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CDG1A/CDZ3A/CDC3A/ MBT3A

BUSINESS STATISTICS

Unit : I - V

CDG1A/CDZ3A/CDC3A/MBT3A – BUSINESS STATISTICS

CDG1A/CDZ3A/CDC3A/MBT3A – BUSINESS STATISTICS 2

UNIT I

Introduction Meaning and definition of statistics Collection and tabulation of statistical data Presentation of statistical data Graphs and diagrams

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

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.

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

CDG1A/CDZ3A/CDC3A/MBT3A – BUSINESS STATISTICS CDG1A/CDZ3A/CDC3A/MBT3A – BUSINESS STATISTICS

COLLECTION OF DATA

PRIMARY DATA

SECONDARY

METHODS OF COLLECTING PRIMARY DATA

DIRECT PERSONAL INTERVIEWS INDIRECT ORAL INTERVIEWS INFORMATION FROM CORRESPONDENTS MAILED QUESTIONNAIRE METHOD SCHEDULES SENT THROUGH ENUMERATORS

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.

• 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.

CLASSIFICATION OF DATA

CLASSIFICATION TYPES

GEOGRAPHICAL

CHRONOLOGICAL

QUANTITATIVE

QUALITATIVE

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

REPRESENTATION OF DATA TYPES OF DIAGRAMS

ONE DIMENSIONAL OR BAR DIAGRAMS

TWO DIMENSIONAL OR

AREA DIAGRAMS

THREE DIMENSIONAL OR VOLUME DIAGRAMS

PICTOGRAMS AND CARTOGRAMS

TYPES OF DIAGRAMS

TYPES OF GRAPHS

HISTOGRAM

FREQUENCY POLYGON

FREQUENCY CURVE

OGIVES

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

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

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.

ARITHMETIC MEAN

GEOMETRIC MEAN

HARMONIC MEAN

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.

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

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.

RANGE QUARTILE DEVIATION MEAN DEVIATION STANDARD DEVIATION

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

• 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

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.

Sub Code - Sub Name 31

METHODS OF STUDYING SKEWNESS

UNIT III

CORRELATION ANALYSIS

DEFINITION AND TYPES

SCATTER DIAGRAM METHOD

KARL PEARSON METHOD

SPEARMAN’S RANK CORRELATION

REGRESSION ANALYSIS

REGRESSION EQUATIONS

CORRELATION

Correlation is a statistical method used to study the relationship

between two or more variables.

CORRELATION AND CAUSATION • Causation implies correlation. But correlation does not always imply causation.

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

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

METHODS OF STUDYING CORRELATION

Scatter diagram method. Karl Pearson’s method.

Spearman’s Rank Correlation method.

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.

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

RANK CORRELATION

−−= ∑

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

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.

REGRESSION EQUATIONS • Regression Line of X on Y:

• Regression Line of Y on X :

DIFFERENCE BETWEEN CORRELATION AND REGRESSION

UNIT IV

TIME SERIES ANALYSIS

MEANING AND DEFINITION

COMPONENTS OF TIME SERIES

METHODS OF MEASURING TREND

METHODS OF MEASURING SEASONAL VARIATION

TIME SERIES

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.

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.

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

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.

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.

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.

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.

FREE HAND OR GRAPHIC METHOD

METHOD OF SEMI AVERAGES.

METHOD OF MOVING AVERAGES.

METHOD OF LEAST SQUARES.

METHODS OF MEASURING TREND

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

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

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.

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.

TYPES OF INDEX NUMBERS

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.

METHODS OF CONSTRUCTING INDEX NUMBERS

UNWEIGHTED INDICES

SIMPLE AGGREGATIVE METHOD : ∑p1 P01 = ------ x 100 ∑p0 SIMPLE AVERAGE OF PRICE RELATIVE METHOD : (Using Arithmetic Mean)

(Using Geometric Mean ) ∑log P P01 = antilog ------------ x 100 N

WEIGHTED INDEX NUMBERS WEIGHTED AGGREGATIVE INDICES

100index Laspeyres 101 ×=∑∑

LASPEYRE’S INDEX

PAASCHE’S INDEX

Paasche’s index

FISHER’S IDEAL INDEX : BOWLEY’S INDEX :

MARSHALL EDGEWORTH METHOD:

WEIGHTED AVERAGE OF RELATIVES 1. Using arithmetic mean, ∑PV P01 = ------ ∑V 2. Using geometric mean, ∑V log P P01 = Antilog ---------- , V = p0q0 ∑V

• For example, refer http://www.emathzone.com/tutorials/basic-statistics/weighted-index-

numbers.html •

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

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

Chain Base And Fixed Base Indices

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

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.

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