Monday, November 28, 2011

Concept of Sampling

Concept of Sampling
Statistical analysis – Data Analyzing
Collection of Data
Census Method
Sample Method
Universe or population
Average and variance of sample = Sample statistic
Such values of population is parameters (µ , б)

Census Method
Information collected from each and every unit of population
Also called as Complete Enumeration Method
Reliable and accurate data
Extensive Information
More expensive
More time consuming
More labor required
Not suitable for Specific Problem

Sampling Method
Data is collected from the sample of items selected from population
Saving time and money
Intensive study
Organizational Convenience
More reliable results
More scientific
Less accurate
Wrong conclusion
Less reliable
Not suitable
Difference between Census and Sampling
All Items
Expensive time ,money and labor
Investigation with limited field
Each and every unit

Few items
Investigation with large field
Few unit

Sampling Method
Probability Sampling Method
Simple random sampling
Lottery method
Tables of random numbers
Free from personal bias
Equal chance of being selected
Save time , labor and money
Sample size is small , then sample is not adequately
Universe small , not suitable
Stratified Random sampling
Different strata acc to characteristics
More likelihood of representation of unit
Comparative study
More accuracy
Limited scope
Possibility of prejudice

Systematic random sampling
Systematically arranged and numbered
Sample unit , equal interval
Simple method
Little time
Each unit doesn’t stand equal chance

Multistage Random sampling
Many stages
Regional basis
Decision on the basis of sample alone
Lot of time and labor
Cluster Sampling
Applied in pharmaceutical industry

Non - Probability Sampling Method
Judgment sampling
Less expensive
Simple and easy
Greater chance of prejudice
Not very accurate and reliable
Quota Sampling
Greater chance important unit being included
Inquiry is more organized
Convenience Sampling
Extensive sampling
Merits of Sampling
Less time
Less cost
More reliable
Mors detailed information
Inaccurate and misleading
Absence of qualified staff
Sampling and Non Sampling Errors
Error = Difference between Sample static and Population parameter
Sampling errors = error arising due to drawing interferences about the population on the basis of few observation
Two types of error
Sampling error
Non sampling error
Errors may be occur in the collection , processing and analyzing of data
Sampling Errors
Biased errors
Unbiased errors
Faulty selection of the sampling method
Faulty demarcation(Boundaries) of sampling unit
Variability of the population which has different characteristic
Bias in analysis

Method of reducing Sampling errors
Sample size – larger – less error

Non Sampling Errors
Faulty planning
Faulty selection of the sample unit
Lack of trained and experienced staff
Errors in compilation
Errors due to wrong statistical measures
Framing of a wrong questionnaire
Incomplete investigation of the sample survey

Principle of Sampling
Principle of Statistical Regularity
According to king this law states that a moderately large number of items chosen at random from a large group are almost sure on the average possess the characteristic of large group
Principle of Inertia of Large number
Corollary of the principle of Statistical regularity
Larger the size of the sample , more accurate result likely to be.
Estimation of parameters
Statistical inference is the estimation of population parameters from the corresponding sample static
Statistical estimation
It is the procedure of using a sample statistic to estimate a population parameter.
Statistic used to estimate a parameter is called estimator
Value taken by the estimator is called an estimate
SE can be divided in two
Point estimation and interval estimation
Estimation of parameters
Properties of good estimator
Average of the sample values = population parameter
Estimator is unbiased = expected value of estimator = population
Sample size increases and decrease in error
Variance of estimator is small , the distribution of estimator will be better in that its value is closer to Parameter value

Sir R.A. Fisher
A sufficient estimator is one that uses all information about the population parameter contained in the sample
Test of Hypothesis
It is an assumption about the population parameter to be tested based on sample information
Hypothesis testing for making decision
In attempting to reach decision , it is useful to make assumptions or guesses about the populations involved. Such assumption , which mat or may not be true are called statistical hypothesis
Test of Hypothesis
Procedure of hypothesis testing
Set up the hypothesis
Null hypothesis denoted by H0
Alternate hypothesis by H1
Set up the suitable significance level
Determination of a suitable test statistic
Test statistic = sample statistic – hypothesized PP
Standard error of SS
Determine the critical region
Doing computation
Making decision

Type 1 and type 11 errors
The hypothesis is true but our test rejects it
The hypothesis is false but our test Accepts it
The hypothesis is true but our test accepts it
The hypothesis is false but our test rejects it

One tailed and two-tailed test
One tailed and two-tailed test
Central limit theorem
It is widely used in the field of estimation and inference. This states that if we select random sample of large size n from any population with mean and SD and compute the mean of each sample , then sampling distribution of mean approaches normal distribution with mean and SD б/√n. This is true even if population itself is not normal.

Monday, October 17, 2011

Statistical Quality Control


  • Growing competition
  • Watch over quality
  • Mass production unable to check the quality at each and every level
  • SQC refers to use of statistical techniques in controlling the quality of manufacturing goods


  • SQC should be viewed as a kit of tools which may influence decision to the function of specification , production or inspection
  • An economic and effective system of maintaining and improving the quality of outputs throughout the whole operating process of specif. , prod. & insp. Based on continuous testing with random samples


  • Control quality standard
  • Exercise during production process
  • Determine the variation
  • Statistical charts


  • Quality under control or not
  • Eliminate assignable causes
  • Lower inspection cost
  • Protect interest of consumer
  • Healthy influence on the psychology of workers
  • Earn the goodwill
  • Guide for new plant

Causes & Methods

Causes of variation

  • Assignable causes
  • Chance causes

Methods of SQC

  • Process control
  • Product control

Acceptance Sampling

Acceptance sampling is concerned with the decision to accept a mass of non – conforming the quality. The decision is reached through sampling


How to conduct Acceptance sampling or Types of sampling Inspection Plan

  1. Single Sampling Plan
  2. Double Sampling Plan
  3. Multiple Sampling Plan

Operating Characteristic Curve (OC Curve)

  • Graphic measure of assessing the ability of sampling plan in distinguishing between good and bad items
  • Depicts the relationship between the probability of acceptance the lot for different lot quality expressed in terms of percentage defectives

Control Charts

  • +3Sigma Upper Control Limit
  • Central Control Limit
  • -3Sigma Lower Control Limit

Purpose & uses of control charts

  • Determining the quality standards
  • Detecting assignable & Chance Variation
  • Reveals variation from desired level
  • Necessary steps for correction
  • simple to construct & easy to interpret
  • Less inspection cost

Types of control charts

  • On the basis of Variables
  1. Mean Chart
  2. Range Chart
  3. SD Chart
  • On the Basis of Attributes
  1. p Chart (Fraction Chart)
  2. np Chart (No of defects)
  3. C Chart (No of defects per unit)

Tuesday, November 25, 2008

Marginal Costing &Break Even Analysis
Marginal Cost & Marginal Costing
Acc to ICMA
Marginal cost represents "the amount of any given volume of output by which aggregates costs are changed if the volume of output is increased by one unit"
In practice it is measured by total variable cost attribute to one unit
Marginal Cost & Marginal Costing
Acc to Blocker & weltmore
"marginal cost is the increase or decrease in total cost which results from producing or selling additional or fewer unit of product or from a change in the method of production or distribution such as the use of improved machinery ,addition or exclusion of a product or territory"
Marginal Cost & Marginal Costing
Marginal costing as " the ascertainment of marginal costs and of the effect on profit of changes in volume or type of output by differentiating between fixed & variable cost"
Marginal costing is also know as "variable costing"
Characteristics of marginal costing
Analysis & presentation
Classification of cost (fixed, variable, semi variable)
Variable cost are regarded as cost of product
Fixed cost is treated as period cost
Finished goods & work in progress are valued as marginal cost
Contribution = sales or SP – marginal cost of sales
Assumption of marginal costing
Variable cost remain constant per unit of output
SP per unit remain unchanged
Fixed cost remain unchanged

It is difference between sales & variable cost or marginal cost
Excess of SP over variable cost per unit
Also know as contribution margin or gross margin

If SP = 20/-
Variable cost = 15/-
Fixed exp = 50000/-
Total no of unit sold 8000
C = 20-15 = 5
Total contribution = 8000*5 = 40000
Fixing selling prices
Assist break even point
Suitable product mix
Alternative method of production
Purchase or manufacture
Adding new product
Marginal costing equation
Sales – variable cost = contribution
Sales = variable cost + contribution
Sales = variable cost + fixed cost + profit/loss
Sales – variable cost = fixed cost + profit/loss
S-V = F + P
Cost – Volume profit analysis
Studying the relationship between cost , volume & profits.
Cost of manufacture , volume of sales ,SP of product
In words of Herman C. Heiser
"the most significance single factor in profit planning of the average business is the relationship between the volume of business , cost & profits"
Break-Even Analysis
In two senses
Narrow senses
Broad senses

In broad sense break even analysis refers to the study of relationship between cost , volume , and profit at different levels of sales or production
In narrow sense it refers to a technique of determining that level of operation where total revenue equal total expenses no profit no loss point.
All element of cost
Variable cost remain constant per unit
Fixed cost remain constant
SP remain unchanged
Volume of factor is only influence cost
No change in general price level
Break even point
Point of sales volume at which total revenue is equal to total cost.
No profit no loss point
Total sales is equal to total cost
Also called as Critical point or Equilibrium point or balancing point
Managerial application of marginal costing
Pricing decision
Profit planning
Make or but decision
Selection of suitable sales mix
Effect of change in sales price
Alternative method of production
Optimum level of activity
Capital investment decision
Advantages of marginal costing
Simple to operate
Removes complexities
Help management in production planning
No possibility of fictitious profits
BEP calculation
Decision making
Helpful in cost control
Profit planning
Management reporting
SP don’t remain constant
Ignores time factor
Budgeting & Budgetary Control
Planning is basic managerial function
Achieving goal
Control is to check
Budget & Budgeting
Budget is monetary and quantitative expression of business plan & polices to be pursued in future time period
Budgeting is used for preparing budgets & other procedures for planning, coordinating and controlling of business enterprises

Budget & Budgeting
Acc to CIMA , Official terminal
"Budget is a financial and quantitative statement prepared prior to be defined period of time"

Budgetary Control
Process of determining various budgeted figures for the enterprises for the future period
then comparing the budgeted figures with the actual performance for calculating variance

Acc to J.Batty
"A system which uses budgets as a means of planning and controlling all aspect of producing and selling commodities and services"

Budgetary involves
Objects are set by preparing budgets
Business is divided into various responsibility centres
Actual figures are recorded
Budget , Budgeting , Budgetary control
Budget is a blue print expressed in quantitative term
Budgeting is technique for formulating budget
Budgetary control refers to principles , procedures and practice of achieving given objective through budgets
Objectives of budgetary control
Ensure planning for future
Co ordinate the activities
Operate various cost centres & departments
Elimination of wastage
Centralize the control system
Fixation of responsibilities of various individuals
Characteristics of Good Budgeting
Involve person at different level
Proper fixation of authority & responsibility
Target of budget should be realistic
Good system of accounting
Support of top management
Impart budgeting education

Elements of budget
Operations & Resources
Financial term
Specified future period
Comprehensiveness (Master Budget)
Purpose of Budget
Explicit statement of expectation
Expectation as a framework of judging performance
Maximization of profits
Specific aim
Tool of measuring performance
Determining weakness
Corrective action
Reduces cost
Introduction of incentives schemes
Uncertain future
Revision required
Conflict among departments
Depends upon support of top management
Classification & Types
Classification according to time
Long term budgets
short term budgets
Current budgets
Classification on the basis of function
Operating budget
Financial budget
Master budget
Classification on the basis of flexibiltiy
Fixed budget
Flexible budget
Acc to time
Long term budgets
Between 5 to 10 years
Short term budget
1 to 2 years
Current budget
Months or weeks
On basis of function
Operating budget
Sales budget , production budget , purchase budget , raw material budget ,
Financial budget
Cash budget , working capital budget , capital expenditure budget
Master Budget
On the basis of flexibilty
Fixed budget
Flexibility budget
Performance Budget
Budget based on functions , activities & projects.
The budgeting system in which input costs are related to the performance i.e. end result
System which provides appraisal & measures
Conventional budgets
"The performance budget is a budget based on function , activities and projects which focus attention on the accomplishments , the general and relative importance of the work to be done and the services to be rendered rather than upon the means of accomplishments such as personnel , service , supplies , equipments. Under this system the function of various org unit would be split into programmes of activities and estimated would be presented for each"
Establish relationship between inputs and their direct output
It involves
Developments of performance criteria for various programmes
Assessment of performance of each programme
Assessment of performance of each responsibility unit
Comparison of the actual performance with budget
Undertake periodic review
Zero Based budgeting
Latest technique of budgeting
First introduced in America in 1962
It starting from scratch
Normal technique use previous year cost level
Last year as a guide and what to be done
In zero based budgeting every year is taken as new year
Zero Based budgeting
Justified acc to present situation
Manager is to justify why he want to spend
Spending on various will depend upon their justification
Traditional budgeting Vs Zero based budgeting
More accounting oriented then decision oriented
Monitoring toward expenditure
Inc. or Dec. in expenditure
Vertical communication
Zero base
Decision oriented
Towards achievement of objective
Cost benefit analysis
Vertical & horizontal communication
Process or steps
Objective of budgeting should be determined
Extent should be decided
Decision packages
Cost & benefit analysis
Selecting ,approving decision , finalising the budget
Allocate funds
Efficiency of management
Identify wasteful & economical areas
Optimum use of resources
Evaluate the performance
Organizational goals
Is not possible in non financial matters
Difficult in formulation & ranking of decision packages
Lot of time
Lot of cost