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CDG1A/CDZ3A/CDC3A/
MBT3A
BUSINESS STATISTICS
Unit : I - V
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UNIT I
Introduction
Meaning and definition of statistics
Collection and tabulation of statistical data
Presentation of statistical data
Graphs and diagrams
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DEFINITION
STATISTICS AS „NUMERICAL DATA‟
“By statistics we mean aggregates of facts affected to a
marked extent by multiplicity of causes numerically
expressed, enumerated or estimated according to reasonable
standards of accuracy, collected in a systematic manner for a
pre-determined purpose and placed in relation to each other.”
- PROF.HORACE SECRIST
STATISTICS AS STATISTICAL METHODS
“ The science which deals with the collection, analysis
and interpretation of numerical data.”
- CROXTON AND COWDEN
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FUNCTIONS OF STATISTICS
Statistics presents the fact in definite form
It simplifies mass of data.
It facilitates for comparison.
It facilitates in formulating policies
It tests hypothesis
It measures the trend behaviour
LIMITATIONS OF STATISTICS
Statistical methods does not study individuals.
Statistics laws are true only on an average.
Statis tical methods are not suited to study qualitative data.
If sufficient care is not exercised in collecting, analyzing and
interpretation the data, statistical results might be misleading.
Only a person who has an expert knowledge of statistics can
handle statistical data efficiently.
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SCOPE OF STATISTICS
Statistics in Business
Statistics in Economics
Statistics in Mathematics
Statistics in Banking
Statistics in Administration
Statistics in Accounting and Auditing
Statistics in Natural and Social Sciences
Statistics in Astronomy
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COLLECTION OF DATA
DATA
PRIMARY DATASECONDARY
DATA
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METHODS OF COLLECTING PRIMARY
DATA
DIRECT PERSONAL INTERVIEWS
INDIRECT ORAL INTERVIEWS
INFORMATION FROM CORRESPONDENTS
MAILED QUESTIONNAIRE METHOD
SCHEDULES SENT THROUGH ENUMERATORS
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SOURCES OF SECONDARY DATA
Published Sources:
Official publications of Central and local governments.
Official publications of semi government statistical organization.
Official publication of foreign government or international bodies
like the UNO, World Bank, ADB, WTO, UNESCO, etc.
Reports and publications of Trade union, Chamber of Commerce,
Commercial Banks, Co-operatives, Stock Exchange etc.
Report submitted to economists, re-search scholars, universities
and various educational and research institutions.
Reports of various committees and commissions appointed by
government.
Newspaper and Periodicals.
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• Unpublished Sources: The statistical data needn‟t always be
published. There are various sources of unpublished statistical
material such as the records maintained by
Private firms
Business enterprises
Scholars
Research workers, etc.
They may not like to release their data to any outside agency.
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CLASSIFICATION OF DATA
CLASSIFICATION TYPES
GEOGRAPHICAL
CHRONOLOGICAL
QUANTITATIVE
QUALITATIVE
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TABULATION
• Tabulation is the process of condensing classified data in the form of
a table so that it may be more easily understood and so that any
comparisons involved may be more readily made.
TYPES OF TABLES
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REPRESENTATION OF DATA
TYPES OF DIAGRAMS
ONE DIMENSIONAL OR
BAR DIAGRAMS
TWO DIMENSIONAL OR
AREA DIAGRAMS
THREE DIMENSIONAL OR
VOLUME DIAGRAMS
PICTOGRAMS AND
CARTOGRAMS
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TYPES OF DIAGRAMS
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TYPES OF GRAPHS
HISTOGRAM
FREQUENCY POLYGON
FREQUENCY CURVE
OGIVES
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MEASURES OF CENTRAL TENDENCY
ARITHMETIC MEAN
MEDIAN
MODE
HARMONIC MEAN
GEOMETRIC MEAN
MEASURES OF VARIATION
RANGE
QUARTILE DEVIATION
MEAN DEVIATION
STANDARD DEVIATION
MEASURES OF SKEWNESS
SYMMETRICAL DISTRIBUTION
POSITIVELY SKEWED DISTRIBUTION
NEGATIVELY SKEWED DISTRIBUTION
UNIT II
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MEASURES OF CENTRAL TENDENCY
MEANING
A CENTRAL VALUE IS A SINGLE VALUE WHICH DESCRIBES
THE CHARCTERISTICS OF THE ENTIRE DATA.
MEASURES
ARITHMETIC MEAN
MEDIAN
MODE
HARMONIC MEAN
GEOMETRIC MEAN
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ARITHMETIC MEAN
• Arithmetic mean is usually called as average and is given by sum of
all observations divided by the total number of observations given.
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MEAN
x
ARITHMETIC MEAN
GEOMETRIC MEAN
HARMONIC MEAN
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MEDIAN
• The median is a simple
measure of central tendency.
To find the median, we arrange
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 even number of
observations, the median is the
average of the two middle
values.
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MODE
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For various methods of calculating mean, median, mode for different
types of data, follow the links
https://sol.du.ac.in/mod/book/view.php?id=1317&chapterid=1065
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MEASURES OF DISPERSION The average measures the center of the data. Another feature of
the observation is how the observations are spread about the
center. The observations may be close to the center or they may
be spread away from the center. If the observations are close to
the center (usually the arithmetic mean or median), we say that
dispersion, scatter or variation is small. If the observations are
spread away from the center, we say dispersion is large.
TYPES
RANGE
QUARTILE DEVIATION
MEAN DEVIATION
STANDARD DEVIATION
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MEASURES OF DISPERSION
ABSOLUTE MEASURE OF DISPERSION :
It measures the distribution in original units of data.
Variability in two or more series can be compared, provides they
are in the same unit and same average.
RELATIVE MEASURE OF DISPERSION :
It is free from unit of measurement of data.
It is the ratio of the measure of absolute dispersion to the
average, from which absolute deviations are made.
It is called as coefficient of variation
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• For formulae, merits and demerits of various measures of dispersion
refer
http://www.yourarticlelibrary.com/statistics-2/4-commonly-used-measures-of-
dispersion-statistics/92258
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MEASURES OF SKEWNESS
• Skewness is a term in statistics used to describes asymmetry from
the normal distribution in a set of statistical data. Skewness can
come in the form of negative skewness or positive skewness,
depending on whether data points are skewed to the left and
negative, or to the right and positive of the data average. A dataset
that shows this characteristic differs from a normal bell curve.
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METHODS OF STUDYING
SKEWNESS
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UNIT III
CORRELATION ANALYSIS
DEFINITION AND TYPES
SCATTER DIAGRAM METHOD
KARL PEARSON METHOD
SPEARMAN‟S RANK CORRELATION
REGRESSION ANALYSIS
REGRESSION EQUATIONS
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CORRELATION
Correlation is a statistical method used to study the relationship
between two or more variables.
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CORRELATION AND CAUSATION
• Causation implies correlation.
But correlation does not always imply causation.
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TYPES OF CORRELATION
A. Positive and Negative Correlation
Positive Correlation:
If the two variables vary in the same direction i.e., if both the variables
increase or decrease in the same direction then there exists a positive
correlation.
Eg : Income and expenditure
Negative Correlation:
If the two variables vary in the opposite direction i.e., if one variable
increases the other decreases or vice versa, then there exists a negative
correlation.
Eg : No of men and work
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LINEAR AND NON-LINEAR
CORRELATION Linear Correlation:
The ratio of change in between the variables is the same.
Example
Non-Linear Correlation:
The amount of change in one variable does not bear a constant
ratio to the amount of change in the other variable.
Example:
If the amount of rainfall is doubled, the yield of a crop is not
necessarily doubled.
X 1 3 2 4 5 6
Y 2 6 4 8 10 12
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METHODS OF STUDYING
CORRELATION
Scatter diagram method.
Karl Pearson’s method.
Spearman’s Rank Correlation method.
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SCATTER DIAGRAM METHOD
Scatter diagram is a graphical method of finding correlation.
It is one of the simplest procedures to judge correlation
between variables. One variable is taken along the x- axis and other
variable is taken along the y-axis.
From the plotted points, we can find whether the variables are
correlated or not.
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KARL PEARSONS‟ METHOD
• Karl Pearson’s Coefficient of Correlation is widely used
mathematical method wherein the numerical expression is used to
calculate the degree and direction of the relationship between linear
related variables.
• Pearson‟s method, popularly known as a Pearsonian Coefficient of
Correlation, is the most extensively used quantitative methods in
practice. The coefficient of correlation is denoted by “r”.
•
For example refer,
http://www.stat.wmich.edu/s216/book/node122.html
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RANK CORRELATION
)1(1
2
2
NN
D
This method is based on Ranks.
It is useful when the data is of qualitative nature like
honesty, efficiency, intelligence, beauty etc.,
The rank correlation coefficient is given by
Where N is the number of observations and D is the difference
between number of observations
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REGRESSION
Regression is a statistical method which is used to estimate the
unknown value of one variable using known value of other variable,
provided the variables are correlated.
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REGRESSION EQUATIONS
• Regression Line of X on Y:
• Regression Line of Y on X :
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DIFFERENCE BETWEEN CORRELATION
AND REGRESSION
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UNIT IV
TIME SERIES ANALYSIS
MEANING AND DEFINITION
COMPONENTS OF TIME SERIES
METHODS OF MEASURING TREND
METHODS OF MEASURING SEASONAL VARIATION
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TIME SERIES
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MEANING
• A time series is a set of observations arranged in chronological
order.
DEFINITIONS
• A time series consists of statistical data which are collected,
recorded and observed over successive increments.
• When quantitative data are arranged in the order of their
occurrence, the resulting series is called a time series.
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EXAMPLES
The hourly series of
temperature recorded.
The weekly series of
attendance in a company.
The monthly series of steel
production.
The annual series of national
income.
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COMPONENTS OF TIME SERIES
The factors that are responsible for bringing about changes in a time
series are called the components of time series.
• SECULAR TREND
• SEASONAL VARIATIONS
• CYCLICAL VARIATIONS
• IRREGULAR VARIATIONS
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SECULAR TREND
The secular trend refers to the general direction and movement of time series.
EXAMPLES.
UPWARD TREND : The series concerning Population, national income, bank deposits etc.
DOWNWARD TREND : Series concerning death rates specially in deaths by epidemics etc.
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SEASONAL VARIATIONS
Seasonal variations refer to a recurrent pattern of change within the
period due to climate or custom at different periods of time.
EXAMPLES
In each year more ice creams sold during summer and less in
winter.
More woolen clothes are sold during winter and less in summer.
Increase in sales of garments in festive seaons.
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CYCLICAL VARIATIONS
• Cyclical variations are oscillatory movements in a time series with
period of oscillation greater than
one year.
• Cyclical movements are defined as up and down movements which
are different from seasonal fluctuations because they extend over
longer period of time.
• The cyclical fluctuations are not necessarily uniformly periodic.
• A cycle (one complete period) normally lasts from 7 to 9 years.
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IRREGULAR VARIATIONS
Irregular variations are fluctuations in time series that are short
in duration, erratic in nature and follow no regularity in the
occurrence pattern.
• These variations are usually caused by nonrecurring factors
like floods, wars, earthquakes, strikes and lock-outs, epidemics etc.
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FREE HAND OR GRAPHIC METHOD
METHOD OF SEMI AVERAGES.
METHOD OF MOVING AVERAGES.
METHOD OF LEAST SQUARES.
METHODS OF MEASURING TREND
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METHODS OF MEASURING SEASONAL
VARIATIONS
METHOD OF AVERAGES
MOVING AVERAGES METHOD
RATIO TO MOVING AVERAGE METHOD
RATIO TO TREND METHOD
FOR PROBLEMS, REFER
https://sol.du.ac.in/mod/book/view.php?id=1317&chapterid=1071
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UNIT V
INDEX NUMBERS
TYPES OF INDEX NUMBERS
AGGREGATIVE AND RELATIVE INDEX
CHAIN AND FIXED INDEX
WHOLESALE INDEX
COST OF LIVING INDEX
STATISTICAL QUALITY CONTROL
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INDEX NUMBERS
Index numbers are developed for measuring the effect of change in
prices. They are described as barometers of economic activity.
DEFINITIONS :
Index numbers are devices for measuring differences in the
magnitude of a group of related variables – Croxton and Cowden.
An index number is nothing more than a relative number which
expresses the relation between two figures, which one of them is
used as a base. - Morris Hamberg.
• It is a numerical value characterizing the change in complex
economic phenomena over a period of time or space – Maslow.
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USES OF INDEX NUMBERS Index numbers measure the economic and business behaviour,
and is called the barometers of economic activity.
The primary purpose of index numbers is to measure the relative
temporal or cross sectional changes in a variable or set of
variables over some base figure.
Management for any organization uses index numbers for
efficient planning and formulation of business policies.
Index numbers are specially used to study the general trend for a
time series data. They can be used to forecast future events.
The cost of living index numbers help in computing real wages.
Index numbers are used to for deflating net national product or
income calculated at current prices.
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TYPES OF INDEX NUMBERS
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1. PRICE INDEX
This compares the prices of a group of commodities at a certain
time or place with prices of the base period or place respectively.
2. QUANTITY INDEX
This index measures the changes in the volume of goods produced,
purchased or consumed
Eg : indices of agricultural production, industrial production, imports,
exports etc.
3. VALUE INDEX :
This index compares the total value of some period with the total value of the base period.
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METHODS OF CONSTRUCTING INDEX
NUMBERS
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UNWEIGHTED INDICES
N
p
p
o
100
P
1
01
SIMPLE AGGREGATIVE METHOD :
∑p1P01 = ------ x 100∑p0
SIMPLE AVERAGE OF PRICE RELATIVE METHOD :
(Using Arithmetic Mean)
(Using Geometric Mean )
∑log PP01 = antilog ------------ x 100
N
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WEIGHTED INDEX NUMBERS
WEIGHTED AGGREGATIVE INDICES
100index Laspeyres1
01
oo
o
qp
qpP
LASPEYRE‟S INDEX
PAASCHE‟S INDEX
Paasche‟s index
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FISHER‟S IDEAL INDEX :
BOWLEY‟S INDEX :
MARSHALL EDGEWORTH METHOD:
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WEIGHTED AVERAGE OF RELATIVES1. Using arithmetic mean,
∑PVP01 = ------
∑V
2. Using geometric mean,
∑V log PP01 = Antilog ---------- , V = p0q0
∑V
• For example, refer
http://www.emathzone.com/tutorials/basic-statistics/weighted-index-
numbers.html
•
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QUANTITY INDEX NUMBERS
Quantity indices are obtained by changing p to q and q to p in the
various formulas.
VALUE INDEX NUMBERS
The value of a single commodity is the product of its price and
quantity.
∑p1q1
V01 = ------ x 100
∑p0q0
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TESTS OF ADEQUACY
To know about the various tests for index numbers and the list
index numbers which satisfy the tests, refer
https://gradestack.com/CA-CPT/Index-Numbers/Tests-for-Adequacy-
of/22579-4555-56931-study-wtw
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Chain Base And Fixed Base
Indices
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CONSUMER PRICE INDEX
Consumer price index numbers is also known as cost of living index
numbers, are generally intended to represent the average change
overtime in the prices paid by the ultimate consumer of a specified
basket of goods and services.
METHODS:
Aggregate Expenditure Method
Family Budget Method
For problems refer
https://gradestack.com/CA-CPT/Index-Numbers/Consumer-Price-Index/22579-
4555-56930-study-wtw
TM
CDG1A/CDZ3A/CDC3A/MBT3A – BUSINESS STATISTICS 75
Statistical Quality Control
• Statistical quality control refers
to the use of statistical
methods in the monitoring and
maintaining of the quality of
products and services. It uses
graphical displays known as
control charts to determine
whether a process should be
continued or should be
adjusted to achieve the
desired quality.