Statistical Tools for Organizational Decision Making

The report emphasizes the significance of statistical tools in supporting organizational decision-making processes. It discusses various statistical tools used to analyze data, compare actual outcomes, and determine current financial positions. The document also mentions the use of graphic content to facilitate understanding of changes and trends within an organization.

Statistics
For
Management

Table of Contents
INTRODUCTION...........................................................................................................................3
TASK 1............................................................................................................................................3
(a) Testing Hypothesis for mean earning in public sector..........................................................3
(b) Testing hypothesis for mean earning in private sector:.........................................................4
(c) Earnings-Time Chart for each group by using excel:............................................................5
(d) Calculation of Annual Growth Rate:.....................................................................................7
TASK 2............................................................................................................................................9
a) Use of ogive to estimate the median hourly earnings and the quartiles..................................9
b) Calculation of Mean and Standard Deviation of hourly earning:.........................................11
TASK 3..........................................................................................................................................13
a) Calculation of Economic order quantity:..............................................................................13
b) Calculation of re order duration of Tee Shirts......................................................................14
c) Calculation of Inventory Policy Cost:...................................................................................14
d) Calculation of current level service to the customers:..........................................................15
e) Calculation of Re order level................................................................................................15
TASK 4 .........................................................................................................................................16
(a) Graphical representation to show changes in price index as per CPI, CPIH and RPI:........16
(b) Creating Ogive using table 1...............................................................................................17
CONCLUSION..............................................................................................................................18
REFERENCES..............................................................................................................................19

INTRODUCTION
Business statistics simply implies use of various techniques and tools of statistics in
business to solve organisational problems which helps organisation to take vital decisions. It
includes application of such techniques and tools with respect to areas like finance, marketing,
research and development, employee management etc. in order to derive relevant and signifiant
information for decision-making activities (Steinberg, 2016). It provide a framework for analysis
of growth and performance of business organisation. This report covers practical use of such
tools and techniques such as ogive, EOQ, reorder level, mean, median, mode etc., and graphical
representation to analyse and interpret information and data.
TASK 1
Hypothesis is an critical explanation or approach that is temporarily followed to interpret
or analyse any event or circumstance and to give a proper guideline for further examination or
critical analysis. It generally applied by entities to evaluate the inter-relationship among different
variables. It provide assistance to managerial personnels to take actions towards achievement of
organisation's objectives. In order to measure hypothesis some major methods like dispersion,
central tendency etc. are used (Tran, Lester and Sobin, 2014). It is applied to asses the validity
and correctness of statement and evaluation of assumptions or explanation that is used for a
specific set of information and data. It provide outcomes in form of hypothesis accepted or
rejected. For validation of particular statement null hypothesis(H0) and alternative hypothesis(H1)
are generally used.
(a) Testing Hypothesis for mean earning in public sector.
Under given case study and scenario random sample is selected from 1000 persons
earning which is classified as gender: Men and Women, For this following hypothesis is
considered:
Null Hypothesis (H0) :- Here, Earning of men related to public sector is not substantially higher
than women's earning in public sector.
Alternative Hypothesis (H1) :- Here, Earning of men related to public sector is substantially
higher than women's earning in public sector.

As per above table it is evaluated that in 2009 there was a pay gap of £5,414 between
earning of Men and Women. Although such gap has been reduced to £ 5173 till year 2014 but
these is a an increase reported in 2015 and 2016. As per observation of above table it is clear that
in 2010 a maximum percentage change is reported. So from overall analysis it has been
concluded that overall earning of men related to public sector is not substantially higher than
women's earning in public sector which refers that H0 or null hypothesis is acceptable and on
other side H1 or alternative hypothesis is rejected (George, Haas and Pentland, 2014).
(b) Testing hypothesis for mean earning in private sector:
In this case scenario also 1000 persons are selected from whole population and, divided
in earning of men and women. For these following hypothesis are considered:
Null Hypothesis(H0): :- Here, Earning of men related to private sector is not substantially higher
than women's earning in private sector.
Accepted Hypothesis(H1): Here, Earning of men related to private sector is substantially higher
than women's earning in private sector.

From the analysis of data of above table it has been analysed that during the period 2009-
2016 there is aggregate increase of £2047 in earning of men and in case of Women such
increment is £2700. In term of percentage such increases are 7.41 % and 13.81 % respectively
which points out that growth in income of women are more than earnings growth of men. It is
notable that in both group pay gap is minimised in 2014 and 2016 which is £7,425 and £7,428 in
respective years which is an indication that effective methods are applied by player in industry to
control such earning gap. On the basis of such observations, the hypothesis holds true for the
data extracted resulting in acceptance of H0 while H1 is rejected.
(c) Earnings-Time Chart for each group by using excel:
 Graph exhibiting earnings men in public sector :-
2009 2010 2011 2012 2013 2014 2015 2016
28000
29000
30000
31000
32000
33000
34000
35000
30638
31264 31380
31816
32541 32878
33685 34011
Earnings
Time
Earnings
 Graph exhibiting earnings of women in public sector:

 Graph exhibiting earnings of men in private sector:
 Graph exhibiting earnings of women in private sector:

(d) Calculation of Annual Growth Rate:
In term of finance Annual Growth Rate simply defined as a rate or certain percentage that
indicates how fast organisation is achieving new growth standards. It act as a tool that assist in
developing a groundwork for taking appropriate decisions related to investment (Granato, 2014).
Computation of annual rate of growth encourage a comparative analysis and compatibility to
asses actual growth and performance of business organisation. Here annual growth rate is
calculated using following equation:
% / Growth Rate (annual) = [(Numeric value of current year less numeric value of
previous year)/ Numeric value of previous year] * 100
Based on above formula following is growth rate of earning of men and women in
respect of both public and private sector, as follows:
 Earnings of Men in Public Sector:

In 2016 annual growth rate has been reduced from 2.45% to .97% which indicates that
these is negative growth overall growth as compare to previous years. However overall rate of
growth is accounted equal to 11%.
 Earnings of Women in Public Sector:
The overall annual growth i.e. 10.61% in income earned by women in respective industry
has been inconsistent and highly uncertain because such rate is continuously decreasing from
2013.
 Earnings of Men in Private Sector:
During the year 2009 to 2016 earning of men in private sector is increased and overall
growth rate is 7.41 % as accounted from above graph. It is observed that in private sector
increased payment is made against their service employment.
 Earnings of Women in Private Sector:

There is inconsistent annual growth rate during 2009 to 2016 in earning of women in
private sector. Although there is overall growth rate of 13.81% in this sector for women. In 2016
there is maximum growth rate of 3.96%.
TASK 2
a) Use of ogive to estimate the median hourly earnings and the quartiles.
Ogive curve: It is also called as cumulative histogram that is applied to identify values
given from a data group below or above a particular class. It is most popular and widely used
tool of statistic which is help to asses the median value of selected sample from population.
Under ogive curve 2 curves are prepared based on given data and these two curve represents as
“less than ogive” and “more than ogive” (Kotz and Johnson, 2012). Under more than ogive the
value which is more than particular interval or class are presented where under less than ogive
values are shown which are less than particular class or interval. The intersecting point of these
two curve lines is refers to median value.

More than ogive
Less than ogive
Ogive curve
Below 10
10 but under 20
20 but under 30
30 but under 40
40 but under 50
Total
0
10
20
30
40
50
60
No. of Leisure central staff
(f)
More than O-give
Cumulative frequency
Less than O-give
Cumulative frequency

According to above chart based on ogive it has been evaluated that intersection point the
median which is obtained from the intersection point of less than ogive and more than ogive is
approx 25.5. It establishes that the hourly earning of leisure central staff of London is 25.5.
Quartiles: It is a statistical measure which is applied to classify or divide whole
observations into 4 parts or equal intervals. Quartiles provides a framework for comparison of
whole population and samples with such calculated intervals or quartiles. In quartiles data is
systematically classified into Q1 (first quartile), Q2 (second quartile) and Q3 (third quartile).
First quartile is lower half of data specified into sample which indicates variables that are less
then second quartile or median value (Kwon, Lee and Shin, 2014). It denoted 25% of sample
data. Just opposite to first quartile, Q3 covers last one forth of data. Q2 is simply the rest part or
median of sample data. In given case context following is the calculations for computation of
quartiles:
…. .. … .....................First Quartile = (25% of (n+1)) = (0.25* (50+1)) = £12.75
… ...........................Third Quartile = (75% of (n+1)) = (0.75* (50+1)) = £38.25
. . . . …..................Inter-Quartile Range = Q3- Q1 = 38.25 - 12.75 = £25.5
b) Calculation of Mean and Standard Deviation of hourly earning:
Mean: It simply refers to average of value data in sample. It is simple average of data
which indicates a representative value of data in a given sample. Mean or average is classified as
Arithmetic mean and Geometric mean. The mean of a whole population is known as mean
population. It is most widely used static to compute centre of given sample data (Baglin and Da
Costa, 2012).
Standard Deviation: it is a statistical measure that helps to calculate amount of
dispersion or variation of a particular data set. It generally considered as risk indicator. A lower
standard deviation points out that values given in sample data are very close to the mean value
whereas a higher standard deviation indicates that value are in unstructured form and
spearheaded in wider range (Borio, 2013).

working notes:
Comparison between the earning in two region:

As per above comparison it is clear that the median of hourly earning in respect of leisure
centre staff in Manchester is 14 and in case of London is 19. Beside these mean and Interquartile
range in case of Manchester is higher then hourly earning of staff in London.
TASK 3
a) Calculation of Economic order quantity:
Economic Order Quantity(EOQ): Economic order quantity refers to certain quantity of
stock that required to be ordered by organisation in order to optimise cost of inventory
acquisition. It assist organisation to mange or handle inventory in way that the no stoppage in
production process and sales occur. EOQ is major part of inventory and supply chain
management (Leon, Stewart and Yamagishi, 2012). It simply provide assistance to companies to
manage and control their reorder cost of inventory, storage cost and all ancillary cost related to
activities of inventory management. Following is formulae to calculate the economic order
quantity:

Calculation of EOQ:
b) Calculation of re order duration of Tee Shirts.
Re order duration refers to period in which a business organisation should replace an
order for stock. In order to find out re order duration first calculation of re order level or point is
required to calculate (Otero, Castle and Johnson, 2012). A reorder level point or level is
minimum benchmark level of stock quantity at which organisation should place order for
inventory. To compute reorder organisation should determine lead time of delivery. Following is
the calculation for Re order point and re order frequency or duration as stated below:
c) Calculation of Inventory Policy Cost:
Inventory policy cost: According to this policy the total cost that holds each and every variables
and all related fixed cost that are being implemented at the time of raw product and finished
commodity. It is one of the best cost accounting method to calculate and determine the actual
expenses of stocks. This method is refereed to be a crucial part of inventory cost system as it also
evaluate the actual value of variable cost that is connected with reordering of different stock
within company. Thus the management of Jenny Jones used to calculate the cost of inventory
that help to figure out the expenses with the help of specific formula along with calculations is
discussed underneath:

d) Calculation of current level service to the customers:
In business scenario, the current and actual level services to consumer is the definable
stage of customer that an organisation can satisfy by producing different product and services. In
recent market customer are the one those create demand of different product and company
focuses to fulfil by providing the same at decent price (Kim, Kumar and Kumar, 2012). From the
mention case the customer satisfaction level is 95% as it is observed that demand for T shirt have
been raised from 40 to a decent volume within the last ten week. The underneath calculation
shows the current service level of customer for the Jenny Jones:
e) Calculation of Re order level.

TASK 4
(a) Graphical representation to show changes in price index as per CPI, CPIH and RPI:
Retail Price Index

(b) Creating Ogive using table 1
Hourly Earnings (£) No. of Leisure Centre Staff Cumulative Frequency
Less than 10 4 4
Less than 20 23 27
Less than 30 13 40
Less than 40 7 47
Less than 50 3 50

Total 50
0 10 20 30 40
0
10
20
30
40
50
60
4
27
40
47 50
Ogive
Cumulative
Frequency
Upper Class Boundaries
Cumulative Frequency
CONCLUSION
From the above presented report, it has been concluded that different statistical tools are
essential for an organisation that support to make meaningful decision and also aid to determine
the current trends within market. Tool also benefits to compare the actual outcomes for the last
five year so that performance can be improved. Thus it support to disclose the current and
accurate financial position and strength for respective company. It is also concluded that some
useful statistical tools are being implemented by management to make sure that changes are
favourable and trends do not lead down the performance. With the aid of the graphic content of
the information it is casual for the individual to understand the alteration.

REFERENCES
Books and Journals:
Steinberg, D. M., 2016. Industrial statistics: The challenges and the research. Quality
Engineering. 28(1). pp.45-59.
Tran, D., Lester, H. and Sobin, N., 2014. Toward statistics on construction engineering and
management research. In Construction Research Congress 2014: Construction in a
Global Network (pp. 1139-1148).
George, G., Haas, M. R. and Pentland, A., 2014. Big data and management.
Granato, G. E., 2014. Statistics for stochastic modeling of volume reduction, hydrograph
extension, and water-quality treatment by structural stormwater runoff best management
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Kotz, S. and Johnson, N. L. eds., 2012. Breakthroughs in Statistics: Methodology and
distribution. Springer Science & Business Media.
Kwon, O., Lee, N. and Shin, B., 2014. Data quality management, data usage experience and
acquisition intention of big data analytics. International journal of information
management. 34(3). pp.387-394.
Baglin, J. and Da Costa, C., 2012. An experimental study evaluating error management training
for learning to operate a statistical package in an introductory statistics course: Is less
guidance more?. International Journal of Innovation in Science and Mathematics
Education (formerly CAL-laborate International). 20(3).
Borio, C., 2013. The Great Financial Crisis: setting priorities for new statistics. Journal of
Banking Regulation. 14(3-4). pp.306-317.
Leon, P. L. D., Stewart, B. and Yamagishi, J., 2012. Synthetic speech discrimination using pitch
pattern statistics derived from image analysis. In Thirteenth Annual Conference of the
International Speech Communication Association.
Otero, F., Castle, T. and Johnson, C., 2012, July. Epochx: Genetic programming in java with
statistics and event monitoring. In Proceedings of the 14th annual conference
companion on Genetic and evolutionary computation (pp. 93-100). ACM.
Kim, D. Y., Kumar, V. and Kumar, U., 2012. Relationship between quality management
practices and innovation. Journal of operations management. 30(4). pp.295-315.