
important tool for government and businesses as it is helpful in the measuring inflation and
deflation. And than according to changes the government make decisions. The CPIH is consumer
price index housing cost which is an addition to consumer price index, this includes housing cost
of owner occupiers is measured. The consumer price index housing cost 12 months inflation rate
was 2.4% in August 2018, up from 2.3% in July 2018. and the consumer price index was 2.7%
for the month august 2018 and in July it was 2.5%. As there is declining and reason for decline is
that prices daily consumption goods and services has been continuously declining.
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As from the above bar graph it can be seen that there is continuous fluctuation in CPI
from the year 2007 to 2017. In 2007 it was 4.3 and in year 2015 it was lowest to -.1. If CPI
increases than it has good impact on government but its bad for consumers.
CPIH
Year Value
2007 2.4
2008 4.8
2009 1
2010 2.4
2011 4.5
2012 2.1
2013 2.4
2014 1.3
2015 0.2
2016 1.3
2017 2.8
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As the CPIH was 2.4 in 2007 but it increases in 2008 and reached to 4.8. But it was
lowest in 2015 and it came to .2. There is changes in index of every year.
RPI:
Retail price index is used to index the different prices and incomes which includes the
allowance, state benefits and pensions. This shows list of prices of typical goods which shows
how much the cost of living changes from one month to next month. These are published
monthly by government and display changes in prices of goods selected as necessary items in
budget of household. The RPI was 3.5% in month of August and it was 3.3% in September.
RPI:
2007 4.3
2008 4
2009 -0.5
2010 4.6
2011 5.2
2012 3.2
2013 3
4

2014 2.4
2015 1
2016 1.8
2017 3.6
The RPI was 4.3 for year 2007 and in the year 2017 it reaches to 3.6. as variability can be
seen in index in every year.
c. Difference between these indices
CPI CPIH RPI
It is a consumer price index
which includes regular use of
goods and services by
consumers.
This is new addition to
consumer price index which
includes housing cost (Jiang
and Pang, 2011).
This is a retail price index.
This displays variation in rate
of regular use of goods in
market.
It is a new addition to CPI so it
is similar to that but it includes
housing cost of owner
occupies.
The RPI is helpful in analysing
of inflation.
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It is tools which mostly used
by government and companies.
This shows variation in
average residential price.
As it measures cost of retail
goods and services.
D. How consumer price index helps in calculation of inflation rate
As consumer price index can be very useful in order to measure the inflation. The
decreasing consumer price index leads to effect on the inflation rate of country. The change rate
is given name of rate of percentage in order to determine the inflation. Consumer price index for
2017 has been risen in compare to year 2016 that is 1. Overall difference if of 2% and which has
resultant in risen of rate of inflation.
Importance of having information of inflation
Inflation is a quantitative measure of rate at which average price level of a basket of
definitive products and services in nation within a given time of period. This is very important
for organisations to have information of inflation so they formulate strategy according to the
inflation rate of country. The managers needs to have detailed information regarding the inflation
in order to determine the prices of produced goods and services accordingly. As overall it is
crucial for business in order to be sustainable and competitive in market.
LO2
A, Scatter diagram and association between the hot drink sales and average weekly temperature
Scatter diagram refers to the mathematical diagrammatic representation that depicts the
values of two different variables for a set of data. It is the form of the graphical representation
which is used to evaluate and maintain the costs and revenues of the specified accounting period.
It comprises the cost charted on Y axis and unit pointed on X axis. This helps the managers in
evaluating the cost of per unit production cost. These diagrams are designed periodically
throughout the year as it may be monthly, quarterly and annually. As these diagrams help to
appraise positive or negative relationship among both elements. There is a positive relationship
prevails among the temperature and hot drink sales. An increment in temperature results in
increment in selling of hot drinks. As same as if temperature falls down then sales would also
gets decreases. So it can be said that there is proper positive relation between the hot drink sales
and temperature.
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The above scatter plot displays information of hot drink gross sales and temperature. So it
can be notice from this scatter drawing that there is a constructive relationship among the sales
and average temperature. When the temperature increases people demand for more hot drinks
and when temperature gets decreases than demand of hot drinks gets decreases, so this relation
can be seen clearly from the above scatter diagram. As in the week 2nd and 4th sales is equal to
temperature. As in week 9th sales is at their lowest similarly the temperature is low. So there is a
positive relationship between temperature and hot drink sales.
B. Determination of correlation coefficient and coefficient determination.
Correlation coefficient concerned as the statistical measurement methodology used to
find out strength of a relations among relative movement of two variables. If the range of values
of correlation coefficient is bounded by the -1 to 1. As if correlation coefficient more than 1 and
lesser than -1 than it will be termed as incorrect. The absolute correct correlation of -1 termed as
negative correlation. And correlation 1 is termed as perfect positive correlation. If correlation is 0
than there is no relations prevails among two variables. The correlation coefficient evaluate the
degree of relation among two different variables and it quantifies only linear relationship. It is
termed as the impossible to quantify a non linear relationship between two variables. The
strength of relationship depend on value of correlation coefficient. This correlation of coefficient
is very useful tool and it is used to forecast the information. This tool is used by the government,
business house and individuals in order to forecast the future data according to need. The various
authors has given different different formulas in order to calculate the correlation coefficient. As
a basic formula which is used to calculate correlation of coefficient.
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Calculation of correlation of coefficient:
Formula= N∑xy - (∑x) (∑y)/ √[N∑x2 - (∑x)2] [N∑y2- (∑y)2]
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Coefficient determination:
As it is an output which comes from the analysis of regression. This is interpreted as
proportion of variance in the dependent variable which is predictable from independent variable.
This is the square of correlation (r) which predicted between y and x. Its range is 0 to 1. The fall
of data points within regression equation can be predicted from the coefficient determination.
This can be denoted in percentage also as .8 can be written as 80% . The higher coefficient of
determination is an indicator of good fit for the observation. Where as the lower coefficient of
determination is not considered as good fit for observation. This shows fluctuation in the two set
of data. There is two variables in determination one is dependent and other one is independent.
These variables are denoted by X and Y. As formula of determination is discussed below:
Formula: (Correlation coefficient)2
As above table shows correlation coefficient is .8 where as coefficient determination is
the .64. So both coefficient are positive so it can be said these are good fit for the observation.
These are the tools which is very helpful for organisation, government and individuals in order to
know values for equations.
C. Equations for prediction of sales for future time period
The equations are very useful for predicting or forecasting future sales of companies. As
they provide quantitative data which shows authenticity. So with the help of these equations
manager can get to know about future sales of any product and then they can plan it accordingly.
These equation enable a business to maximise their profits by accurate prediction of sales. If
clients wants to know estimated sales for particular temperature in accordance with sales then
one can obtain following equation (Gollier, 2011). These are prepare as
Formula: Sales for week A + Sales for week B / 2
Sales of week A = Average temperature sales is below the temperature of desired sales
Sales of Week B = Sales of average temperature above the temperature of desired sales
As when the customer is willing to predict its sales on that temperature which is more than the
higher temperature on which has to be achieve yet by client.
Formula: Sales of proximity temperature of higher temperature – Sales at higher achieved
temperature * difference between higher temperature and desired temperature.
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D. Prediction of sale at a particular temperature
Sales at 17oC = week 2 sales = week 6 sales / 2
10+14 / 2
= 12
Sales at 25oC = sales of week 5 – sales for week 6 * ( desired temperature – temperature in 5 th
week)
= 18 – 14 ( 25 – 20 )
= 4 * 5
= 20
As from the above calculation it can be said that estimated sales at 17oC would be 12 hot
drink for client c and likewise at temperature 25oC would be approximate 20 hot drinks.
E. Reliability of predictions
The forecasting or prediction is basically done on the past data. The prediction assist
companies to formulate better strategy in order to achieve the estimated sales. As it has been
estimated that upto 25oC temperature the sales would be 20 hot drinks. If the temperature is
17oC than the sales would be 12 hot drinks. These predictions can be reliable up to a certain level
because these are made on the basis of past sales data which was given by company.
Forecasting:
Forecasting refers to the prediction of future possible situation which can have great
impact on the business activities. This is reason that forecasting is done by companies by using
past performance data. This is an helpful for business organisation to formulate strategy
accordingly. There is an estimation which has been used for client C to predict sales at particular
level of temperature.
Use of Excel SPSS:
The excel is used to cut down pressure of using different formulas and equations in order
to calculate adequate results. The correlation coefficient and determination has been also
calculated with the help of excel in order to save time. There is two different methods are used to
evaluate accurate result for client C. As correlation coefficient and determination is being used to
get the evaluate the relationship between average temperature and sales of hot drinks (chinose
and Yamamoto, 2011).
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ACTIVITY 3
There are various statistical tools and methods which are used by the organisation in
order to formulate strategies and better plans and policies. There are various tools and techniques
which are as:
A. Economic order quantity
Economic order quantity (EOQ) refers to the ideal level of quantity which a company
must buy its inventory. The main objective of economic order quantity is to reduce the inventory
cost and maximise its profits. This method assist companies to reduce the holding and ordering
cost. This method is most famous and oldest production scheduling models.
(a) EOQ = √(2AO / H)
= √(2*2000*15/2
= √30000
= 173.21 or 174 quantity
where, A = annual demand
O = ordering cost
H = Holding cost per unit
Note: Ordering cost shall include sum of delivery cost and cost of tee shirt.
B. Re order level
The re order level of stock in business is a level which is pre set in the business. But at
this level business places a new order with its supplier to obtain to make delivery of raw
materials or any other finished good inventory (Lin and et. al., 2011I). It is important for every
business to have a sufficient level of finished stock or raw stock. This kind of practices is being
adopted by the business for sustaining continuity or production in case of raw materials and
continuity of sales in case of finished goods. This is calculated as below:
So, Jenny Jones is need to place an order when stock level reached 150 tee-shirts.
C. Inventory policy cost
The inventory administration is crucial task for all organisation. As it is important to
maintain optimum level of inventory in order to reduce to cost and maximize profits. The
inventory management is helpful for organisation to maintain inventory in efficient manner so
that smooth functioning can be executed with in organisational context. The stock management
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assist the enterprise to keep up their stock level in ideal dimensions (Asante and Armstrong,
2012). As there are diverse methodologies like Just in Time inventory management system can
be utilized to analyse the stock in viable manner. There is stock approach cost which is facial
hair by business is determined below:
= Delivering cost + Purchase cost + Inventory holding cost
= 5 + 10 + (20/100*10)
= 17 per unit of tee-shirt
Note: Inventory policy cost includes all the cost related to inventory such as delivery cost,
holding cost etc.
D. Current Service level to customer
(d) Current service level = 40*50*95%
= 2000*95%
= 1900
E. Re order level at desired service level
=(maximal regular usage rate* lead time)+ condition stock
= (5.71* 0.95) +25
= 30 units
The customer inevitably to sale at least 30 units to achieve the desirable company level.
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ACTIVITY 4
A. Using of suitable charts finding.
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As from the above mentioned, data for CPI has huge changes from year 2007 to 2017. In
year 2007 values of CPI is 4.3 that keeps on fluctuate throughout the years and in 2017 the value
is 3. It has been observed that there is decreasing trend in CPI. It was also seen that in year 2015
the CPI shows the negative value in UK.
CPIM:
2007 2.4
2008 4.8
2009 1
2010 2.4
2011 4.5
2012 2.1
2013 2.4
2014 1.3
2015 0.2
2016 1.3
2017 2.8
15
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
0
1
2
3
4
5
6
2.4
4.8
1
2.4
4.5
2.1 2.4
1.3
0.2
1.3
2.8

From the above presented table, it has been observed that CPIM is keeps on changing and
there is ups and down in the values from year 2007 to 2017. It is seen that in 2007 the values of
CPIM is 2.4, in 2008 the values increases up to 4.8. after that it keeps on decreasing expect in
year 2011 as the values were 4.5. The values in 2015 were seen to be lowest at 0.2. so this
presentation shows that there is great fluctuating in values of CPIM index of UK.
RPI ( Retail Price Index)
2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017
-1
0
1
2
3
4
5
6
4.3 4
-0.5
4.6
5.2
3.2 3
2.4
1
1.8
3.6
It is observed that, RPI index in UK has been perpetually keeps on chaining over the last
few year. The table shows that in year 2007 the value of RPI is 4.3 that keeps on decreasing to -
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0.5 in year 2009. In year 2011 the values of RPI shows 5.2 and in year 2017 is goes to 3.6. so it
can be observed that the values keeps on changing throughout the years.
B. Scatter diagrams that represent the data for hot drinks.
Scatters diagrams are said to be part of mathematical presentation of data that is exploited
to show belief and values for two variable of a complete set of information. These two kind of
variable are represented below:
Independent These uncertain are those that have different values in any elements and
that may alteration the values of different element (Groumpos, 2015).
Dependent : These factors are consider to those factors that changes only in responses to
an independent variable.
Histogram: These are said to be the visual interpretation of quantitative data that display
number of information points decreasing within a nominative ranges of values.
Week Average Temperature Hot Drinks Sales
1 18.5 15
2 16 10
3 13 13.5
4 19.5 15
5 20 18
6 19 14
7 15.5 13
8 14 8.5
9 12.5 6
10 15 9
17

0 2 4 6 8 10 12
0
5
10
15
20
25
15
10
13.5
15
18
14 13
8.5
6
9
18.5
16
13
19.5 20 19
15.5
14
12.5
15
Average Temperature
Hot Drinks Sales
From the above, presentation of scatter diagrams it is observed that there is positive
connection among the hot drinks sales and temperature. It shows that when temperature goes
down the sales of hot drinks also reduces.
CONCLUSION
In the conclusion it can be said that statistical tools are very important for business in
order to planning activities for business. There are different methods and techniques for
inventory management which can be useful for business for maintaining optimum level
inventory. The scatter diagrams and bars are very useful for prediction of sales. There is
determination and correlation of coefficient are implemented through organisation for deciding
fixation equation. As various statistical instrument can utilized in business organization planning.
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REFRENCES
Books and Journals
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