Name : PRASHANT D. DEVALE

Roll Number : 510932455

Learning Centre : KARROX TECHNOLOGIES LTD, Andheri

Subject : Statistics for Management

Date Of Submission : 13th June, 2009

Assignment No. : MB0024

STATISTICS FOR MANAGEMENTMB0024

SET – 2

Q1. What do you mean by sample survey? What are the different

sampling methods? Briefly describe them.

Answer –

sample survey:-

a. Universe or Population : Statistical Survey or enquiries deal with studying various characteristics of unit belonging to a group. The group consisting of all the units is called Universe or Population.Example: In the statistical survey aimed at determining average per capita income of the people in the city, all earning individuals in the city form the population. If the population consists of finite number of individuals, then it is called a Finite Population. A population consisting of infinite number of units or units such that it is practically impossible to observe all the units is called Infinite Population. Although many populations appear to be exceedingly large, no truly infinite population of physical objects actually exists. Given limited resources and time it is practically not possible to count the number of grains of sand on the beach. Such populations are termed as infinite population for our study. Populations may further be classified as Existent or Hypothetical. A population consisting of concrete objects like the books in library is known as existent population. Throwing a coin infinite number of times produces Hypothetical Population.

b. Sample : It is a finite subset of a population drawn from it to estimate the characteristics of the population. Sampling is a tool which enables us to draw conclusions about the characteristics of the population.The advantages of sampling are :

1) In short time we get maximum information about the population.2) It results in considerable amount of saving of time and labour.3) The organization and administration of a sample survey is relatively much less.4) The results obtained are reliable and always possible to attach degree of reliability.5) There is a possibility of obtaining detailed information. In other words there is a greater scope.6) In case of infinite population, it is the only available method.7) If the units are destroyed or affected adversely in the course of investigation, then the only method is sampling.

Q2. What is the different between correlation and regression? What do you understand by Rank Correlation? When we use rank correlation and when we use Pearsonian Correlation Coefficient? Fit a linear regression line in the following data –

X 12 15 18 20 27 34 28 48 Y 123 150 158 170 180 184 176 130

Answer –

Difference between correlation and regression:

1) Correlation measures the relationship between two variables and

Regression measures relation between variables and estimates the

value of another variable having the value of one variable.

2) Correlation are three types :

a) simple correlation

b) Partial correlation

c) multiple correlation

Regression is two types:

a) simple regression

b) multiple regression

Correlation :When two or more variables move in sympathy with other, then they are said to be correlated. If both variables move in the same direction then they are said to be positively correlated. If the variables move in opposite direction then they are said to be negatively correlated. If they move haphazardly then there is no correlation between them.Correlation analysis deals with1) Measuring the relationship between variables.2) Testing the relationship for its significance.3) Giving confidence interval for population correlation measure.Spearman’s Rank Correlation CoefficientKarl Pearson’s correlation coefficient assumes thati) Samples are drawn from a normal population.ii) The variables under study are affected by a large number of independent causes so as to form a normal distribution. When we do not know the shape of population distribution and when the data is qualitative type Spearman’s Ranks correlation coefficient is used to measure relationship. It is defined as 6åD 2 Where N 3 – N D is the difference between ranks assigned to the variables. Value of r lies between – 1 and +1 and its interpretation is same as that of Karl Pearson’s correlation coefficient.

X Y XY X^2 Y^212 123 1476 144 1512915 150 2250 225 2250018 158 2844 324 2496420 170 3400 400 2890027 180 4860 729 3240034 184 6256 1156 3385628 176 4928 784 3097648 130 6240 2304 16900

(i) The regression equation of y on x is given by

Y – Y = byx (X – X)

(ii) The regression equation of x on y is given by _ _

X – X = bxy (Y – Y)

Mean of x = £x /n = 202/8 = 25.25

Mean of y = £y/n=1271/8=158.875

Bxy= (n £ xy – £ x £ y) / (£ y^2 –(£y)^2)

here sum of x= 202 where sum denoted by £

sum of y= £y =1271

sum of x^2=£ x^2=6066

sum of y^2= £y^=2205625

sum of xy =£xy=32254 and n= total number of values= 8

put the above value in the equation

bxy = (8*32254)-(202*1271)/205625-(1271)^2

= 1290/440684 = 0.0029

hence bxy = 0.0029

Similarly byx =(n £ xy – £ x £ y) / (£ x^2 –(£ x)^2)

byx= ((8*32254)-(202*1271)/(6066-(202)^2)

byx= 1290/-40804 = - 0.037

hence Answer is: i) Y – 25.25 = -0.037 (X – 158.875)

ii) X – 158.875 = 0.0029 (Y – 25.25)

Q.3 What do you mean by business forecasting? What are the different

methods of business forecasting? Describe the effectiveness of time-

series analysis as a mode of business forecasting. Describe the method of

moving averages.

Answer –

Business Forecasting:-Business forecasting refers to the analysis of past and present economic conditions with the object of drawing inferences about probable future business conditions. The process of making definite estimates of future course of events is referred to as forecasting and the figure or statements obtained from the process is known as ‘forecast’ future course of events is rarely known. In order to be assured of coming course of events, help is taken of an organized system of forecasting Following are the main methods of business forecastingBusiness Barometers :-Business indices are constructed to study and analyze the business activities on the basis of which future conditions are predetermined. As business indices are the indicators of future conditions, so they are also known as “Business Barometers” or ‘Economic Barometers’. With the help of these business barometers the trend of fluctuations in business conditions are made known and by forecasting a decision can be taken relating to the problem. The construction of business barometer consists of gross national product, wholesale prices, consumer prices, industrial production, stock prices, bank deposits etc. These quantities may be concerted into relatives on a certain base. The relatives so obtained may be weighted and their average be computed. The index thus arrived at in the business barometer.

The business barometers are of three types:

i. Barometers relating to general business activities : it is also known as general index of business activity which refers to weighted or composite indices of individual index business activities. With the help of general index of business activity long term trend and cyclical fluctuations in the ‘economic activities of a country are measured but in some specific cases the long term trends can be different from general trends. These types of index help in formation of country’s economic policies.ii. Business barometers for specific business or industry : These barometers are used as the supplement of general index of business activity and these are

constructed to measure the future variations in a specific business or industry.iii. Business barometers concerning to individual business firm : This type of barometer is constructed to measure the expected variations in a specific individual firm of an industry

Time Series Analysis Time series analysis is

also used for the purpose of making business forecasting. The forecasting through time series analysis is possible only when the business data of various years are available which reflects a definite trend and seasonal variation. By time series analysis the long term trend, secular trend, seasonal and cyclical variations are ascertained, analyzed and separated from the data of various years.Meritsi. It is an easy method of forecasting.ii. By this method a comparative study of variations can be made.iii. Reliable results of forecasting are obtained as this method is based on mathematical model.Demeritsi. This method is expensive, difficult and time taking.ii. This method deals with past data only.iii. This method can only be used when the data for several years are available

Method of Moving AveragesThis method is used for smoothing the time series. That is, it smoothens the fluctuations of the data by the method of moving averages. When Period of moving average is odd: To determine the trend by this method, we use the following method:i. Obtain the time seriesii. Select a period of moving average such as 3 years, 5 years etc.iii. Compute moving totals according to the length of the period of moving average.If the length of the period of moving average is 3 i.e., 3 yearly moving average is to be calculated, compute moving totals as follows:a + b + c, b + c + d, c + d + e, d + e + f….. for 5years moving average, moving totals are computed as follows:a + b + c + d + e, b + c + d + e + f, c + d + e + f + g….. Placing the moving totals at the centre of the time span from which they are computed. iv. Compute

moving averages by moving totals in step (3) by the length of the period of moving average and place them at the centre of the time span from which the moving totals are computed. These moving averages are also called the trend values.By plotting these trend values (if desired) one can obtain the trend curve with the help of which we can determine the trend whether it is increasing or decreasing. If needed, one can also compute short term fluctuations by subtracting the trend values from the actual values.

Q.4 What is definition of Statistics? What are the different characteristics

of statistics? What are the different functions of Statistics? What are the

limitations of Statistics?

Answer: -

Definitions of Statistics:

A.L.Boddington defined Statistics as ‘The science of estimates and

probabilities’. According to Croxton and Cowden, ‘Statistics is the science of

collection, presentation, analysis and interpretation of numerical data.’ Thus,

Statistics contains the tools and techniques required Characteristic of

Statistics

1. Statistics Deals with aggregate of facts: Single figure cannot be analyzed.

Thus, the fact ‘Mr Lee is 170 cms. tall’ cannot be statistically analyzed. On the

other had, if we know the heights of 60 students of a class, we can comment

upon the average height, variation, etc

2. Statistics are affected to a marked extent by multiplicity of causes: The

statistics of yield of paddy is the result of factors such as fertility of soil,

amount of rainfall, quality of seed used, quality and quantity of fertilizer used,

etc.

3. Statistics are numerically expressed: Only numerical facts can be

statistically analyzed. Therefore, facts as ‘price decreases with increasing

production’ cannot be called statistics.

4. Statistics are enumerated or estimated according to reasonable standards

of accuracy: The facts should be enumerated (collected from the field) or

estimated (computed) with required degree of accuracy. The degree of

accuracy differs from purpose to purpose. In measuring the length of screws,

an accuracy up to a millimeter may be required, whereas, while measuring the

heights of students in a class, accuracy up to a centimeter is enough.

5. Statistics are collected in a systematic manner: The facts should be collected

according to planned and scientific methods. Otherwise, they are likely to be

wrong and misleading.

6. Statistics are collected for a predetermined purpose: There must be a

definite purpose for collecting facts. Eg. Movement of wholesale price of a

commodity for the collection, presentation, analysis and interpretation of

data. This definition is precise and comprehensive. According to Prof.Horace

Secrit Statistics deals with aggregate of facts, affected to marked extent by

multiplicity of causes, numerically expressed, enumerated or estimated

according to a reasonable standard of accuracy, collected in a systematic

manner for a predetermined purpose and placed in relation to each other.

7. Statistics are placed in relation to each other: The facts must be placed in

such a way that a comparative and analytical study becomes possible. Thus,

only related facts which arearranged in logical order can be called statistics

Limitation of Statistics

Functions of Statistics1. It simplifies mass data2. It makes comparison easier3. It brings out trends and tendencies in the data4. It brings out hidden relations between variables.5. Decision making process becomes easier.

Major limitations of Statistics are:

1. Statistics does not deal with qualitative data. It deals only with

quantitative data.

2. Statistics does not deal with individual fact: Statistical methods can be

applied only to aggregate to facts.

3. Statistical inferences (conclusions) are not exact: Statistical inferences

are true only on an average. They are probabilistic statements.

4. Statistics can be misused and misinterpreted: Increasing misuse of

Statistics has led to increasing distrust in statistics.

5. Common men cannot handle Statistics properly: Only statisticians can

handle statistics properly.

Q.5 What are the different stages of planning a statistical survey?

Describe the various methods for collecting data in a statistical survey.

Answer –

Planning of a Statistical Survey : The relevance and accuracy of data

obtained in a survey depends upon the care exercised in planning. A properly

planned investigation can lead to best results with least cost and time. The

planning stage consists of the following sequence of activities.

1. Nature of the problem to be investigated should be clearly defined in an

unambiguous manner.

2. Objectives of investigation should be stated at the outset. Objectives

could be to obtain certain estimates or to establish a theory or to verify

a existing statement to find relationship between characteristics etc.

3. The scope of investigation has to be made clear. It refers to area to be

covered, identification of units to be studied, nature of characteristics to

be observed, accuracy of measurements, analytical methods, time, cost

and other resources required.

4. Whether to use data collected from primary or secondary source should

be determined in advance.

5. The organization of investigation is the final step in the process. In

encompasses the determination of number of investigators required,

their training, supervision work needed, funds required etc.

Collection of Data :

a.Collection of data is the first and most important stage in any statistical surveyb. The method for collection of data depends upon various considerations such as objective, scope, nature of investigation, availability of resources.c. Data collected for the first time keeping in view the objective of the survey is known as primary data. They are likely to be more reliable. However cost of

collection of such data are much higher.d. Collection of primary data can be done by anyone of the following methods. i. Direct personal observationii. Indirect oral interviewiii. Information through agenciesiv. Information through mailed Questionnairesv. Information through schedule filled by investigatorse. In Direct personal observation the investigator collects data by having direct contact with units of investigation. The accuracy of data depends upon the ability, training and attitude of theinvestigator. This method is suitable where

i) The scope of investigation is narrowii) Investigation requires personal attention of the investigatoriii) Investigation is confidentialiv) Accuracy of data is important.

Advantages arei) original dataii) more accurate and reliable iii) Satisfactoryinformation can be extracted by the investigator through

indirect questionsiv) Data arehomogeneous and comparable v) additional information can be gatheredvi] Misinterpretation of questions can be avoided. However it consumes more time and cost.

f. Indirect oral interview is used when area to be covered is large. The data is collected from a third party or witness or head of institution. This method is generally used by police department.

Advantages are i) economical in terms of time, cost and man powerii) confidential information can be collected iii) information is likely to be unbiased and reliable. However the

degree of accuracy of information is less.

g. Method of collecting information through local agencies or correspondents are generally adopted by newspaper and T.V. Local agents are appointed in

different parts of the area under investigation. They send the desired information at regular intervals. It used where the area to be covered is very large and periodic information is required. The information is likely to be affected by the bias of the correspondents or agencies.

h. Very often information is collected through Questionnaires. The questionnaires are filled by of questions pertaining to the investigation. They are sent to the respondents with a covering letter soliciting cooperation by giving correct information and mailing it back. The objectives of investigation are explained in the covering letter together with assurance for keeping information provided by them as confidential.This method is generally adopted by research workers and other official and nonofficial agencies, It covers large area of investigation. It is more economical and free from investigator’s bias. However it results in many “nonresponse”situations. The respondent may be illiterate. They can provide wrong information due to wrong interpretation of questions.i. Success of Questionnaire method of collection of data depends mainly on proper drafting ofthe questionnaire. Following general principle are considered.i. The number of questions should be less.ii. Lengthy questions should be avoided.iii. Answers to them should be short.iv. Questions regarding personal matters should be avoided.v. It should be unambiguous.vi. There should not be any scope for misinterpretation.vii. They should have been arranged in logical sequenceviii. A covering letter should accompany.

j. Information can be collected through schedules filled by investigator through personal contact. In order to get reliable information, the investigator should be well trained, tactful, unbiased and hard working. It is suitable for extensive area of investigation through investigator’s personal contact. The problem of nonresponse is minimized.

k. The data used for the investigation of the current problem from the data collected and used by some other agency or person for his investigation is known a secondary data. Their accuracy, reliability, objectives and scope should be examined thoroughly before use.

l. Primary data are collected by census method. In other words information with respect to each and every individual of the population is observed. Whereas secondary data may be collected either by census or sampling methods.m. Pilot survey: It is a small trial survey undertaken before main survey. It gives a measure of efficiency of the Questionnaire. It reduces the inconveniences and loss of information. It helps us to introduce necessary changes.Q.6 What are the functions of classification? What are the requisites of a

good classification? What is Table and describe the usefulness of a table

in mode of presentation of data?

Answer-

Functions of classificationThe functions of classification are :a. It reduce the bulk datab. It simplifies the data and makes the data more comprehensible.c. It facilitates comparison of characteristics.d. It renders the data ready for any statistical analysis

Requisites of a good classificationRequisites of good classification are :i. Unambiguous: It should not lead to any confusionii. Exhaustive: every unit should be allotted to one and only one classiii. Mutually exclusive: There should not be any overlapping.iv. Flexibility: It should be capable of being adjusted to changing situation.v. Suitability: It should be suitable to objectives of survey.vi. Stability: It should remain stable through out the investigationvii. Homogeneity: Similar units are placed in the same class.viii. Revealing: Should bring out essential features of the collected data

Types of classificationThe very important types are:1)Geographical classification: Data are classified according to region.2) Chronological classification: Data are classified according to the time of its occurrence.

3) Conditional classification: Data are classified according to certain conditions.4) Qualitative classification: Classification of data that are nonmeasurable.E.g. Sex of a person, marital status, colour etc.5) Quantitative classification: Classification of data that are measurable either in discrete or continuous form.6) Statistical Series: Data arranged logically according to size or time of occurrence or some other measurable or nonmeasurable characteristics.