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
