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Introduction
Statistics is considered as one of the mathematical analysis that would be used in qualifying models representations, for given set of data and actual verifications. It is generally used to analyse, modified and draw a valid conclusions from data. An organisation or individual can summarize business data using various methodologies of statistics (Gui and Aslam, 2017). The report is made to analyse the concept of statistics of management for evaluating economical data extracted from published National Statistics.These data are further represented in charts and other forms of graphical method. Furthermore, concept of economic order quantity for inventory management is also described in present assignment.
Activity 1
a) National Statistical Data
Consumer Price Indices:
Inflation can be defined as rate of changing price of basic commodities which influence mostly the interest rate on mortgages, saving and more. These rates generally affects state pension level as well as benefits of the same too. CPI refers to measure the inflation rate and purchasing power of national currency (Qiu, Qin and Zhou, 2016). This method expresses current price of basic goods as per difference in price of same year to previous one. It includes bread, meat, milk and other essential household products.
This will indicate effect of inflation on current situation of marketplace. In context with CPIH, as per National Statistics, it has evaluated that Consumer Price Index which includes housing costs of owners refers to most encompassing measure of inflation. Thus, information provided as per CPI and CPIH helps organisations as well as individuals in estimating the changing price of economy in future also.
Retail Price Index:
RPI is generally used by governmental bodies for several purposes like amount payable on indexlinked securities, wage negotiation, inflation rates etc. The data which is not included in CPI such as mortgage interest payments, building insurance, house depreciation and more included in retail price index (Gikhman and Skorokhod, 2015). It also tracks changes in the cost of fixed or basic commodities.
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 
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) Graphical representation of national statistical data
Graphical representation of Consumer Price Index from year 20072017:
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 
Graphical representation of Consumer Price Index from year 20072017:
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 
c) Differences between CPI, CPIH and RPI Indices
CPI 
CPIH 
RPI 
Data and information gathered as per consumer price index forms basis for inflation as per targeted by Government (Lu and et. al., 2013). It excludes mortgage interest payments and housing costs also. 
It is another method like CPI which is made just to to measures owner occupiers' housing costs. For this purpose, CPIH uses technique like rental equivalence for measuring OOH which includes housing, water, fuels, electricity and more. 
This method is to calculate variance in price of basic products of previous and current year. Unlike CPI, it also includes housing costs like mortgage interest payments and council tax. 
It is considered as one of the main method which helps in deciding the cost of living and rate of inflation as well. 
Since components including under OOH are slightly increased therefore, CPIH seems to be lower than or equal to CPI over a certain period (Groves, 2016). 
As compare to CPI or CPIH, retail price index measure changes in price rates on monthly basis. 
d) Use of collected data form Consumer price Index to determine annual inflation
The consumer price index as per above mentioned national statistical data, Bureau of Labour Statistics reported that it has slightly increased to near about 2% (Lam, 2012). An increase in electricity and gasoline, used cars, trucks and other basic transportation, food items etc. is majorly affect purchasing power of people. Along with this, consumption of some goods like new vehicles, indexes for communication and recreation all, also has also declined slightly from 2016 to 2017.
e) Significance of calculating inflation rate
Measuring inflation rate is considered as most difficult task for statisticians. For this process, a number of various goods and services which refers to representative of economy will put together in a basket (Keller, 2015). Further, cost of this basket will then compare with past data to analyse the inflation rate. For this purpose, mostly statistician use CPI to measure price changes in goods and services which includes food, gasoline, automobile and more.
Activity 2
Hourly pay rates in different regions of UK
a) Ogive curve to determine Median
Ogive curve refers to statistical tool which is used for measuring the value of median of a certain data. Under this process, two types of curves are drawn viz. Morethan type and Lessthan type, where point of inflexion are termed as median of given data. Basically, this kind of curve is drawn on cartesian plan of 2D data where Xorigin represents classinterval and Yorigin shows cumulative frequencies (Jessop, 2016). Concept of both kind of Ogive curve can be elaborated by following example:
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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 


Median determined in terms of Morethan and Lessthan type Ogive curve:
Therefore, the point where both kinds of Ogive curve that are lessthan and morethan is considered as Median. From this process, median for hourly earning for leisure centre staff of London area is calculated as near about £19.0.
Quartile:
A quartile is a statistical term which helps to define or explain a division of observations into four equal intervals based upon values of data and how they are used to compare entire set of observations (Walters, 2016).
 First quartile: It is denoted by Q1 and is termed as median of lower half of any given data set. This can further be said that 25 % numbers lie below Q1 and 75% lie above it.
 Third quartile:It is symbolically represented by Q3 and is known to be median of upper half of any given data set. So, this can further be said that 75% numbers fall under Q3 and 25% lie above it.
Interquartile:
Inter quartile or inter quartile range is a statistical measure of variability. It is based on dividing any given data set into quartiles.
Now Quartiles can be calculated as per:
Therefore, First Quartile of deviation can be calculated as per:
Here lower limit (l) = 10, frequency (f)
= 23, Class interval (h)
= 10 and Total frequency (N/4)
= ∑F/4 = 12.5, cf = 4
Q_{1 }= L + (N/4 – cf)/ f x h
= 10 + (12.5 – 4)/ 23 x 10
= 10 + 85/ 23
= 13.7
While, Third Quartile of deviation can be calculated as per:
Here l = 20, f = 13, h = 10 and 3N/4 = ¾ of ∑F = 37.5, cf =27
Q_{3 }= L + (3N/4 – cf)/ f x h
= 20 + (37.5 – 27) / 13 x 10
= 20 + 105/13
= 28.07
Therefore, Interquartile range can be calculated by measuring the difference among first and third quartiles, as shown below:
IQR = Q_{3 –} Q_{1 }
_{ } = (28.0713.7)
= 14.0 (approx)
b) The mean and standard deviation for hourly earnings of London area
Central tendency can be defined as process to show entire data into single manner. This method is given by Professor Bowley which has given various types of techniques to calculate and analyse large information into simpler form (Hecke, 2012). It includes mean, median, mode, quartiles, standard deviations and more. Concept of some of these methods can be explained in following manner:
Mean:
It can be defined as an average of a particular data which can be measured by dividing sum of observation to total numbers. It is also known as arithmetic mean of data which covers entire observations. Therefore, in present context, this methodology helps in calculating average of hourly earning for leisure centre staff in London area.
Median:
It refers to middle data or second quartile of central tendency which denotes the midpoint of a frequency distribution (Haimes, 2015). It is calculated by various methods like Ogive curve, frequency distribution method and more.
Standard Deviation:
It can be defined as a measure of central tendency which is used to quantify the amount of dispersions or variations of a set of values.
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 
Calculation
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 and London area
Basis of Comparison 
Manchester area 
London area 
Median 
£14.00 
£19.00 
Interquartile Range 
£7.50 
£14.00 
Mean 
£16.50 
£21.40 
Standard Deviations 
£7.00 
£5.00 
Therefore, on comparison of hourly earning of both area of Manchester and London, it has analysed that
Activity 3
a) Economic Order Quantity (EOQ)
EOQ is the order quantity that determine the total cost and ordering cost. It is considered as one of the most classical production planning methods which was developed by Ford W.Harris in 1913. In depth analysis, EOQ method can be altered to find out different production standard or can be stated as fundamental techniques with large supply series to calculate variable cost (Bedeian, 2014).
Economic Order Quantity can be calculated by using below mentioned formula :
EOQ = √( 2 x D x Co / Ch)
Where, D = Demand per year;
Co = Cost per order;
Ch = Cost of holding per unit of inventory
As per present case study,
Demand of tshirt = 2000;
cost per tshirt is £5 and
cost of holding=2
Therefore, EOQ = square root of (2 x 2000 x 5)/2
= 100 Units
 b) Re Order teeshirts
It is essential for companies to have a knowledge about dimension of crude and completed stock which helps in increasing effectiveness of production process (Barrett and et. al., 2012). In case of loss of control on inventory level of stock, an organisation can face problems like shortage in cost. Therefore, under such condition, firm will also not in state to cover revenue as well or meet demand of customers on time.
In context with present case, Ms Jones are required to reorder following number of teeshirts as shown in below calculation:
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
It is essential for organisations or individuals to calculate inventory policy cost so that expenses can be reduced and manage stock also (Andreeva and Kianto, 2012).
Inventory Policy Cost = Purchase cost + Cost per order + Carrying cost
= 10 + 5 + 2
= £17
As inventory covers all kinds of expenses and cost of managing stock therefore, it is obtained as £17.
 d) Current service level to customers
Current Level of service = Demand per week x Availability of tshirt
= 95% of 40
= 38 units
 e) Work out the reorder level to achieve desired service level
Reorder level (ROQ) = (Average usage x Lead time) + additional 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 type 
Cumulative frequency 
Less than type 
Cumulative frequency 
Below 10 
4 
8.00% 
More than 0 
50 
Less than 10 
4 
10 but under 20 
23 
46.00% 
More than 10 
46 
Less than 20 
27 
20 but under 30 
13 
26.00% 
More than 20 
23 
Less than 30 
40 
30 but under 40 
7 
14.00% 
More than 30 
10 
Less than 40 
47 
40 but under 50 
3 
6.00% 
More than 40 
3 
Less than 50 
50 
Total 
50 





Conclusion
From this assignment it has analysed that to analyse any data in appropriate manner, mostly organisations use statistical concepts. It provides various methods like central tendencies, deviations, dispersion and more which helps in analysing data in simple manner. An effective knowledge of statistics as well as ability for applying such applications can help in resolving various problems.
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.