Introduction
Business statistics can be defined as science of good decisions which make under case of uncertainty such as financial analysis, auditing operations and production etc. It generally covers statistical study and descriptive stats for collecting, analysing and interpreting the data. Statistical analysis helps an organization or individual in representing the data and information in graphical manner (McPherson and Pincus, 2017). Present report is going to evaluate business and economic data which is obtained from published sources. For this purpose, various types of statistical methods are used such as quartiles, correlation coefficient, central tendencies etc. These methods are also applied in further business planning.
Activity 1
a) National Statistical Data
Consumer Price Indices:
CPI can defined as a comprehensive measure which is used for estimating price changes in goods and services as per consumption expenditures. In other words it helps in examining the weighted average of prices of consumer goods like transportation, medical care and food products (Lu and et. al., 2013). It is calculated by measuring changing price of each item against consumption then further averaging them. Inflation period of economy is usually measured by using this concept which calculate rate at which price of items or services purchased by households either rise or fall. Therefore, it is widely used as economical indicator through which effectiveness of economical policy of government can be determined. CPI provided detail information to regulatory bodies, organisations as well as individuals about changing price of economy. While CPIH refers to consumer price index in terms of housing and considered as most comprehensive measure of inflation.
Statistical data in terms of CPI index
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 
Retail Price Index:
It provides a list of price of particular goods and services which entail the changing rate of cost of living changes on monthly basis (Lam, 2012). It also refers as a primary tool for determining the way people are experiencing fall or rise in price rates. Therefore, it can be calculated as a weighted average of price of those household goods which are bought by end customers.
Statistical data in terms of RPI Index
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 
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 
b) Charts of statistical data
Chart of Consumer Price Index from year 20072017:
Chart of Retail Price Index from year 20072017:
c) Differences between CPI, CPIH and RPI Indices
CPI 
CPIH 
RPI 
It can be defined as a weighted average value of purchased goods and services. 
It refers to new measure of price inflation from ONS (Keller, 2015). 
It is used for revalorisation of taxation or excise duty and uprating the indexlinked gilts as well. 
It measures the consumer price inflation which is produced to international standards. 
It is based on CPI which measures housing costs of goods and services purchased by final consumers. 
It shows changes in cost of living. 
This method is mostly used by regulatory bodies to determine changes in price of particular products (Melnykov, 2013). 
This type of technique is used ONS (Office for National Statistics) for publishing a high range of indices which is also called the consumer price index including housing costs. 
It is generally used by business, government and economists for measuring the inflation rate. 
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d) Usage of Consumer price Index data for calculating annual inflation
Annual inflation rate can be defined as changes in price of particular products where regulatory bodies use consumer price index method to calculate the same. This would help organisations to decide expansion (Jessop, 2016). As per above national statistical data, consumer value list in the year 2017 has been measured as 1587.6 which is much increased as per previous year 2016 which is approximate 2% as ascended rate of expansion.
e) Importance of determining rate of inflation
Inflation can be defined as increase in price level of certain goods and services over a particular period of time in economy. Whenever price of products are hiked then it directly impacts on purchasing power of people. This would also impact on demand of items also therefore, it affects economical condition of country both in negative and positive manner ( Paté‐Cornell, 2012). Government and public organisations measure inflation rate in order to determine expansion rate of economy with cost of living index.
Also Read: Developing Global Management Competencies Level 3 GSM london Unit 5
M1 Evaluation of sources other than the NSO with regard to the gender pay gap
It has analysed from National Statistics data that organisations of UK provide employment to male candidates mostly as compared to female. It leads to causes high gender gap as subjected to Consumer Index Price in this nation. For example As per survey, it has evaluated that under textiles group, the gender pay gap is recorded as 88% that shows it pay less consideration to female working staff then males (Gender pay gap in UK, 2018).
M2 Differences in statistical application in activity 2
In activity 2, for calculating median of given data, Ogive curve has used while other variables like quartiles, standard deviations and interquartile range, frequency distribution has taken. The main difference among both methods is that ogive curve is easy to interpret the result while frequency distribution method requires a tough calculation. But in terms of accuracy, frequency distribution gives more accurate and correct data as compared to graphical representation.
D1 Difference between descriptive, exploratory and confirmatory analysis with examples
Descriptive 
Exploratory 
Confirmatory 
· It aims at exploring the situations of a research in detailed manner. · It describes functions and characteristics of data 
· It focuses on giving insights into and an understand of issues faced by investigators during collection of data. · It discovers new ideas and thoughts. 
· It uses traditional methodology like significance, confidence and inference to evaluate evidence of data. · It covers all basis of gathering, presenting and testing the evidence of data. 
M3 the use of the statistical methods used in activity 3
In order to manage the inventories and handle stock level properly, it is better to use Economic order quantity analysis, This costing method helps in analysing the optimum quantity of orders, reorders as well as stock levels. Furthermore, purchasing cost, cost per order and carrying cost is evaluated to analyse inventory policy cost.
D2 Recommendation and judgements made in activity 3
Using economic order quantity, owners of Jenny Jones gets success to manage quality of inventory and complete order of customers on time. Further, it is recommended to its management team to ascertain the reorder level structure for avoiding additional overhead expenses and overcome from shortage of cost as well.
M4 Justification regarding graphical representations used in activity 1 and 2
Bar charts and Ogive curve methods of graphical representation are used to represent the data of Activity 1 and Activity 2. Ogive helps in evaluating the median and quartiles of data while Bar chart is to represent the CPI and RPI data of Statistical National of year 2007 to 2017.
D3 Use of graphical and tabular representations used in 1 and 2 activities
Both tabular and graphical representation of data is essential to summarise the entire data into single form. Tabular formation is used to represent National Statistics data into quantitative manner which is helpful for analysing data in more appropriate manner. While Ogive curve is used to analyse the basic difference among hourly earning by staff member of Manchester and London area.
Activity 2
Hourly pay rates in different regions of UK
a) Ogive curve to determine Median
Ogive curve can be defined as a statistical tool to measure median of a particular data. It represent data into graphical manner by plotting frequency of data against cumulative distribution functions (Hecke, 2012). In general, Ogive curve can be classified into major parts LessThan and Morethan. Under lessthan type Ogive curve, upper limit of class interval is plotted against corresponding cumulative frequency. While more than type of Ogive curve is used lower class limit. The point where both kinds of curves are meet is considered as median of the particular data.
More than Ogive curve
Hourly earning in Euro (Class Interval) 
No. of Leisure central staff (f) 
More than Ogive 
Cumulative frequency 
Below 10 
4 
More than 0 
50 
10 but under 20 
23 
More than 10 
46 
20 but under 30 
13 
More than 20 
23 
30 but under 40 
7 
More than 30 
10 
40 but under 50 
3 
More than 40 
3 
Total 
50 


Less than Ogive Curve
Hourly earning in Euro (Class Interval) 
No. of Leisure central staff (f) 
Less than Ogive 
Cumulative frequency 
Below 10 
4 
Less than 10 
4 
10 but under 20 
23 
Less than 20 
27 
20 but under 30 
13 
Less than 30 
40 
30 but under 40 
7 
Less than 40 
47 
40 but under 50 
3 
Less than 50 
50 
Total 
50 


Ogive curve
From the above graphical representation, Median obtained is approximate £19.0 for hourly earning for leisure centre staff of London area (Zhou and Luo, 2015). While interquartile range can be obtained as :
Q1 can be defined as first quartile range which is calculated by taking 25% of data. While Q3 is sated as third quartile range that used 75% of total population. Along with this, Interquartile range can be defined as a quantum of statistical dispersion it is also known as mid spread and middle 50%. It is first quartile which is subtracted from third quartile. It is mainly a quota of variability which is based on dividing of a data set into quartiles. InterQuartile is basically a measure where extended values lies.
Q_{1 }= L + (N/4 – cf)/ f X h Here l = 10, f = 23, h = 10 and N/4 = ∑F/4 = 12.5, cf = 4
= 10 + (12.5 – 4)/ 23 x 10
= 10 + 85/ 23
= 13.7
Q_{3 }= L + (3N/4 – cf)/ f X h Here l = 20, f = 13, h = 10 and 3N/4 = ¾ of ∑F = 37.5, cf =27
= 20 + (37.5 – 27) / 13 x 10
= 20 + 105/13
= 28.07
So, Interquartile range can be obtained as = Q_{3 –} Q_{1 }
_{ } = (28.0713.7)
= 14.0 (approx)
b) Mean and standard deviation for hourly earnings of London area
Mean:
It is average of range of quantities or values calculated by adding all data and after then divide it by total of all numbers. End result is mean or average which is also called arithmetic mean as well. This is most common measure of midpoint in a set of values . It is use to derive central tendency of data in a question (Zyphur and Oswald, 2013). This type of statistical calculation erase accidental errors. This will help to acquire more accurate conclusion. Mean also helps in interpretation of statistical data.
Median:
It is a value that separates higher half from lower half in a given data sample. It is commonly use to measure properties of set of a data. It is very easy to understand and simple to calculate. Median can be use as location parameter in large descriptive statistics. To identify median, an individual arrange observation in a order from small to large value. If odd number is there in observation, then middle value is median (Bedeian, 2014). Whereas if even number is there in observation , then average of two middle value is median.
Standard Deviation:
It can be calculated as square root of variance. Standard deviation helps in measuring spread of data about mean value. There are mainly two types of standard deviations which includes population and sample standard deviation. It is a measure which is use to compute amount of given variations in a data value sets. Standard deviations of statistical population, data sets, random variable and probability distribution is square root of their variance (Haimes, 2015). It is mainly use to measure assurance in a statistical conclusion.
Mean is calculated by taking average of sum of observation as shown below:
Hourly earning in Euro (Class Interval) 
No. of Leisure central staff (f) 
Middle data
(x) 
(F*x) 
Middle data
(x^{2}) 
(F*x^{2})

Below 10 
4 
5 
20 
25 
100 
10 but under 20 
23 
15 
345 
225 
5175 
20 but under 30 
13 
25 
325 
625 
4225 
30 but under 40 
7 
35 
245 
1225 
8575 
40 but under 50 
3 
45 
135 
2025 
6075 
Total 
50 

1070 

24150 
Working notes:
Mean = ∑Fx / ∑F
= 1070/50
= 21.4
Standard deviation = √ (∑Fx^{2} / ∑F)  (∑Fx / ∑F)^{2}
= √(24150/50) – (21.4)^{2}
^{ }= √483 – 457.96
= √25.04
= 5. 0 (approx)
Thus, as per above calculation, mean and standard deviation for London area are obtained as £21.4 and £5.0 respectively.
c) Comparison of earning of London and Manchester area
Hourly earning for leisure centre staff in Manchester area:
Median 
£14.00 
Interquartile Range 
£7.50 
Mean 
£16.50 
Standard Deviations 
£7.00 
Hourly earning for leisure centre staff in London area:
Median 
£19.00 
Interquartile Range 
£14.00 
Mean 
£21.40 
Standard Deviations 
£5.00 
Therefore, on comparing the above data, it has interpreted that hourly earning for leisure centre staff of London area is more than Manchester area.
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Activity 3
a) Economic Order Quantity (EOQ)
EOQ refers to optimum quantity of goods that can be bought only at one time for minimising the annual total cost to order holding items in inventory (Barrett and et. al., 2012). This method is used by organisations in order to minimise cost of inventory as well as can meet needs of customers on time.
Economic Order Quantity can be calculated by using below mentioned formula :
EOQ = √(2 x demand x cost per order) / cost of holding per unit of inventory)
EOQ = √( 2 x D x Co / Ch)
Where, D = Demand per year;
Co = Cost per order;
Ch = Cost of holding per unit of inventory
According to present case, Demand of tshirt is 2000 and cost per tshirt is £5; cost of holding=2
EOQ = √ (2 x 2000 x 5)/2
= 100 Units
 b) Re Order teeshirts
The EOQ method is generally used to measure reorder point through which organisations can control inventories as well as can fulfil demand of customers on time (Andreeva and Kianto, 2012). If any business runs out of its inventory level of stock then it leads to cause shortage in cost. This would also taken as revenue lost as under this condition, company cannot become able to fill an order on time. Therefore, as per present scenario, Ms Jones needs to order teeshirts in following manner:
Reorder level (ROQ) = (Lead time x daily average usage) + safety stock
= (28 x 2)+150
= 206 units
Frequency of Reorder = Demand per year / ROQ
= 2000 / 206
= 9.7 or 10 days
c) Calculation of inventory policy cost
Inventory Policy Cost = Purchase cost + Cost per order + Carrying cost
= 10 + 5 + 2
= £17
The inventory cost is £17 because inventory includes all the cost of maintaining stock.
 d) Current service level to customers
Current Level of service = Demand per week x Availability of tshirt
= 40 x 95%
= 38 units
 e) Work out the reorder level to achieve desired service level
Reorder level (ROQ) = (Lead time x daily average usage) + safety stock
= (28 x 2) + 150
= 206 units
Activity 4
a) Charts and tables on the basis of office of national statistics produce line
CPI (Consumer Price Index)
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 
Retail price 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 
b) An Ogive curve of cumulative % of staff versus hourly earning
More than Ogive curve of cumulative % staff versus hourly earning
Hourly earning in Euro (Class Interval) 
No. of Leisure central staff (f) 
In percentage form 
More than Ogive 
Cumulative frequency 
Below 10 
4 
8.00% 
More than 0 
50 
10 but under 20 
23 
46.00% 
More than 10 
46 
20 but under 30 
13 
26.00% 
More than 20 
23 
30 but under 40 
7 
14.00% 
More than 30 
10 
40 but under 50 
3 
6.00% 
More than 40 
3 
Total 
50 



Less than Ogive curve of cumulative % staff versus hourly earning
Hourly earning in Euro (Class Interval) 
No. of Leisure central staff (f) 
In percentage form 
Less than Ogive 
Cumulative frequency 
Below 10 
4 
8.00% 
Less than 10 
4 
10 but under 20 
23 
46.00% 
Less than 20 
27 
20 but under 30 
13 
26.00% 
Less than 30 
40 
30 but under 40 
7 
14.00% 
Less than 40 
47 
40 but under 50 
3 
6.00% 
Less than 50 
50 
Total 
50 



Ogive Curve:
Conclusion
This mentioned report defines the importance of statistics in collecting, measuring, analysing and interpreting the data. For measuring inflation and deflation period of economy, governmental bodies or organisations can use number of statistical methods. It includes consumer price index, retail price index, central tendencies like mean, median, standard deviations etc. In addition to these methods, tools like economical order quantity can help companies in minimising their inventory cost as well as complete order of customers on time.
References
 Andreeva, T. and Kianto, A., 2012. Does knowledge management really matter? Linking knowledge management practices, competitiveness and economic performance. Journal of knowledge management. 16(4). pp.617636.
 Barrett, K. C and et. al., 2012. IBM SPSS for introductory statistics: Use and interpretation. Routledge.
 Bedeian, A. G., 2014. “More than meets the eye”: A guide to interpreting the descriptive statistics and correlation matrices reported in management research. Academy of Management Learning & Education. 13(1). pp.121135.
 Haimes, Y. Y., 2015. Risk modeling, assessment, and management. John Wiley & Sons.
 Hecke, T. V., 2012. Power study of anova versus KruskalWallis test. Journal of Statistics and Management Systems. 15(23). pp.241247.
 Jessop, A., 2016. StatsNotes: Some Statistics for Management Problems. World Scientific Books.
 Keller, G., 2015. Statistics for Management and Economics, Abbreviated. Cengage Learning.