Statistics for Management: Nature, Process, and Evaluation of Data

This document provides an overview of statistics for management, including the nature and process of business and economical data. It discusses the evaluation of data from various sources using different statistical methods. The importance of inflation rate and the differentiation between descriptive, exploratory, and confirmatory analysis are also covered.

Statistics
For
Management

Table of Contents
INTRODUCTION...........................................................................................................................1
ACTIVITY 1....................................................................................................................................1
Activity 2.........................................................................................................................................8
Activity 3.......................................................................................................................................12
ACTIVITY 4..................................................................................................................................14
CONCLUSION..............................................................................................................................17
REFERENCES..............................................................................................................................19

INTRODUCTION
Statistics for management is a investigation of information and practical application to
interpret the dynamics of management by using statistical tools and techniques. Statistical
analysis is a elements of analytical data. It is used to collect and scrutinize all sample of data in a
unit of items from where the samples are drawn (Abdelhak, Grostick and Hanken, 2014). This
report covers nature and process of business and economical data obtained from published
sources. Analysis and evaluation of raw business data by using different statistical methods are
mentioned. Statistical methods are applied in business planning. Along with this data and
information are presented in a tabular and charts form are also mentioned in this report.
ACTIVITY 1
P1. Nature and process of business and economical data from different published source
Business data is a information of things, people, place, rules of business and activity
related to business operations. Economic data is a quantitative measures that shows accurate
report of past and present economy.
Consumer Price Indices
Consumer price index (CPI):
CPI is a comprehensive measures which is used to estimate the change in retail price of
goods and services which represents consumption of expenditure in economy. This is an
essential economic indicator as it analyse economy according to weighted average price of
goods. It is measured by taking change price of every items in preset basket of goods. Any
occurrence in CPI is used to evaluate the price changes that is related to cost of living. It is
mostly used statistics to identify inflation and deflation periods. It gives ideas about change price
of economy to businesses, citizens and governments.
1

CPIH:
CPIH is a new method that is used to analyse inflation of consumer price considering
evaluation of owner occupiers housing costs(OOH). It is comprehensive measures which
comprises the appraising process of management and consumer inflation for improved findings
and transactions. It is considered as a better evaluator for Different type of inflation rate and
analysis for ascertaining an understanding budgets case (Qiu, Qin, and Zhou, 2016).
Retail price index(RPI):
RPI is one of the essential index that evaluate inflation of consumer produced by UK's
office for national statistics. It is generally used to measure the inflation rate and like GNP
deflector. This examine annual rate promulgated on basis of tax allowances, salaries and wages.
This index is mostly used to handle many requirements that happen because of various RPI's. It
represents the expenses position of living reportt according to changes rate of goods and
services.
2

Differentiate between indices.
Basis CPI CPIH RPI
CPI was firstly CPIH measures the RPI was introduced in
3
29/06/1905
30/06/1905
01/07/1905
02/07/1905
03/07/1905
04/07/1905
05/07/1905
06/07/1905
07/07/1905
08/07/1905
09/07/1905
0
50
100
150
200
250
300
RPI

established in
European union in the
year 1996.
inflation of consumer
price including cost of
house owned by
owners.
united kingdom in
year 1956.
aim It aim is to analyse
euro countries for
evaluating the
utilisation capacity on
salary basis (Gaynor,
and Muir, W, 2014).
It aim is to assess the
abstracted charge on
residential rents.
The aim of RPI is to
monitor living cost on
the basis of
government planning
and various consent.
Exclusions In this indices, price of
houses, cost of
purchase house ,
council tax and
interest payments of
mortgage are
excluded.
In this indices, people
from private or
businesses sectors are
excluded because of
their own agency of
evaluation.
In this indices, life
insurance charges,
national insurance ,
pension charges and
income tax are
excluded.
d. use of data collected from consumer price index to elaborate
Consumer price index plays a crucial role for evaluating annual rate of inflation of
company. There is a appropriate examination of information for developing the living index
cost. It effects the fluctuation and differences that are occurs due to changes incurred during
annual inflation rate. CPI assist to merge the group with generating division changes for small
reasons. Many factors are accountable for evaluating the annual rate of inflation and CPI. Bureau
of Labor statistics facilitates information according to annual expenditure by consumers for
specified time period. There are some sections that are examined to ascertain the increase price
because of inflation cost and cost of energy (Coolican, 2017). For deciding the annual rate of
inflation it is necessary to have data associated with utilisation for a for specific time periods.
e. Importance of inflation rate.
It is necessary to examine the rate of growth and CPI of company of an economy.
Inflation rate is an elements according to performance of industry and output of GDP is
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examined and different from each other. Rate of inflation is the important criteria that assist in
management cumulative percentage and RPI for proper development and improvement.
Consumer price index and consideration were examined with housing index payment rate. Rate
of housing was evaluated to influence price that is separated with various criteria.
P2. Evaluation of data from various sources by using different statistical methods.
Data are evaluated by using bar charts and scattered charts with the help of table:
CPI
according to the above information bar charts of shows the fluctuation of CPI during 10 years
from 2007 to 2017. from above information it is examined that CPI is increasing with rate of
3.5% for consequent years (Miah, 2016). There is important differences that was evaluated in
5
29/06/1905
30/06/1905
01/07/1905
02/07/1905
03/07/1905
04/07/1905
05/07/1905
06/07/1905
07/07/1905
08/07/1905
09/07/1905
0
20
40
60
80
100
120
140
CPI

price variation within 10 years. The information is obtained from office of national statistics to
study the variation.
RPI
From the above data bar chart is presented according to retail price index table. It is examined
that a preferred inflation rate is reported in accordance to rate that in increased in year 2007 to
2017. there are essential rate that is 3.85% was calculated in year 2008 and 2009. VARIATION
RATE increased in 2009 and 2010 with 4.62%. It is analysed that charts vary between 3.5% to
4.6%.
M1. Evaluation of price indices other than office of national statistics.
6
29/06/1905
30/06/1905
01/07/1905
02/07/1905
03/07/1905
04/07/1905
05/07/1905
06/07/1905
07/07/1905
08/07/1905
09/07/1905
0
50
100
150
200
250
300
RPI

It is evaluated that company in United Kingdom pay less to female employee other that
male employee. In UK it is origin that females are less committed in consumer index prices.
According to the report of Rectella's it is viewed that sexual orientation pay opening was
recorded. Middle was also ascertained for approximation (Gui and Aslam, 2017).
D1. Differentiate between descriptive, exploratory and confirmatory analysis.
Descriptive Exploratory Confirmatory
This analysis is a well
organised process which
incorporates the abilities and
standard of particular subjects.
Probability and analysing are
used for appropriate reasons.
This analysis study that which
types of data is needed to
dislocation and how it will
highlights the most preferred
way to execute the results.
This analysis is some data that
is used by accepted factual
instruments such as
speculating, quality and
critically.
Activity 2.
(a) I. 1.Median:
The median is a statistical term applied for finding the 'average' of a set of data points. It
is a simple measure of inside tendency (Quirk and Cummings, 2016). To find the median, unify
the observations in order from smallest to largest value.,If there is an odd number of
observations, the median is the middle value. If there is an plane number of observations, the
median is the stereotype of the two middle values.
In median calculation in case data given in range and frequency we use Cumulative frequency
that is defined as a running total of frequencies. The frequency of an element in a set refers to
how many no. of that element there are in the set. Cumulative frequency can also defined as the
sum of all previous frequencies up to the current point.
Hourl
y
Earni
ng
Class
Boundaries
No. of
leisure
centre
staff
Cumulative
Frequency
7

(x)
0-9 0-9.5 4 4
10-19 9.5-19.5 23 27
20-29 19.5-29.5 13 40
30-39 29.5-39.5 7 47
40-49 39.5-49.5 3 50
N = 50
N 50
2 2
= 25
Cf = 27
f = 23
L = 9.5
N = 25
M
= Cf - N * i + L = 27-25 * 10+9.5
f 23
= 10.37
2.Quartiles:
Quartiles in statistics refers to values that divide population data into quarters. However,
quartiles divide data into four segments equal to where the numbers fall on the number line. In
quantile, there is three points that divide sorted data set into four equal groups by count of
numbers, each representing a fourth of the distributed sampled population (Kiruthika and Dilsha,
2015).
The upper quartile corresponds to the 75th percentile i.e. 75% of the total
frequency.
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75% of the total frequency 75%*50 = 37.5
The lower quartile corresponds to the 25th percentile i.e. 25% of the total
frequency
25% of the total frequency 25%*50 = 12.5
The interquartile range = upper quartile – lower quartile
37.5-12.5
= 25
(II)
(1.)Mean:
Mean refers to the midpoint or stereotype that is used to derive the inside tendency of the
data in question. It is unanswerable by subtracting all the data points in a population and then
dividing the total by the number of points. The resulting number is known as the mean or the
average (Purohit, Deshmukh and Gore, 2015).
Hourly Earning No. of leisure centre staff
Cumulative
Frequency
f x nx
0-9 4 4.5 18
10-19 23 14.5 333.5
20-29 13 24.5 318.5
30-39 7 34.5 241.5
40-49 3 44.5 133.5
50 1045
9

Mean = 1045 20.9
50
(2.) Standard Deviation:
The standard deviation is tool that measures the breakup of a dataset relative to its
midpoint and is calculated as the square root of the variance. It shows the variation between each
data point relative to the mean. If the data points are not accurately calculated from the mean,
which showa there is higher deviation within the data set thus by doing the increasingly spread
out the data, gets higher standard deviation.
f x (X-Xbar) (X-Xbar)² f*(X-Xbar)²
0-9 4 4.5 -16.4 268.96 1075.84
10-19 23 14.5 -6.4 40.96 942.08
20-29 13 24.5 3.6 12.96 168.48
30-39 7 34.5 13.6 184.96 1294.72
40-49 3 44.5 23.6 556.96 1670.88
50 Total of f*(X-Xbar)² = 5152
Variance Total of f*(X-Xbar)² = 103.04
Totral of f
Standard deviation = square root of 'Variance' i.e 10.15
(b).Comparison:
Given Calculated
Median 14 10.37
Interquartile 7.5 25
Mean 16.5 20.9
Standard deviation 7 10.15
10

OR
(2)
(a) Scatter Diagram:
The scatter diagram graphs pairs of number-based data, with one number or thing that
changes on each axis, to look for a relationship between them. If the numbers that change/things
that change are related, the points will fall along a line or curve. The better the relationship, the
tighter the points will hug the line.
Weak Average Temperature Hot Drink 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
11

Association between average temperature and hot drink sales:
Weather directly or indirectly affects the business of an entity as an macro environmental
factor. In food and beverage industry business is extremely depends upon weather in relation to
sales and storage of products. In this context it may be noted that hot drink is a product that is
purely depends on weather or temperature. As per given circumstances range of hot drink sales is
6 to 18 and average turnover ranges between 12.5 to 20 but its is considerable that in scatter
diagram there is to points cuts each other that shows that higher the temperature – higher hot
drink sales relationship(Chen, 2016).
(b)Calculation of Correlation coefficient (r) and Coefficient of determination:
Weak Average temp.(x) Hot Drink Sales(y) xy x² y²
1 18.5 15 277.5 342.25 225
2 16 10 160 256 100
3 13 13.5 175.5 169 182.25
4 19.5 15 292.5 380.25 225
5 20 18 360 400 324
6 19 14 266 361 196
7 15.5 13 201.5 240.25 169
8 14 8.5 119 196 72.25
9 12.5 6 75 156.25 36
12
(Scatter Diagram)

10 15 9 135 225 81
Total= 163 122 2062 2726 1610.5
REGRESSION STATISTICS
Observations 10
Correlation coefficient (r) using above formula 0.799
Coefficient of determination (r-squared) 64%
Activity 3.
(a)Paired T-test :
A paired t-test is applied for testifying the null hypothesis that the average of the
differences between a series of paired observations is zero. Observations are paired when, for
example, they are performed on the same samples or subjects. The paired t-test assumes that the
differences between pairs are usually in a common and regular way distributed, If the differences
between pairs are very much non-usual, it would be better to use other tests. The paired t–test
does not assume that observations within each group are normal, only that the differences are
normal and also it does not assume that the groups are homoeostatic.
Employee Old system New system new - old
1 40.5 39.2 -1.3
2 42.9 40.7 -2.2
3 52.8 50.6 -2.2
4 51.7 50.7 -1
5 77.2 71.4 -5.8
6 66.7 70.5 3.8
7 65.2 71.1 5.9
8 49.2 47.7 -1.5
9 55.6 52.1 -3.5
10 58.3 55.5 -2.8
13

Average difference: -0.424
N: 25
Degrees of freedom: 24
t-value: 0.976561
P-value: 0.338528
Here p = 0.338528 , which is < 0.05, so the difference is significant.
(b)Usual condition for T-test: Usual condition for a given proposition test is a value for which a
P-value less than or equal to is considered statistically significant. Level of significance is
5.00%. These values correspond to the probability of observing such an latter most value by
chance. In the test score example above, the P-value is 0.338528, so the probability of
observing such a value by chance is less that 0.05, and the result is significant at the 0.05 level.
(c)
Old System New System Confidence Level 0.99
40.5 39.2
42.9 40.7 RESULTS
52.8 50.6 Group 1 Group 2
51.7 50.7 n 10 10
77.2 71.4 Mean 56.010 54.95
66.7 70.5 Std Dev 11.259 12.121
65.2 71.1 SE 3.560 3.833
49.2 47.7 t 2.878
55.6 52.1 Sp 11.698
58.3 55.5 Margin of Error 15.059
Point Estimate 1.060
Lower Limit -13.999
Upper Limit 16.119
14

ACTIVITY 4
P5. Tables and charts are used to explain findings.
CPI
RPI
15
1 2 3 4 5 6 7 8 9 10 11
0
500
1000
1500
2000
2500
Year
CPI
Total

b. Ogive for cumulative %.
16
1 2 3 4 5 6 7 8 9 10 11
0
500
1000
1500
2000
2500
3000
3500
Year
RPI
Total

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)
In percentage form
More than O-give
Cumulative frequency
Less than O-give
Cumulative frequency
17

M4. Justification of graphical representation from activity 1 and 2.
There are different data that is shown in graphical form with the help of tables, charts and
graphs. Bar charts and scatter diagrams are used in activity 1 and 2 to evaluate appropriate
methods so that information can be clarified and business are summarized in an effectual way.
Bar charts are basically used to show the data in respect of CPI and RPI form (Cooke and et.al,
2016).
D3. evaluation of tables and graphs that is used in activity 1 and 2.
A appropriate opinion method are needed to represent information and data in a
reasonable and understandable manner. Suitable information are used to ascertain condition and
balances with changes occurs in activity 1 and activity 2. column charts and bar charts are made
to represent the statistical data and collection in an effectual way.
CONCLUSION
From the above report it is concluded that economic data and business data or
information are important for representation of data in proper and understandable way. It
summarise that all statistical information in more appropriate way by describing the activities.
With the use of statistical method are crucial to relate relations and differences with the
changeable. With proper use of techniques and methods for management of business it state that
stocks can be handle with methods and analysis of statistics.
18

REFERENCES
Books and Journals
Abdelhak, M., Grostick, S. and Hanken, M. A., 2014. Health Information-E-Book: Management
of a Strategic Resource. Elsevier Health Sciences.
Qiu, Z., Qin, J. and Zhou, Y., 2016. Composite Estimating Equation Method for the Accelerated
Failure Time Model with Length‐biased Sampling Data. Scandinavian Journal of
Statistics. 43(2). pp.396-415.
Gaynor, J. S. and Muir, W. W., 2014. Handbook of Veterinary Pain Management-E-Book.
Elsevier Health Sciences.
Coolican, H., 2017. Research methods and statistics in psychology. Psychology Press.
Miah, A. Q., 2016. Applied statistics for social and management sciences. Springer.
Gui, W. and Aslam, M., 2017. Acceptance sampling plans based on truncated life tests for
weighted exponential distribution. Communications in Statistics-Simulation and
Computation. 46(3). pp.2138-2151.
Quirk, T. J. and Cummings, S., 2016. Excel 2013 for Health Services Management Statistics.
Springer International Publishing:.
Kiruthika and Dilsha, M., 2015. A neural network approach for microfinance credit scoring.
Journal of Statistics and Management Systems. 18(1-2). pp.121-138.
Purohit, S. G., Deshmukh, S. R. and Gore, S. D., 2015. Statistics using R. Alpha Science
International.
Chen, C.H., 2016. Optimum process mean setting based on variable sampling plan with
producer’s and consumer’s risks. Journal of Statistics and Management Systems. 19(3).
pp.491-498.
Cooke, G. D. and et.al., 2016. Restoration and management of lakes and reservoirs. CRC press.
online
CPIH, 2018 [Online]. Available through
<http://www.economicsonline.co.uk/Managing_the_economy/Measuring_inflation.html
>
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