Introduction
Statistical management is the process of formulating right decisions so that uncertainties can be faced appropriately in future. It is used in financial analysis, auditing, production, econometrics and operations that are performed to modify services and market research. The procedure of statistical management involves collection and scrutinisation of business data. Managers of the organisations need to collect quantitative history of occurrence elements on optimal repairs and procedures. It helps to forecast the use of material in every sector of the business so that the shortage can be ignored. It is very important for a business entity as it can help to ensure quality, make connections and for provide effective judgements.
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This report covers various topics such as evaluation of business, economic data, raw business data by using a number of statistical methods, application of statistical methods in business planning, communication of findings by using appropriate charts and tables.
TASK 1
P1 Evaluation of business and economic data
Nature of data and information can help to manipulate them by different techniques of statistical analysis. There are two different types of data these are qualitative and quantitative. First one is qualitative that includes characteristics and the another type contain the data in numeric format. Data can be turned into information and information in to knowledge (Carlson and Wu, 2012). Data is unprocessed facts and figures that are recorded without interpretation when the recorded data get interpreted than it will become information. Knowledge is the combination of different type of information.
CPI, CPIH and RPI by using office of national statistics website and appropriate tables and graphs for all of them:
CPI and CPIH: Consumer price index is used to measure the changes ion the price level of the market and CPIH is a new addition in the CPI in which housing cost of owner occupiers is measured. CPIH rate was 2.2% in September 2018 which has been decreased as compare to 2.4% which is for August 2018. Consumer price index rate was 2.4% in September 2018 which has been decreased as compare to August which is 2.7%. the rate has been decreased because prices of food, non alcoholic beverage, transport, recreation, culture and clothing sector has declined between the month of August and September.
CPI:
Year

Value

2007

4.3

2008

5.2

2009

1.1

2010

3.1

2011

5.2

2012

2.2

2013

2.7

2014

1.2

2015

0.1

2016

1

2017

3

From the above chart it can be summarised that there is frequent fluctuation in the CPI of UK as in year 2007 it was 4.3% and now after 10 years has reduced up to 3% which is related to year 2017 (Chen and et. al., 2012).
CPIM:
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

From the above chart it can be summarised that rate of CPIM in fluctuating continuously and it has been increased in year 2017 as compare to year 2007. It has increased up to 2.8% from 2.4 %.
RPI: Retail price index is a measure of inflations that are monthly published by Office for national statistics. It represents the changes in the cost of retail goods and services. RPI rate has been decreased in month of September in year 2018. it was 3.5% in August month and declined up to 3.3% in September (DezsÅ‘, Ross and Uribe, 2016).
Year

Value

2007

4.3

2008

4

2009

0.5

2010

4.6

2011

5.2

2012

3.2

2013

3

2014

2.4

2015

1

2016

1.8

2017

3.6

From the above graph it can be analysed that RPI rate of UK is fluctuating continuously. In year 2007 it was 4.3% and 3.6% for year 2017.
Difference between CPI, CPIH and RPI:
CPI

CPIH

RPI

It is consumer price index.

It is consumer pricing index for housing.

It is retail price index.

It is used to measure the changes in prices of the market.

It is a new measure which is used to measure housing cost of owner occupiers.

It is used to measure the inflations that are published monthly by Office for National Statistics.

It is government preferred measure of inflations.

It represents the changes in average residential rates.

It helps to analyse the changes in the cost of retail goods or services.

Calculation of inflation rate with the help of consumer price index:
Inflation rate is calculated with the help of consumer price index which is shown by Office of national statistics on monthly basis. If the CPI is continuously decreasing than it will affect the inflation rate of the nation and will also result in fluctuation of inflation rates. The changed rate is converted to the percentage to calculate inflation (EasterbySmith, Thorpe and Jackson, 2012). As CPI of year 2017 has increased as compare to 2016 which is 1. Hence the total difference is 2% which has resulted in the increment of inflation rate.
Why it is important to have information of Inflation:
For every organisation it is very important top have information of inflation rate as it directly affect the efficiency of executing business operations. It helps to plan for upcoming year's activities so that, this may not result adversely. If the managers of the companies are having proper information of inflation than they may formulate effective strategies to perform their operational activities efficiently at the time of increased or decreased inflation rate.
TASK 2
P2 Evaluation of raw business data using a number of statistical methods
Difference between sample and population:
Basis

Sample

Population

Meaning

Sample is the sub group of total selected population selected for a particular research.

Population is the collection of all the factors processing same characteristics that reflects universe.

Measurement

It is measured in statistic.

It is measured in parameter.

Focus

It is focused wit5h making inferences regarding the population.

It is focused with identifying the characteristics.

Method of data collection

Data is collected by sample survey or sampling process.

Data is collected by complete recites or census.

Techniques of sampling: There are two different sampling techniques that can be used by a researcher while the research program. Both the methods are described below:
 Probability sampling: This techniques of sampling is based on random sample of the selected population for research purpose. It make sure that every element of the population get an equal chance to be the part of the sample so that an accurate result can be received. It is also known as random sampling (Fleming and et. al., 2013).
 Non Probability sampling: It does not depends upon the random selection of sample form the selected population. It is more dependent upon the researcher's cognition to select elements for a sample. It is also known as non random sampling technique. There is possibility that the outcome of this method can be biased and make it difficult for all the factors of selected population to be the part of sample evenly.
Scatter diagram to show relation between hot drink sale and average weekly temperature.
Use of scatter plots: It can be defined as the use of multidimensional data measurement and visualisation in which the data has been presented upon a chart in the form of dots and all of them show the fluctuations in the data. In this report scatter diagrams are used to analyse the relationship between average temperature and hot drink sales. From the diagram it can be identified that there is positive or negative relation between both of the elements. In this diagram there is a positive relation between both the factors as the sales increases or decreases with the changes in temperature (Froeschl, 2013). If the temperature increases than it has resulted in the increment in the sales. Decrease in average temperature has been resulted in the decreased amount of sales.
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

From the above scatter diagram it can be analysed that there is a positive relationship between average temperature and hot drink sales because when the temperature decreased the sales will also decrease with the same and when the temperature increases than the sales will also increases with the time. In third week temperature meet the sales and in ninth week the sales has decreased too much and temperature was also at the lower level.
Calculation of correlation coefficient and coefficient of determination:
Correlation coefficient: It is used to analyse relationship between two variables. It is mainly used in liner regression. If it results in positive 1 than it means that there is a increase in one variable and increase in fix proportion of other variable and if it shows 1 as a result than it means than there is a positive increment in one variable and decrease a fixed proportion in other variable (Ghertman, Obadia and Arregle, 2013). It is denoted by r. Formula to calculate correlation coefficient is as follows:
Formula= N∑xy  (∑x) (∑y)/ √[N∑x^{2 } (∑x)^{2}] [N∑y^{2} (∑y)^{2}]
Here,
N= number of weeks
∑xy= Sum of average temperature and hot drinks sale
(∑x)= Sum of average temperature
(∑y)= Sum of hot drink sales
∑x^{2}= Sum of squared average temperature
∑y^{2}= Sum of squared hot drink sales
Calculation is as follows:
Week

Average Temperature(X)

Hot Drinks Sales(Y)

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


Coefficient correlation

0.80


Determination of correlation

0.64

Determination of correlation: It is denoted by r^{2}. It is used to measure the way in which a statistical data model a data. It also specifies the variation in dependent and independent variables that are shown as x and y. Formula for determination of correlation is as follows:
Formula: (Correlation coefficient)^{2}
from the above table it has been identified that correlation of coefficient for client c is 0.80 and determination of coefficient is 0.64.
Equation that may help to predict sales for a upcoming period.
If client want to estimate sales for a particular temperature which is lower then the highest temperature on which the sales has been attained than following equation can be implemented:
Formula: sales of week A+ Sales of week B /2
Here,
Sales of week A= Sales of average temperature below the temperature of desired sales.
Sales of week B= Sales of average temperature above the temperature of desired sales.
When the client is willing to estimate the sales on that temperature which is more than the higher temperature on which has not yet been achieved by client.
Formula: Sales of the nearest temperature of higher temperature sales at the higher achieved temperature* the difference between higher temperature and the desired temperature (Hipel and Fang, 2013).
Prediction of the sales at a particular temperature:
Sales at 17^{o}C= sales of week 2 = sales of week 6/ 2
= 10+14/2
= 12
Sales at 25^{o}C= Sales of week 5 – sales of week 6*( Desired temperature temperature in week 5)
= 1814 (2520)
= 4*5
= 20
From the above calculation it has been estimated that at 17^{o}C estimated sales is 12 hot drinks for client C and at 25^{o}C temperature is is approximated that sales will be 20 hot drinks.
Reliability of the predictions
As the prediction that are made are mainly based on past data and it has been estimated that if the client increase the temperature up to 25^{o}C than the sales will be 20 hot drinks and if the temperature is 17^{o}C than the sales will be 12. the predictions are reliable as all of them are made according to the data of past week which has been provided by the client.
Forecasting: It refers to the estimation of possible future conditions that may affect the operational activities of an organisation. There is an estimation which has been used for client C to estimate the sales at a particular level of temperature.
Use of Excel and SPSS: Excel is used to reduce the burden of counting various formulas and equations help to calculate the appropriate and accurate result. It has also been used while calculating correlation and Coefficient as there are various formulas that may help to calculate them easily without wasting time of the calculations of others. SPSS stands for Statistical Package for the Social Sciences which is a software and used to get appropriate result of the data which has been inserted by the user (Keller, 2015).
Two different methods are used to analyse the right result for client C. Correlation coefficient and determination of correlation are used to analyse the relationship between average temperature and sales of hot drinks. It has also been identified that there is a favourable relation between both of them.
TASK 3
P3 Application of statistical methods in business planning
Statistical methods are the mathematical formulas and equations that are used by the owner or accountants of an firm to form effective decisions for business. There are two different techniques are used as the statistical management tools. These techniques are as follows:
 Inventory management: It is the supervision of non capitalized stocks that are used by manufacturing companies in order to produce goods. It helps the managers to supervise the supply chain while taking good in warehouses.
 Capacity management: It is a technique which is used to by managers of the companies to meet current needs to the future so that the operations can be executed effectively.
Calculation of EOQ:
EOQ: It stands for economic order quantity. Main purpose of this approach is to minimise variable inventory costs with the help of a formulated equation which is as follows:
EOQ= square root of [(2* demand* ordering cost) /carrying cost]
= √2*40*5/10
= 6.32 units.
Reorder level to order t shirts:
Reorder level: It is used to calculated that when the company or firm should order the stock before the warehouses go out of stock (Murphy, Myors and Wolach, 2014). Formula to calculate the level is as follows:
Formula: (maximum daily usage rate* lead time)+ safety stock
= (5.71* 0.95) +15
= 19.76 or 20 units
Client should order the t shirts when there are only 20 units of t shirts left in the ware house.
Calculation of inventory policy cost:
It is the holding cost for the client which is calculated as follows:
= total time  holding period
= 7 days 95%
= 0.35 days is the holding period for the client which is inventory policy cost on every units which is sold 0.35*40 which is 14 units or t shirts.
Current service level of client:
Service level: The number of quantities delivered in time/ the total quantity of the demand
= 4015
= 25 units
The clients is now delivering 25 units
Reorder level at desired service level:
=(maximum daily usage rate* lead time)+ safety stock
= (5.71* 0.95) +25
= 30 units
The clients needs to sale at least 30 units to attain the desired service level.
TASK 4
P4 Using of appropriate charts finding communicate.
A)Charts indicating the changes in CPI.
CPI:
Year

Value

2007

4.3

2008

5.2

2009

1.1

2010

3.1

2011

5.2

2012

2.2

2013

2.7

2014

1.2

2015

0.1

2016

1

2017

3

From the above diagram it can be identified that there is a fluctuation in the CPI of UK as it is continuously decreasing and increasing in all years.
CPIM:
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

From the above presentation it has been concluded that CPIM in unsteady continuously and it has been accrued in year 2017 as compare to year 2007. It has increased up to 2.8% from 2.4 %.
RPI
Year

Value

2007

4.3

2008

4

2009

0.5

2010

4.6

2011

5.2

2012

3.2

2013

3

2014

2.4

2015

1

2016

1.8

2017

3.6

B) Scatter diagram of hot drinks.
Variables: It is defined as the total number, quantity that increase or decrease over time or it is related to the changes in the values of product ans services in different situation (Re and et. al., 2014). In business there are basically some types of variable that are described below:
 Independent variable: These kind of variable are defined as the differentiate values in any factor that may change the variable of other factors.
 Dependent variable: These type of variable is related to the different changes only in response to an independent variable.
In every organisation it is necessary for them to accurately analyse the data, as this process is develop to provide accurate answer through examination and representation of data. The basic step in this analytic process consist of determining problem, ascertain the availability of appropriate data, analysing that which method would be champion in command to have best result and applying assorted process and evaluating, compact and communication the result. There are different kind of analysing and interpretation of collected data within a company that are described below:
Nominal Variable: It is also called categorical variable, that means it has two or more parts, but there is no natural order between these categories. They are consider to be the variable that do not have any numerical values, like occupation or political party pretence. For instance, gender of any living organising is nominal variable that have two or more categories such as male and female, at the same time there is no integral value ordering to the categories.
Ordinal Variable: This is also just similar to the nominal or categorical, but it has a clear ordering of the variable in context. These kind of variable are considers to be in between that categorical and quantitative variable of economy. For example,in and economic the people living have various kind of status these are arranged on the basis of different order categories low, medium and high.
Interval variable: These variable have a cardinal characteristics that could be measured along a time and they have a quantitative value. Ratio variable are part of interval variable but has some changes in the recording system that shows that Zero does not have a definite variable For example, suppose there is an annual income that was measured in dollar and three individual are supposed to be provided $1000, $15000, $20000 respectively. It is observed that the ordinal person makes $5,000 much than the first individual and $5,000 less than the 3rd person and the range of these measure is the identical.
Frequency table: It is a method related to organising of raw material in a compact manner that display a series of data in ascending or descending order, with a column showing the frequencies that represent the number of time a single digit occur in the respective data set.
Simple tables: This is related the presentation of selected data in tabular form that is taken from a large number of people so that proper examine can be done in order to find something interesting, unique about this group.
Pie chart: It is relate to the presentation of collected and analyse data in the circular form that is further divided into various segment depending on the information about the group. Division of circle according to data in different slice help in comparison to one another or to the whole segment (Wheeler, Shaw and Barr, 2013).
Histogram: This is related to an accurate display and presentation of numerical data. It basically represent the reputation of specific phenomena that lies within a specific range of value.
Frequency curve: It is related to a smooth curve that react to the confining case Histogram computed for a frequencies arrangement of a endlessly distribution as the figure of data became very large.
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

In the above mention scatter diagram, it has been analysed that positive relationship among temperature and hot drinks sales, because when there is decrease in the temperature the sales will also go down and vice versa.
Conlusion
From the above project report it has been concluded that statistical management can help an organisation to evaluate all action that needs to be taken in future to enhance profitability and productivity. Various inventory management techniques can be used by the managers to identify that what amount of inventory is required to retain in the warehouses. It can be calculated by using economic order quantity, reorder level and other techniques.
References
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 Chen, C. W., and et. al., 2012. Hazard management and risk design by optimal statistical analysis. Natural hazards. 64(2). pp.17071716.
 Dezso, C. L., Ross, D. G. and Uribe, J., 2016. Is there an implicit quota on women in top management? A large sample statistical analysis. Strategic Management Journal. 37(1). pp.98115.
 EasterbySmith, M., Thorpe, R. and Jackson, P. R., 2012. Management research. Sage.
 Fleming, P. S., and et. al., 2013. Are clustering effects accounted for in statistical analysis in leading dental specialty journals?. Journal of dentistry. 41(3). pp.265270.
 Froeschl, K. A., 2013. Metadata management in statistical information processing: a unified framework for metadatabased processing of statistical data aggregates. Springer.
 Ghertman, M., Obadia, J. and Arregle, J. L. eds., 2013. Statistical models for strategic management. Springer Science & Business Media.
 Hipel, K. W. and Fang, L. eds., 2013. Stochastic and Statistical Methods in Hydrology and Environmental Engineering: Volume 4: Effective Environmental Management for Sustainable Development (Vol. 10). Springer Science & Business Media.
 Keller, G., 2015. Statistics for Management and Economics, Abbreviated. Cengage Learning.