Under this chapter we learn following topics

Statistics and its applications

Data **collection** technique

Distinction between primary and secondary data

Presentation of data in textual and tabular

Cumulative frequency and frequency distribution

Graph using histogram, frequency polygon and pi chart

Use of statistic :

Statistic is used in all subjects like management, commerce, mathematics, social sciences etc.

It also used in public service like defence, banking, insurance, tourism, police, military, hospitality etc.

It collects the data, analyses it and apply in statistic inferences

It has universal application

Government, businessman, political party and research scholar use the statistics

Hence it is required to study

History

There are various views for its origin

This word was used in ancient and medieval period.

Its origin may be from any of the following term.

Latin- status, Italian- statista, German- statistik, French- statistique

Then it is known as a state because it collects and maintains data of the people belonging to the state.

In the 4th century B.C. , Kautilya had written Arthashastra during Chandragupta’s reign.

In the 16 century A.D. , Abu Fazl had written Ain-i- Akbari on agriculture

Definition

It can be used in singular or plural sense

In plural it is qualitative and quantitative

In singular it collects, analyses and present the data hence it is known as science of counting on science of a average

Applications of the statistics

Economics

Roots of economics are in statistics

Certain chapters like time series analysis, index number, demand analysis are included in both.

There is a branch of economics known as a econometrics which interact with statistics

Socio economic survey are based on statistical methods

In economics for the future projection of the demand, sale price, quantity regression analysis is used

Business management

In earlier days, decision was taken by managers on the basis of trial and error.

Now a days due to complexity in the business decisions are taken on the basis of quantitative techniques which is based on statistical method and operation research.

Statistics provides inferences about universe on the basis of sample.

Statistics in commerce and industry

Due to globalisation businesses are expanded without any limit.

Hence it needs various accounting data and statistical applications.

Limitations of statistics

It is based on aggregate hence individual item has no importance except it is a part of aggregate

It is concerned with quantitative data hence in case of qualitative data it is difficult to convert in a numerical.

Future projections are based on set of conditions.

It is based on sample samples are unrepresentative result may not be correct four population.

Collection of data

There are two types of data 1 quantitative 2 qualitative

Quantitative data is known as a variable

There are two types of variable 1 discrete 2 continuous

Discrete means isolated single value example road accidents, misprints in a book, petals in a flower

Continuous means any value from an interval example height, weight, sale, profit,

Variable can be finite or infinite.

Qualitative characteristic is known is an attribute example nationality gender colour etc.

Classification of the data

Primary – first time collected

Secondary – collected data used by another person

Methods of collection of primary data

Interview method – direct (personal) interview – investigator meets directly used in natural calamity

It is accurate method

Indirect interview – when there is a problem to reach there, information is collected from the associated person.

Telephone interview – quick, non expensive and covers large area but non response is maximum

Mailed questionnaire – well drafted and soundly sequenced questionnaire – all important aspects- with guideline- pre paid stamp. It covers large area but maximum non response.

In questionnaire method enumerator directly collect information with questionnaire, Hence non response can be minimised

Observation method – best method used- in height, weight. It is time consuming laborious Hence covers small area only

Scrutiny of data

Data should be accurate and consistence

Errors may arise in writing or copying.

Internal consistency may be checked from two or more series.

Example density = area/ population

Information submitted by enumerator can be verified and if bias is reflected errors can be rectified Or data can be collected again.

Presentation of data

After Collection of data, it should be verified for its homoginity, Compatibility, Association and consistency then it is required to present in neat and condensed form and analyse it.

Types of classification of data

Chronological, temporal or time series – year wise CA details

Geographical or spatial series data – State wise unemployment

Qualitative or ordinal data : intelligence, beauty, nationality

Quantitative or ordinal data : height weight profit etc.

Qualitative and quantitative are frequency group data

Time series data and geographical data are non frequency group

Mode of presentation of data

Textual presentation – paragraphs- official reports

It is simple and layman can use

But it is also dull, monotonous and comparison is difficult

Tabular presentation

It is a systematic presentation with raw, column, footnote, title and reference number

Caption is upper part of table

Box head is the entire upper part off the table

Stub is the left part of the table describing the raws `

Body is the main part of the table

It is used for comparison

Without table statistical analysis is not possible

Diagrammatic representation of the data

It can use chart diagrams and program

It is used for both educated and uneducated

Trend can be noticed

Types of diagram

Line diagram or histogram

Vary over time – year wise profit

In case of fluctuation logarithm ratio chart is used

When two or more time series data in a same unit multiple line chart is used and in a different units multiple axis chart is used

Bar diagram

In horizontal bar diagram qualitative data varying over space while in vertical bar diagram quantitative data are used in multiple or g Rectangles are equal or varying length.

Bar diagram can be subdivided or it can be presented in percentagerouped bar diagram.

Pie chart pie diagram or circle diagram is used for comparison

Frequency distribution

It is a tabular presentation of data in ascending order

Data can be variable or attribute

It can be divided in number of categories or classes which are mutually exclusive and exhaustive

Number of times the class occurs will be Shown as a corresponding to a particular class

It is known as a frequency of that class

It distributes total frequency into number of classes

When data is discrete tabulation is known as discrete ungrouped or frequency distribution

When data is continuous tabulation is known as continuous frequency distribution

How to form frequency distribution table

Find the range. Range = largest minus smallest

Find the number of classes. Number of classes= range/ class length

Apply tally mark count the tally Mark show in the next column which is known as frequency column

Total frequency should be matched with total number of observation

Class limit- in a class interval minimum value is known as lower class limit and maximum value as a upper class limit

Class boundaries

In overlapping or exclusive classification class boundary and class limit both are equal. Used in continuous variable 10-20

In non overlapping all mutually inclusive. 10-19 LCB=LCL-D/2 AND UCB=UCL+D/2

Midpoint or mid value or class mark= LCL+ UCL/2 OR LCB+UCB/2

Width OR size of the class interval =- UCB- LCB OR UCL-Lcl

Cumulative frequency it can be less then or more than cumulative frequency. number of observations less than or equal to value or class boundary – less than cumulative frequency

Number of observations More than or equal To value – More than cumulative frequency

Frequency density frequency of that class to corresponding class length

Relative frequency or the percentage frequency of a class interval ratio of class frequency to total frequency if it is in percentage multiply with hundread

Graphical representation of frequency distribution

Histogram or area diagram

Class limits are converted to the corresponding class boundaries and a series of adjacent rectangles in class intervals

When class intervals are not uniform it is erected. Mode can be calculated easily.

Frequency polygon

it is known as single frequency distribution

It can be used in grouped frequency also when width of the class interval remains the same midpoint of the interval are connected.

It starts with the histogram. Mid points of upper sides of rectangles are connected.

Ogives or cumulative frequency graph :

Plot cumulative frequency against class boundary

There are two type of ogive less than or more than. Both should be presented in vertical axis.

Quartiles can be calculated perpendicular from the point of intersection of two ogive on horizontal axis. it is known as median it can be used for short term projection.

Frequency curve : it is a smooth and free hand curve total area is an Unity it is a limiting form of histogram for the frequency polygon

There are types of frequency curve

Bell shaped curve – starting from a lower value gradually reaches at maximum value at Central Part then decrease gradually at its lowest value

U shaped curve minimum at Central Part and maximum the two extremes Kolkata commuters at morning to evening

J shaped curve starts with the minimum frequency than increased to maximum frequency Kolkata commuters early morning to pick morning.

Combination of the frequency curve known as a mixed curve

Measures of Central tendency and dispersion

learning objectives

Central tendency – Mean, Median, Mode, Geometric mean and harmonic mean. – advantages and disadvantages – when these are used.

dispersion means volatility. range, mean deviation, standard deviation and quartile deviation.

Central tendency

definition

at starting low frequency newly increased to the maximum