# Statistics For Management

## 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 index-linked 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 2007-2017:

 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 2007-2017:

 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, auto-mobile and more.

## Activity 2

Hourly pay rates in different regions of UK

### a) O-give curve to determine Median

O-give 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. More-than type and Less-than type, where point of inflexion are termed as median of given data. Basically, this kind of curve is drawn on cartesian plan of 2-D data where X-origin represents class-interval and Y-origin shows cumulative frequencies (Jessop, 2016). Concept of both kind of O-give curve can be elaborated by following example:-

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#### More than O-give curve

 Hourly earning in Euro (Class Interval) No. of Leisure central staff (f) More than O-give 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 O-give Curve

 Hourly earning in Euro (Class Interval) No. of Leisure central staff (f) Less than O-give 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 More-than and Less-than type O-give curve:

Therefore, the point where both kinds of O-give curve that are less-than and more-than 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

Q1 = 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

Q3 = L + (3N/4 – cf)/ f x h

= 20 + (37.5 – 27) / 13 x 10

= 20 + 105/13

= 28.07

Therefore, Inter-quartile range can be calculated by measuring the difference among first and third quartiles, as shown below:-

IQR =   Q3 – Q1

=  (28.07-13.7)

= 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 O-give 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   (x2) (F*x2) 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= √ (∑Fx2 / ∑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 t-shirt = 2000;

cost per t-shirt is £5 and

cost of holding=2

Therefore, EOQ = square root of (2 x 2000 x 5)/2

= 100 Units

1. b) Re Order tee-shirts

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 re-order following number of tee-shirts as shown in below calculation:-

Re-order level (ROQ) = (Lead time x daily average usage) + safety stock

= (28 x 2)+150

= 206 units

Frequency of Re-order = 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.

1. d) Current service level to customers

Current Level of service = Demand per week x Availability of t-shirt

=   95% of 40

=   38 units

1. e) Work out the re-order level to achieve desired service level

Re-order 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 O-give curve of cumulative % of staff versus hourly earning

#### More than O-give 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.617-636.
• 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.121-135.
• Haimes, Y. Y., 2015. Risk modeling, assessment, and management. John Wiley & Sons.
• Hecke, T. V., 2012. Power study of anova versus Kruskal-Wallis test. Journal of Statistics and Management Systems. 15(2-3).  pp.241-247.
• Jessop, A., 2016. StatsNotes: Some Statistics for Management Problems. World Scientific Books.
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