Statistics for Management

2. In the context of today’s competitive business
environment where many organizations find
themselves data-rich but information-poor.
For decision makers, it is important to develop the
ability to extract meaningful information from
raw data to make better decisions.
It is possible only through the careful analysis of
data guided by statistical thinking

3. The views commonly held about statistics are numerous, but
often incomplete. It has different meanings to different people
depending largely on its use.
For example, (i) for a cricket fan, statistics refers to numerical
information or data relating to the runs scored by a cricketer;
(ii) for an environmentalist, statistics refers to information on the
quantity of pollutants released into the atmosphere by all types of
vehicles in different cities;
(iii) for the census department, statistics consists of information about
the birth rate and the sex ratio in different states;
iv) for a share broker, statistics is the information on changes in share
prices over a period of time; and so on.

4.  The average person perceives statistics as a column of figures,
various types of graphs, tables and charts showing the increase
and/or decrease in per capita income, wholesale price index,
industrial production, exports, imports, crime rate and so on.
 The sources of such statistics for a common man are newspapers,
magazines/journals, reports/bulletins, radio, and television. In all
such cases, the relevant data are collected; numbers manipulated and
information presented with the help of figures, charts, diagrams,
and pictograms;
 Efforts to understand and find a solution (with certain degree of
precision) to problems pertaining to social, political, economic, and
cultural activities, seem to be unending.
 All such efforts are guided by the use of methods drawn from the
field of statistics

5.  As statistical data ,
 the word statistics refers to a special discipline or a collection
of procedures and principles useful as an aid in gathering and
analysing numerical information for the purpose of drawing
conclusions and making decisions.
 Since any numerical figure, or figures, cannot be called
statistics owing to many considerations which decide its use,
statistical data or mere data is a more appropriate expression
to indicate numerical facts.
 A definition which describe the characteristics of statistics are
:
 the classified facts respecting the condition of the people in a
state . . . especially those facts which can be stated in numbers
or in tables of numbers or in any tabular or classified
arrangement.

6.  As statistical methods ,
 adopted as aids in the collection and analysis of numerical
information or statistical data for the purpose of drawing
conclusions and making decisions are called statistical
methods.
 Statistical methods, are also called statistical techniques,
are sometimes loosely referred to cover ‘statistics’ as a
subject in whole.
There are two branches of statistics: (i) mathematical
statistics and (ii) applied statistics.
Mathematical statistics is a branch of mathematics and is
theoretical. It deals with the basic theory about how a
particular statistical method is developed.
Applied statistics, on the other hand, uses statistical theory

7.  Statistical methods, broadly, fall into the following two
categories:
 (i) Descriptive statistics
 (ii) Inferential statistics
 DESCRIPTIVE STATISTICS: It includes statistical methods
involving the collection, presentation, and
characterization of a set of data in order to describe the
various features of that set of data.
 In general, methods of descriptive statistics include
graphic methods and numeric measures.
 Bar charts, line graphs, and pie charts comprise the
graphic methods, whereas numeric measures include
measures of central tendency, dispersion, skewness, and
kurtosis

8.  INFERENTIAL STATISTICS :
 It includes statistical methods which facilitate estimating
the characteristics of a population or making decisions
concerning a population on the basis of sample results.
 Sample and population are two relative terms.
 The larger group of units about which inferences are to be
made is called the population or universe, while a sample
is a fraction, subset, or portion of that universe.
 The need for sampling arises because in many situations
data are sought for a large group of elements such as
individuals, companies, voters, households, products,
customers, and so on to make inferences about the
population that the sample represents.

9.  Thus, due to time, cost, and other considerations data are
collected from only a small portion of the population
called sample.
 The concepts derived from probability theory help to
ascertain the likelihood that the analysis of the
characteristics based on a sample do reflect the
characteristics of the population from which the sample is
drawn. This helps the decision-maker to draw conclusions
about the characteristics of a large population under
study

10.  The scope of application of statistics has assumed unprecedented
dimensions these days.
 Statistical methods are applicable in diverse fields such as
economics, trade, industry, commerce, agriculture, bio-sciences,
physical sciences, education, astronomy, insurance, accountancy
and auditing, sociology, psychology and so on.
 United states commissioner has explained the importance of
statistics by saying: to a very striking degree our culture has
become a statistical culture.
 Even a person who may never have heard of an index number is
affected by those index numbers which describe the cost of living.
It is impossible to understand psychology, sociology, economics or
a physical science without some general idea of the meaning of an
average, of variation, of concomitance of sampling, of how to
interprets charts and tables.

11.  A state in the modern setup collects the largest amount of
statistics for various purposes. It collects data relating to
prices, production, consumption, income and expenditure,
investments, and profits.
 Popular statistical methods such as time-series analysis, index
numbers, forecasting, and demand analysis are extensively
practiced in formulating economic policies.
 Governments also collect data on population dynamics in
order to initiate and implement various welfare policies and
programmes.
 In addition to statistical bureaus in all ministries and
government departments in the central and state
governments, other important agencies in the field are the
central statistical organisation (CSO), national sample survey
organization (NSSO), and the registrar general of India (RGI)

12.  Statistical methods are extensively used in all branches of
economics.
 For example:
 Time-series analysis is used for studying the behavior of prices,
production and consumption of commodities, money in circulation,
and bank deposits and clearings.
 Index numbers are useful in economic planning as they indicate the
changes over a specified period of time in prices of commodities,
imports and exports, industrial/agricultural production, cost of
living, and the like.
 Demand analysis is used to study the relationship between the
price of a commodity and its output (supply).
 Forecasting techniques are used for curve fitting by the principle of
least squares and exponential smoothing to predict inflation rate,
unemployment rate, or manufacturing capacity utilization

13.  According to Wallis and Roberts, ‘Statistics may be regarded
as a body of methods for making wise decisions in the face of
uncertainty.’ Ya-Lin-Chou gave a modified definition over this,
saying that ‘statistics is a method of decision-making in the
face of uncertainty on the basis of numerical data and
calculated risks.’
 These definitions reflect the applications of Statistics in the
development of general principles for dealing with
uncertainty.
 Statistical reports provide a summary of business activities
which improves the capability of making more effective
decisions regarding future activities. Discussed below are
certain activities of a typical organization where statistics
plays an important role in their efficient execution.

14.  MARKETING before a product is launched, the market research
team of an organization, through a pilot survey, makes use of
various techniques of statistics to analyse data on population,
purchasing power, habits of the consumers, competitors, pricing,
and a hoard of other aspects. Such studies reveal the possible
market potential for the product.
 Analysis of sales volume in relation to the purchasing power and
concentration of population is helpful in establishing sales
territories, routing of salesman, and advertising strategies to
improve sales.
 Production : Statistical methods are used to carry out R&D
programmes for improvement in the quality of the existing
products and setting quality control standards for new ones.
 Decisions about the quantity and time of either self-manufacturing
or buying from outside are based on statistically analysed data.

15.  Finance: A statistical study through correlation analysis of profits
and dividends helps to predict and decide probable dividends for
future years.
 Statistics applied to analysis of data on assets and liabilities ,
income and expenditure helps to ascertain the financial results of
various operations.
 Financial forecasts, break-even analysis, investment decisions under
uncertainty—all involve the application of relevant statistical
methods for analysis.
 Personnel: (People work for organization) : In the process of
manpower planning, a personnel department makes statistical
studies of wage rates, incentive plans, cost of living, labor turnover
rates, employment trends, accident rates, performance appraisal,
and training and development programs.
 Employer-employee relationships are studied by statistically
analysing various factors—wages, grievances handling, welfare,
delegation of authority, education and housing facilities, and
training and development

16.  Currently there is an increasing use of statistical methods in
physical sciences such as astronomy, engineering, geology,
meteorology, and certain branches of physics.
 Statistical methods such as sampling, estimation, and design of
experiments are very effective in the analysis of quantitative
expressions in all fields of most physical sciences.
 Some specific areas of applications of statistics in social sciences are
:
 Correlation & Regression analysis techniques are used to study and
isolate all those factors associated with each social phenomenon
which bring out the changes in data with respect to time, place, and
object.
 Sampling techniques and estimation theory are indispensable
methods for conducting any social survey.
 In sociology, statistical methods are used to study mortality (death)
rates, fertility (birth rates) trends, population growth, and other
aspects of vital statistics.

17.  The knowledge of statistical techniques in all natural
sciences—zoology, botany, meteorology, and medicine—is of
great importance.
 For example, for a proper diagnosis of a disease, the doctor
needs and relies heavily on factual data relating to pulse rate,
body temperature, blood pressure, heart beats, and body
weight.
 An important application of statistics lies in using the test of
significance for testing the efficacy of a particular drug or
injection meant to cure a specific disease.
 Comparative studies for effectiveness of a particular
drug/injection manufactured by different companies can also
be made by using statistical techniques such as the t-test and
f-test.
 To study plant life, a botanist has to rely on data about the
effect of temperature, type of environment, and rainfall, and
so on.

18.  Computers and information technology, in general, have had a
fundamental effect on most business and service
organizations.
 Over the last decade or so, however, the advent of the
personal computer (PC) has revolutionized both the areas to
which statistical techniques are applied. PC facilities such as
spreadsheets or common statistical packages have now made
such analysis readily available to any business decision-maker.
 Computers help in processing and maintaining past records of
operations involving payroll calculations, inventory
management, railway/airline reservations, and the like. Use of
computer software's, however, presupposes that the user is
able to interpret the computer outputs that are generated

19.  Although statistics has its applications in almost all sciences—social,
physical, and natural—it has its own well, which restrict its scope
and utility.
 STATISTICS DOES NOT STUDY QUALITATIVE PHENOMEANA
 Since statistics deals with numerical data, it cannot be applied in
studying those problems which can be stated and expressed
quantitatively.
 For example, a statement like ‘export volume of India has increased
considerably during the last few years’ cannot be analysed
statistically.
 Also, qualitative characteristics such as honesty, poverty, welfare,
beauty, or health, cannot directly be measured quantitatively.
However, these subjective concepts can be related in an indirect
manner to numerical data after assigning particular scores or
quantitative standards.
 For example, attributes of intelligence in a class of students can be
studied on the basis of their intelligence quotients (IQ) which is
considered as a quantitative measure of the intelligence

20.  By statistics we mean aggregate of facts affected to a marked
extent by multiplicity of factors . . . and placed in relation to
each other.’
 This statement implies that a single or isolated figure cannot
be considered as statistics, unless it is part of the aggregate of
facts relating to any particular field of enquiry.
 For example, price of a single commodity or increase or
decrease in the share price of a particular company does not
constitute statistics.
 However, the aggregate of figures representing prices,
production, sales volume, and profits over a period of time or
for different places do constitute statistics.

21.  The variables or numbers are defined and categorized using
different scales of measurements. Each level of measurement scale has
specific properties that determine the various use of statistical
analysis.
 Using levels of measurement is another way of classifying data.
 Levels of Measurements
 There are four different scales of measurement. The data can be
defined as being one of the four scales. The four types of scales are:
• Nominal scale
• Ordinal scale
• Interval scale
• Ratio scale

22.  Nominal and ordinal scales data from a categorical variable are
measured on a nominal scale or on an ordinal scale.
 A nominal scale (see figure 1.3) classifies data into distinct categories
in which no ranking is implied. In the good tunes customer
satisfaction survey, the answer to the question are you likely to buy
additional merchandise from good tunes in the next 12 months? Is an
example of a nominal scaled variable, as are your favorite soft drink,
your political party affiliation, and your gender. Nominal scaling is
the weakest form of measurement because you cannot specify any
ranking across the various categories. Figure 1.3 examples of nominal
scales categorical variable categories personal computer ownership
type of stocks owned internet provider growth value microsoft
network other AOL other none yes no

23.  AN EXAMPLE OF A NOMINAL SCALE MEASUREMENT IS GIVEN BELOW:
 WHAT IS YOUR GENDER?
 M- MALE
 F- FEMALE
 HERE, THE VARIABLES ARE USED AS TAGS, AND THE ANSWER TO THIS
QUESTION SHOULD BE EITHER M OR F.
 Ordinal Scale:
 The ordinal scale is the 2nd level of measurement that reports the ordering and
ranking of data without establishing the degree of variation between them.
Ordinal represents the “order.” Ordinal data is known as qualitative data or
categorical data. It can be grouped, named and also ranked.

24. • The ordinal scale shows the relative ranking of the
variables
• It identifies and describes the magnitude of a variable
• Along with the information provided by the nominal
scale, ordinal scales give the rankings of those variables
• The interval properties are not known
• The surveyors can quickly analyse the degree of
agreement concerning the identified order of variables

25.  Example:
• Ranking of school students – 1st, 2nd, 3rd, etc.
• Ratings in restaurants
• Evaluating the frequency of occurrences
• Very often
• Often
• Not often
• Not at all
• Assessing the degree of agreement
• Totally agree
• Agree
• Neutral
• Disagree
• Totally disagree

26.  Interval Scale
 The interval scale is the 3rd level of measurement scale. It is
is defined as a quantitative measurement scale in which the
the difference between the two variables is meaningful. In
In other words, the variables are measured in an exact
manner, not as in a relative way in which the presence of zero
zero is arbitrary.
 Example:
• Likert scale
• Net promoter score (NPS)
• Bipolar matrix table

27.  Ratio Scale
 The ratio scale is the 4th level of measurement scale, which is
quantitative. It is a type of variable measurement scale. It allows
researchers to compare the differences or intervals. The ratio scale has a
has a unique feature. It possesses the character of the origin or zero
points.
 Characteristics of Ratio Scale:
• Ratio scale has a feature of absolute zero
• It doesn’t have negative numbers, because of its zero-point feature
• It affords unique opportunities for statistical analysis. The variables can
can be orderly added, subtracted, multiplied, divided. Mean, median,
median, and mode can be calculated using the ratio scale.
• Ratio scale has unique and useful properties. One such feature is that it
that it allows unit conversions like kilogram – calories, gram – calories,
calories, etc.

28.  An example of a ratio scale is:
 What is your weight in kgs?
• Less than 55 kgs
• 55 – 75 kgs
• 76 – 85 kgs
• 86 – 95 kgs
• More than 95 kgs

29. There are a variety of diagrams used to represent statistical data. Different types
of diagrams, used to describe sets of data, are divided into the following
categories:
• dimensional diagrams (i) one dimensional diagrams such as histograms,
frequency polygones, and pie charts.
(Ii) two-dimensional diagrams such as rectangles, squares, or circles.
(Iii) three dimensional diagrams such as cylinders and cubes.
• Pictograms or ideographs • cartographs or statistical maps

30.  These diagrams are most useful, simple, and popular in the
diagrammatic presentation of frequency distributions. These
diagrams provides a useful and quick understanding of the
shape of the distribution and its characteristics.
 The basis of comparison in the bar is linear or one-
dimensional.’ These diagrams are called one-dimensional
diagrams because only the length (height) of the bar (not the
width) is taken into consideration. Of course, width or
thickness of the bar has no effect on the diagram, even then
the thickness should not be too much otherwise the diagram
would appear like a two-dimensional diagram.

31.  The one-dimensional diagrams (charts) used for graphical
presentation of data sets are as follows:
• Histogram
• Frequency polygon
• Frequency curve
• Cumulative frequency distribution (Ogive)
• Pie diagram

32.  The graphic techniques described earlier are used for group
frequency distributions. The graphic techniques presented in
this section can also be used for displaying values of
categorical variables. Such data is first tallied into summary
tables and then graphically displayed as either bar charts or
pie charts.

33.  Bar charts are used to represent only one characteristic of data and there
will be as many bars as number of observations. For example, the data
obtained on the production of oil seeds in a particular year can be
represented by such bars. Each bar would represent the yield of a
particular oil seed in that year. Since the bars are of the same width and
only the length varies, the relationship among them can be easily
established. Sometimes only lines are drawn for comparison of given
variable values. Such lines are not thick and their number is sufficiently
large. The different measurements to be shown should not have too
much difference, so that the lines may not show too much dissimilarity
in their heights. Such charts are used to economize space, specially
when observations are large. The lines may be either vertical or
horizontal depending upon the type of variable—numerical or categorical

34.  The frequency polygon is formed by marking the mid-point at
the top of horizontal bars and then joining these dots by a
series of straight lines.
 The frequency polygons are formed as a closed figure with the
horizontal axis, therefore a series of straight lines are drawn
from the mid-point of the top base of the first and the last
rectangles to the mid-point falling on the horizontal axis of
the next outlaying interval with zero frequency.

35.  Cumulative Frequency Distribution (Ogive) :
 It enables us to see how many observations lie above or below certain
values rather than merely recording the number of observations within
intervals. Cumulative frequency distribution is another method of data
presentation that helps in data analysis and interpretation.
 To draw a cumulative ‘less than ogive’, points are plotted against each
successive upper class limit and a corresponding less than cumulative
frequency value.
 These points are then joined by a series of straight lines and the
resultant curve is closed at the bottom by extending it so as to meet the
horizontal axis at the real lower limit of the first class interval.
 To draw a cumulative ‘more than ogive’, points are plotted against each
successive lower class limit and the corresponding more than cumulative
frequency. These points are joined by a series of

36.  straight lines and the curve is closed at the bottom by
extending it to meet the horizontal axis at the upper limit of
the last class interval.. Similarly, the perpendicular drawn from
the point of intersection of the two curves on the vertical axis
will divide the total frequencies into two equal parts.

37.  These diagrams are normally used to show the total number of observations of
different types in the data set on a percentage basic rather than on an absolute
basis through a circle.
 Usually the largest percentage portion of data in a pie diagram is shown first at
12 o'clock position on the circle, whereas the other observations (in per cent)
are shown in clockwise succession in descending order of magnitude.
 The steps to draw a pie diagram are summarized below:
 (i) Convert the various observations (in per cent) in the data set into
corresponding degrees in the circle by multiplying each by 3.6 (360 ÷ 100).
 (ii) Draw a circle of appropriate size with a compass.
 (iii) Draw points on the circle according to the size of each portion of the data
with the help of a protractor and join each of these points to the center of the
circle.
 The pie chart has two distinct advantages: (i) it is aesthetically pleasing and (ii)
it shows that the total for all categories or slices of the pie adds to 100%.