Business mathematics and statistics by G.Reka

BUSINESS MATHEMATICS
AND STATISTICS
G.REKA
ASSISTANT PROFESSOR
DEPARTMENT OF
COMMERCE
JAMAL MOHAMED COLLEGE
TRICHY -20
INDIA

UNIT-I
INTRODUCTION
The word ‘statistics’ is derived from the Latin word ‘status'
or Italian word‘ statista' or the German word ‘statistik’ or
French word ‘statisque’ each of which means a political state.
Statistics is not a new discipline but is as old as the human
activity itself.
DEFINITION
A.L. Bowley defines "Statistics are numerical statements of
facts in any department of enquiry placed in relation to each
other“

Characteristics or Features of Statistics
• Statistics are Aggregate of Facts
Only data related to facts are termed as statistics. This data
should be plural one. Single or unrelated figures are not statistics.
Since single figure could not be compared, it cannot be termed as
statistics
• Statistics are Affected to a Marked Extent of Multplicity of causes
Only those facts , which are consequential to multiple
causation are statistics.
• Statistics must be Numerically Expressed
Statistics is the study of only those facts which are being
capable of being stated in numbers or quantity .

• Statistics must be Enumerated or Estimated According
to Reasonable Standard of Accuracy
Enumeration means collecting data by actual
counting or measurement complete accuracy may not
be required on all occasion hence , the data may have
to be estimated. This estimation should be done with
the reasonable standard of accuracy.
• Statistics should be Collected in a Systematic Manner
The data collected would be a systematic one. Proper
arrangement in a systematic manner would minimize
the time, as well as provide accurate information.

SCOPE OF STATISTICS OR APPLICATION OF STATISTICS
• Statistics and Business
Statistics is most commonly used in business. The statistical data
regarding the demand and supply of products can be collected and
analysed to take a decision regarding the new business. Thus it helps to
take companies decision regarding whether a company can start a new
business. The existing company can also make a comparative study about
their performance with the performance of other companies through
statistical analysis.
• Statistics and Economics
Some of the uses of statistics in economics are as follows:
* Measures of gross national product and input -output analysis have
greatly advanced overall economic knowledge and opened up entire new
field of study
*Financial statistics are basic in the field of money and banking, short
term credit, consumer studies finance and public finance.
* statistical studies of business cycle , long term growth and seasonal
fluctuations serve to expand our knowledge of economic instability and to
modify older theories.

• Statistics and Physical Sciences
The physical sciences are making increasing use of statistics,
especially astronomy, chemistry, geology, meteorology and physics.
• Statistics and Natural Sciences
Statistical techniques have proved to be extremely useful in the
study of all natural sciences like biology. medicine, zoology, botany.
•
Statistics and Research
Statistics is indispensable in research work. Most of the research
findings in various disciplines of knowledge have great importance along
with subject of statistics.
•
Statistics and Computer
Statistical tools like SPSS package, multiple discriminate analysis,
multiple regression analysis will help all the fields of the management
with the help of computer.

• Statistics and Management
Most of the managerial decisions are taken with the help
of statistics. The data regarding the performance of a
company will facilitate to take decision regarding future.
Statistical techniques like correlation analysis, regression
analysis and time series technique can be used in this regard.
Statistical techniques can also be used for the payment of
wages to the employees of the company.
•
Statistics in Banking and Finance
Statistics are mostly used in banking and finance. In
banks, statistical data regarding loan, the customer deposit
etc. Are represented in statistical data. Financial institution
like industrial development bank of India , state financial
corporation of India also use statistics in projecting the future
and to solve various statistical problems.

DIAGRAMMATIC REPRESENTATION
•
INTRODUCTION
Classification refers to grouping of data into homogeneous class and
categories. Tabulation is the process of presenting the classified data in
tables. Classification and tabulation are applied in order to make the
collected data understandable. Many figures may be uninteresting and
even confusing So, a better way of representing data is by diagram and
graph.
• DIAGRAM
A diagram n is a visual form for presentation of statistical data.
Diagrams refer to the various types of devices such as bars, circles, maps,
pictorials, cartograms. These devices can take many attractive forms.

TYPES OF DIAGRAMS
The following are the important types of diagrams:
(I)One-dimensional diagrams
(II) Two-dimensional diagrams
(III) Three-dimensional diagrams
(IV) Pictograms and Cartograms
(I) One-dimensional Diagrams
One-dimensional diagram can also be called as bar diagram. In bar
diagrams, only the length is considered. The following are the
important types of bar diagram
(i) Simple Bar diagrams
(ii) Sub-divided Bar diagrams
(iii) Multiple Bar diagrams
(iv) Percentage Bar diagrams
(v) Deviation Bar diagrams

(i)Simple Bar Diagrams
Simple bar diagram represents only one variable. It
gives much importance to one characteristic of the data. The
figures like production, sales in factories number of students
in a college year after can be represented by such bars. The
width of the bar is not given any importance.
(ii) Sub-divided Bar Diagrams
Sub-divided bars are used to present such data
which are to be shown in the parts or which are totals of
various sub-division. Each part may explain different
characters of the data. For example, the number of students
of a college may be divided course-wise.

(III)Multiple Bar Diagrams
The techniques of simple bar diagrams can be extended
to represent two or more sets of inter-related data in one
diagram. It supplies information about one phenomenon
(iv)Percentage Bar Diagrams
In percentage bar diagram, the length of all the bars
are equal. Various parts of each bar are converted into
percentage.
(v)Deviation Bar Diagrams
Deviation bar diagrams represent only the difference
of (deviations of) figures which is shown in the shape of bars.
Bars representing positive differences are shown on one side
and those representing negative difference on the other side

(II)Two-dimensional Diagrams
In one-dimensional diagram, only one dimension using heights
(length) is considered. But in two-dimensional diagram, both
lengths as well as width are taken into account. It is also called as
area diagram or surface diagram. The important types of two-
dimension diagram are;
(i) Rectangles
(ii) Squares
(iii) Circles
(iv) Pie Diagram
(i)Rectangles
In a rectangle diagram, both the dimensions (length and width)
of the bars are taken into account. A rectangle is a two-dimension
diagram because it is based on the area principle (length and
breadth)

(ii) Squares
Under this method, each bar diagram is represented in the form of
squares. First we convert the square root of each value of the variable.
Then the value should be represented in the form of bar diagram.
iii) Circles
Circle diagrams are more attractive and appealing than square
diagrams. The area of the circle is directly proportional to its radius. Each
value is taken as area of a circle. The radius is found for each circle, by
dividing with π (227) and then taking the circle, based upon the radius,
circle diagram can be drawn.
(iv) Pie Diagram
Pie diagram means sub-divided circle diagram. It is a representative
of various data on the basis of different segments or sections. It gives a
clear idea about the percentage of the component part to the total. The
percentage/value of any component part is calculated by applying the
following formula, because the angle at the centre of the circle is 360°. It is
also known as angular diagram.

(III)Three-dimensional Diagrams
Three-dimensional diagrams are those in which three dimension
breadth and height are taken into account. They are constructed in the
form ofcubes, spheres, cylinders and blocks.
(IV)Pictograms and Cartograms
(i) Pictograms
Pictograms is the technique of presenting statistical data through
appropriate pictures. Pictures are more attractive and appealing to the
eye. The number of pictures drawn or the size of the pictures being
proportional to the values of the different magnitude to be presented.
ii) cartograms
in cartograms, statistical facts are presented through maps
accompanied by various types of diagrammatic representatives. It is the
presentation of data in geographical basis. It is also called as statistical
maps.

GRAPHICAL REPRESENTATION
Frequency distribution related to discrete and continuous series can be
well drawn in a graph. A graph is a visual form of presentation. Graphical
presentation of statistical data gives a pictorial effect. Graphs are very useful for
studying time series. Graphs are drawn on a special type of paper known as graph
sheet. The special feature of the graphs is that they are more obvious, accurate
and precise diagram.
Classification of Graphs
It is classified into two major heads:
(i) Graphs of frequency distribution
(a) Histogram
(b) Frequency Polygon
(c) Frequency Curve
(d) Ogives or cumulative frequency curve
(ii) Graphs of time series
(a) Nature Scale Method
(i) Line Graph or Line Chart for one variable
(ii) Line Graph or Line chart for two or more variables
(b) Ratio Scale Method

• (i) Graphs of Frequency Distribution
(a) Histogram It is one of the major popular and commonly used devices for
drawing continuous frequency distribution. It is a set of vertical bars. Frequencies
representing the variables should be drawn in a graph in the form of vertical bars.
It is also called as graphs of time series
(b) Frequency Polygon It is another device of distribution. It gives a curve
instead of bars. It is an improved method of histogram. It is drawn for both
discrete
series and continuous series.
In case of discrete frequency distribution, frequency polygon is obtained by
plotting the frequencies on the Y axis against the corresponding values of the
variable on the X axis and joining the points so obtained by straight lines.
c) Frequency Curve A frequency curve is a smooth, free hand curve drawn
through the vertices of a frequency polygon. The object of this curve is to
eliminate
the erratic ups and downs. For drawing the frequency curve, first of draw a
frequency polygon by joining mid-points of each class interval. Then the frequency
polygon should be smoothed.

(d) Ogives or Cumulative Frequency Curve
Ogives, pronounced as olive, is the chart. a graphical presentation of
the cumulative frequency of continuous series. It is
drawn by connecting plots of the cumulative frequency and the class
intervals Ogives can be constructed in two methods:
(i) less than ogives
(ii) more than ogives.
(i) Less than Ogives This consists in plotting the 'less than' cumulative
frequencies against the upper class boundaries of the respective classes.
The points so obtained are joined by a smooth, free hand curve to give
less than ogive. This curve is an increasing curve, sloping upwards from
left to right.
(ii) More than Ogives Similarly, more than ogives are plotted against the
lower class boundaries of the respective classes. The points so obtained
are joined by a smooth free hand curve to give 'more than olives'. It is a
decreasing curve and slope downwards from left to right.

(ii)Graphs of Time Series
Time series is concerned with the representation
of data for different periods of time. Time (year, month
and day) may be takes in x axis and variables
(population, demand, production) may be taken in y
axis. There are two methods for constructing graphs for
Time series. They are
Nature Scale Method
Ratio Scale Method

CLASSIFICATION AND
TABULATION
INTRODUCTION
During every statistical investigation, the collected data, also known as raw data or
ungrouped data, are always in an unorganised form and need to be organised and presented
in meaningful form in order to facilitate further statistical analysis. The first step in the
analysis and interpretation of data is classification and tabulation. Classification means
arranging the data into different groups on the basis of their similarities. The next step is
tabulation which is concerned with the systematic arrangement and presentation of classified
data.
DEFINITION
Classification is the process of arranging the collected data into classes and sub-
classes according to their common characteristics. It can be defined as follows:
Classification is the process of arranging things (either actually or notionally) in the groups
according to their resemblances and affinities and given expression to the unity of attributes
that may subsist amongst a diversity of individuals.
-Prof. Cornor
Classification is the process of arranging data into sequences and groups according to their
common characteristics or separating them into different but related parts.
_ Secrist

TYPES OF CLASSIFICATION
The collected data are classified on the basis of the purpose and
objectives of the investigation or enquiry. Generaly, the data can be
classified on the basis of the following criteria
l. Geographical Classification
2. Chronological Classification
3. Qualitative Classification
4. Quantitative Classification
5. Conditional Classification
1 Geographical Classification
It is also known as spatial classification. Here the data are classified on the
basis of geographical or vocational differences such as state, cities,
districts zones or villages between various items of the data set.
2 Chronological Classification
When data are classified on the basis of differences in time such as years,
months, weeks, days, hours etc., the classification is known as
chronological classification.

3. Qualitative Classification
When data are classified according to some qualitative phenomena
like honesty. employment, intelligence, literacy, beauty, caste, etc., the
classification is termed itative or descriptive or by attributes. Here the
data are classified according to the presence or absence of the attributes.
(a) Simple Classification
When classification is done with respect to one attribute, two
classes are formed. One possessing the attribute and the other not
possessing the attribute. This type of classification is called simple or
dichotomous classification.
(b) Manifold Classification
Here, classification is done simultaneously with for example, sex
and literacy. The population is first classified with respect to ‘sex, into
'males, and females. Each of these classes may further be classified into
'literate' and 'illiterate'. This type of classification manifold classification

4. Quantitative Classification
If data are classified on the basis of
phenomenon which is capable of quantitative
measurement like height, weight, income,
expenditure, sales, profits etc., is termed as
quantitative classification
5 .Conditional Classification
When the data are classified according to
certain conditions, other than geographical or
chronological, it is called a conditional classification.

Business mathematics and statistics by G.Reka

Business mathematics and statistics by G.Reka

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