# B.Com 1st Year Statistical Investigation Short Question Answer Notes

B.Com 1st Year Statistical Investigation Short Question Answer Notes :- In this post You will Find B.com Notes Study material Unit Wise Chapter Wise Topic Wise division of the content. This Post is very useful for all the Student B.A., B.Sc., B.Com., M.A., M.Com. Planning of statistical Investigation, Census and sampling methods, Collection of primary and secondary data, Statistical errors and approximation, Classification and tabulation of data, Frequency distribution. All topic Notes Available in over site parultech.com

Q.1. What is statistical investigation? Give its concept.

Ans. Statistics is defined as data and the procedures for analysis of data. It indicates the use of statistical data and its methods. Investigation means the search for unknown facts or knowledge. So, statistical investigation means search for knowledge related to particular field with the help o statistical methods, on the basis of systematically collected and analysed data. It is a scientific study because it is based on some principles and the mathematical facts. This investigation is essential because statistical analysis is not possible in the absence of statistical data.

The foundation of statistical investigation lies on data hence it includes scientific and systematic collection of data and their analysis with the help of various statistical methods and their interpretation. It is the primary channel to collect data and the necessary information so as to make decisions. In it, the problem should be carefully examined, the real purpose of the investigation should be clearly defined and the methodology should be thoroughly discussed. So, it can be said that the entire procedure start from the planning to draw decision and is known as conducting a statistical investigation.

The person conducting the statistical enquiry is known as investigator and the person who gives information to the investigator during a statistical investigation is called the ‘informant’ or ‘respondent’.

Q.2. What are the main stages of statistical investigation?

Ans. Statistical investigation passes through the different stages as explained under:

1. Planning of Enquiry: It is necessary to plan the investigation before the collection of actual data like the type of investigation, area to be covered, time taken, budget, etc. The concept and definition degree of accuracy, etc. must also be decided.

2. Collection of Data: This is the primary step in a statistical study and data should be collected with care so as to have the results upto the mark.

3. Editing of Data: Mass and complex data are collected after completing the process of data collection, that may contain unnecessary information or wrong data. So, data must be edited that reduces future problems and help in smooth analysis.

4 Condensation and Summarisation of Data: In it, the data is organised, classified, tabulated edited and presented in a suitable form. The data should be organised systematically and the unwanted information is ignored and only the important information is detained. Data is classified according to the object of the enquiry in classification.

5. Analysis of Data: Data presented in tables is complex enough to understand, it is to be summarised to single or simple figures that represent the majority of the features of the data.

6. Interpretation of Data: This is done after the analysis of data and conclusions are drawn. The interpretation of the investigation should be to the point and free from the personal bias of the investigator.

7. Presentation of Report: Report is a device that communicates to the reader about the undertaken work and the conclusion drawn by the investigator. This report should be simple, clear and direct on the basis of facts with logical presentation of the work done and the conclusion drawn.

Q.3. What do you understand by statistical unit? Discuss the characteristics of an ideal statistical unit.

Ans. Statistical Unit: Statistics is basically based on counting, measurement and analysis. Statistical unit is the basis of measurement in which data are collected, analysed and interpreted. It can be defined in the form of measurement of an object or a group of objects selected for counting, measurement and analysis of data.

Characteristics of an Ideal Statistical Unit

An ideal statistical unit must have the following characteristics:

1. Clear Cut Definition: The definition of statistical unit must be simple, clear, appropriate, concise and self explanatory so that there is no confusion in its interpretation.

2 Stable and Standardised. The unit selected should be stable over a long period one be related to places as the data collected at different times will not be comparable

3. Suitability. The unit should be suitable according to the investigation or given engany the changes in general price level, the appropriate unit is wholesale price and to construcc me cost of living indices, the appropriate unit is the retail price.

4. Homogeneity and Uniformity: The unit adopted should be homogeneous throughout the investigation so that measurements obtained are comparable.

5. Appropriate for Mathematical Processing: The unit should be such that there is simplicity and convenience in mathematical processing. So, the decimal measurements are considered more appropriate from this view.

Q.4. Discuss the main types of statistical units.

Ans. Statistical units can be classified as follows:

1. Units of Collection of Enumeration: It refers to those units in terms of which data are collected. Such units can be simple, composite and hypothetical units.

(a) Simple Unit: It is one that is generally expressed by a simple characteristic, e.g. kilogram, hour, litre, etc.

(b) Composite Unit: A simple unit with some qualifying words is called composite unit. It is the result of combination of two or more simple units, e.g. labour hours, educated unemployed, etc.

(c) Hypothetical Unit: It is the unit on the basis of which data are expressed in terms of hypothetical units so as to facilitate comparison, e.g. degree of carat in gold, etc.

2. Units of Analysis and Interpretation: The unit on which data are compared are called units of analysis and interpretation. Such units may be of the following types:

(a) Coefficient: It is the unit used for the comparison of numerator and denominator. The formula is:

C = Number/Total base number

(b) Rate: These are usually expressed per hundred, per thousand or per million, etc., e.g. death rate is expressed in terms of per thousand.

(C) Ratio: It is used to express the relative values of two homogeneous facts, e.g. ratio of males and females will be 4:1 if there are 800 males and 200 females in a factory

Q.5. What are the differences between primary and secondary data?

Or Discuss about primary data and secondary data. (2014)

Ans. The sources of data collection are classified on the basis of the nature of data:

1. Primary Data: Primary data are those data that are collecte euge Bo for a specific purpose by an investigator on the basis of primary O Secondary Sy source of information. Such data are collected directly from the people to whom the enquiry is related and are not earlier processed, grouped, averaged and summarised. Data collected in the population census are called primary data.

2. Secondary Data: Secondary data are those data which are already collected, processed and used by someone else for their own purpose. They are either published or unpublished. Such data refers to that statistical material which is not originated by the investigator himself but which he obtains from someone else’s records. So, the secondary data are collected by any other organisation and subsequently treated and utilised by another organisation. Source from which secondary data are collected is called secondary source.

Distinction between Primary and Secondary Data

Q.6. What is questionnaire? How does a questionnaire differ from a schedule?

Ans. A questionnaire is defined as a set of questions to be answered by the informants without personal aid of an investigator or enumerator. It refers to advices for securing answers to questions by using a form which this respondent fills in himself.

Schedule is the name applied to a set of questions which are asked and filled in by an interviewer in a face-to-face situation with the another person. The main differences between the two are:

1. Questionnaire is filled in by the informants themselves while the schedule is filled in by the

enumerators on the basis of information obtained from informants.

2. There may or may not be a blank space along with question in questionnaire while in a

schedule, blank space is positively provided for giving answer of each question.

3. Normal language is generally used in a schedule while in a questionnaire, the language is used in the form of questions.

4. The questionnaire is generally mailed to informants while in schedule system, the investigator personally approach the informants with prepared questionnaire.

5. Questionnaire method is relatively cheap while the schedule method is the costliest.

6. Questionnaire method can be adopted only when informants are educated while the schedule method can be applicable in the same way to both of the educated or uneducated.

Q.7. What are the essentials of a good questionnaire?

Or What precautions should be taken in drafting a questionnaire?

Ans. Essentials of a Good Questionnaire: Investigation depends to a large extent up the careful and tactful drafting of a questionnaire. So, the size, language and questions of a questionnaire should be designed very carefully so that the information may be obtained with completeness. The following points are to be given with due consideration in it:

1. Covering Letter: The investigator should introduce himself and make the objectives of the survey clear to the informant in this letter. The informant should be assured for the secrecy of the information.

2. Limited Questions: The number of questions should be restricted to the minimum. If there are, unnecessary and more questions in it, it would be more time consuming and respondents may take proper interest in their replies.

3. Simplicity and Clarity: The questions should be clear, unambiguous and precise. The language should be very simple which informants can easily understand.

4. Logical Sequence of Questions: The questions should be arranged in a logical onder and their sequence should be such that there should be a logical flow of thought that facilitate work of classification.

5. Selection of Nature of Questions: The nature of questions should be determined carefully while framing a questionnaire. Such questions are classified into two parts:

(a) Shut Questions: These are the questions in which possible answers are suggested in the questionnaire and respondent is required to select from it. Shut questions can be simple.

alternative or multiple choice.

(b) Open Questions: Those where different opinions can be gathered or obtained from the answers given by different respondents are open questions. They can be specific information or comprehensive information questions.

6. To Avoid Sensitive and Personal Nature Questions: The questions related to religion, personal or political nature should not be asked as they may not give correct information.

7. Cross Checks: The questions that can test the reliability of the information supplied should be asked.

8. Questions Related to Mathematical Calculations Should not be Asked: Such questions must not be asked as all the people are not fully acquainted with mathematical calculations.

9. Necessary Instructions and Definitions Should be Given: The necessary information must accompany the questionnaire so that the informant doesn’t face any difficulty.

10. Appealing the Attractive Get-up: The questionnaire should be attractive and interesting so as to induce high response. Quality of paper used should be good.

11. Pretesting and Rectification: The questionnaire must be tested on a small scale after the finalisation and if needed, necessary modifications can be made.

Q.8. Give a specimen of a questionnaire.

Ans. A questionnaire is a list of questions pertaining to a particular enquiry. A specimen questionnaire for the enumeration of the families that are below poverty line is given as:

1. General information/Identity details

(a) Name of district.

(b) Name of block.

(c) Name of village.

(d) House number.

2. Whether the household is cultivating land more than two hectare.

3. Whether the household possesses a pucca house.(Yes)/(No)

4. Whether any member of the family is earning * 20,000 or more per annum.

(Yes)/(No)

5. Whether the household possesses the following consumer goods:

(a) TV (Yes)/(No)

(b) Refrigerator (Yes)/(No)

(c) Fan (Yes)/(No)

(d) Motor-cycle/Scooter  (Yes)/(No)

(e) Three wheeler  (Yes)/(No)

6. Whether the household is the owner of the following agricultural equipments:

(a) Tractor (Yes)/(No)

(b) Power tiller  (Yes)/(No)

(c) Joint thresher/Harvester  (Yes)/(No)

Q.9. What do you mean by sample and sampling? What are the essentials of a good sample?

Ans. Sample is a part of the population that is selected for analysis. It is a fraction or a subset of population drawn through a valid statistical procedure so that it can be regarded as the representative of the entire population.

Sampling is the valid statistical procedure of drawing a sample from the population. Essentials of a good sample are:

1. Adequacy: The number of units in the sample should be adequate so as to make accurate results.

2. Independence: In a simple sampling, the individual items composing the sample must be independent of each other.

3. Representativeness: The sample selected should have similar characteristics of the original universe from which it has been selected.

4. Homogeneity: There should not be any basic difference in the nature of units of the universe and that of the sample.

5. Similar Regulating Conditions: The regulating conditions should be same for every individual instance in the sample.

Q.10. Write a note on census investigation method. Also, give the merits and demerits of this method.

Ans. Census Investigation Method: It is the oldest method of collecting the data and is a straight forward technique in which an investigator observes each and every item within the scope of enquiry. It is also called as complete enumeration, complete survey or census.

This type of method is suitable where scope of enquiry is limited, intensive study of each unit is required, greatest accuracy is expected and resources of investigator are sufficient.

Merits: The merits of this method are:

1. Results are more accurate and reliable.

2. Intensive information is obtained from each and every item.

3. It is an appropriate method where units of diverse characteristics constitute the universe. Demerits: The demerits of this method are:

1. It is an expensive or costly method.

2. It requires more labour time.

3. It is not possible in some circumstances.

Q.11. Write a note on sample investigation method. Also, give the merits and demerits of this method.

Ans. Sample Investigation Method: Under sample investigation, a few elements of the population are selected that are taken as the representative of the population. Thus, sampling is a tool that helps to know the characteristics of the universe or population by examining only a small part of it. This method is more suitable than a census method:

1. If the universe is very large or complex.

2. If the area of investigation is very wide.

3. If quick and best results are required.

4. When we cannot use the census method.

5. If the units are destroyed in the course of testing.

Merits: The merits of this method are:

1. It is an economic method.

2. It saves time and labour.

3. More reliable results can be obtained.

4. It gives more detailed information.

5. Its organisation and administration is easy.

6. It is the only scientific method for estimating the character of population.

Demerits: The demerits of this method are:

1. The conclusions are inaccurate and misleading.

2. It covers lack of experts.

3. It provides heterogeneous units.

4. It is impossible to frame a sample.

Q.12. Write short note on law of statistical regularity.

Ans. Law of statistical regularity is a corollary of the theory of probability that clarifies that inspite of diversity in universe, the law of regularity applies. This law indicates that a moderately large number of items chosen from a given universe possess the characteristics of the given universe.

‘If a relatively large number of items be chosen at random from a group, such items are an average almost sure to have the characteristics of the group.’

This law lays down that moderately a large number of items is selected at random from a given population. This law holds good only when:

1. Items are selected at random from the universe.

2. Law will be true on an average.

3. The number of items are sufficiently large so. as to avoid under influence of abnormal items The large number of items, the more reliable is the information secured.

Q.13. Write a note on law of inertia of large numbers.

ANS. Law of inertia of large numbers is a corollary of the law of statistical regulay called as principle of stability of mass data. According to this law, larger samples have 8 cancelamy, steadiness and consistency than small ones. Such small numbers depict greater variation in different directions over a short period of time. Prof. F.C. Mill clarifies this law as ‘While there is variation in nature, the degree of such variation is limited, there is some uniformity in natural processes.

The property of inertia precludes the possibility of change with the passage of time. It means that when the numbers that are involved are of great magnitude, the change is more regular in cases where small quantities are involved. -Prof. W.1. King Law of inertia of large numbers occupies an important place in statistics. It argues that the larger the number of observations the more closely will they tend to be representative of the total population from which they are drawn. The results will be accurate if the number of items in the random sample are greater as the diverse tendencies of the items will cancel each other thus indicating the true picture of the universe.

Q.14. What is approximation? State its objectives.

Or Give the methods of approximation.

Ans. Approximation is the basis of rounding off the figures in order to simplify them and to make them fit for analysis and interpretation without impairing the standard of reasonable accuracy. Its autent depends upon the degree of accuracy desired in the data. It enables a clear and easy grasp of figures and facilitates calculation and comparison.

Objectives: The objectives of approximation are:

1. Such figures facilitate comparison.

2. They are easy to remember.

3. They simplify the big numbers with a view to make them more intelligible.

When approximations are made, the figures should about facts. Before rounding of the figures, it should i.e. up to three, two or one decimal point or unit. The various methods of approximation are:

1. By dropping certain digits entirely to the round numbers, where where approximation is less than actual, e.g. 7,27 can be written in nearest tens as 7,820.

2. By raising the actual figure to the next higher whole number, where approximation is greater than the whole number, e.g. 7,229 can be written in nearest hundreds as 7,300.

3. By approximating to the nearest whole number, e.g. 7,827 can be written to the nearest hundreds as 7,800.

Q.15. What is statistical error? Give its sources.

Ans. Statistical Error: The difference between the approximated estimated value and the true value is called the statistical error: “The statistical error is the difference between the true figure and the approximation.’ -Prof. Buddington

‘He explained that the statistical error should not be considered a mistake. They arise due to a large number of factors:

1. Errors of Origin: These errors arise in the process of data collection and can be minimised to a great extent by a well-planned, systematic and bias free data collection process.

2. Errors of Inadequacy: Such errors arise due to the sampling technique on account of the inadequacy of the size of the sample or due to inadequate information.

3. Errors of Manipulation: These errors arise due to manipulation in counting, measurement, description or approximation and can be minimised if proper care is taken in the analysis of data.

4. Errors of Interpretation: These errors arise because of carelessness, biasness or in experience of the investigator.

Q.16. What are the ways in which errors can be measured? Illustrate with examples.

Ans. Statistical errors can be measured either absolutely or relatively. So, errors are of two types on the basis of measurement:

1. Absolute Error: It is the difference between the actual value and estimated value.

‘The absolute error of an estimate is the actual difference between the estimates and the true value counted as positive or negative according to the estimate is greater or less than the true value.’ -L.R. Conner

Absolute error = Actual value – Estimate value

Or

A.E. = a-e

For example; If the number of students in a college is estimated at 3,500 while actually, it is 3,600. Find the absolute error.

Here a = 3,600 and e=3,500

Absolute error, A.E. = 3,600 – 3,500 = 100

2. Relative Error: It is the ratio of absolute error to the estimated value of a certain quantity.

Relative error =  Absolute error/Estimate value Or R.E. = a-e/e

For example; In the above example, find the relative error.

Relative error, R.E. – 100/3,500 = 1/35 = 0.022

Relative error when multiplied by 100 is called as percentage error.

R.E. x 100 = Percentage error

Q.17. Give the meaning and characteristics of classification.

Ans. Classification is grouping of data according to their identity, similarity or resemblances. It is the process of arranging the collected data into homogeneous classes in order to exhibit its common characteristics.

‘Classification is the process of arranging data into sequences and groups according to their common characteristics or separating them into different but related parts! -Secrist

Classification is an important technique for the statistical treatment and analysis of numerical data. An ideal classification should possess the following characteristics:

1. Unambiguity or Exactness: The classes should be rigidly defined and should not lead to any ambiguity or confusion.

2. Exhaustive and Mutually Exclusive: The classification must be exhaustive and should be free from the residual class.

3. Slabinty: Classification must proceed with one principle which should be maintained throughout.

4. Flexibility: A good classification should be flexible and should have the capacity of adjustment to changed situations.

5. Homogeneity: Items included in classification must be homogeneous.

6. Arithmetical Accuracy: The total of items included must match with the total of the universe.

7. Suitability: The classification should be suitable for the purpose of enquiry.

Q.18. What are the main features and objects of classification?

Ans. Features: The main features of classification are:

1. The facts are classified into homogeneous groups having similar chala

2. The basis of classification is unity in diversity.

3. The classification may be either actual or notional.

4. The classification may be according to either attributes or characteristics or measurements.

Objects: Following are the main objects of classification:

1. To Bring Out Relationship: Classification helps in finding out cause-effect relationship if it exists in the data.

2. To Facilitate Comparison: A classified data helps in comparison and gives the idea of status of people with respect to their income.

3. To Condense the Mass of Data: Large number of figures with common features can be arranged in few classes such that similarities and dissimilarities can be readily apprehended.

4. To Prepare the Basis for further Analysis: Classification is necessary for any statistical treatment to a mass of data.

5. To Show the Similarities and Dissimilarities of Data: Classification shows the similarities and dissimilarities of data so as to grasp them easily.

Q.19. What do you mean by statistical series?

Ans. A series in which two variable quantities can be arranged side by side so that measurable difference is the one that corresponds with measurable differences in the other is statistical series.

A statistical series may be defined as things or attributes of things arranged according to some logical order!

Statistical series can be divided on the basis of their general character and construction as shown:

1. Statistical Series Based on General Qualities or Characters:

(a) Time Series: In it, data is presented with respect to different periods of time.

(b) Spatial Series: In it, data is listed in alphabetical order.

(c) Condition Series: Data is presented with reference to some condition.

Statistical Series Based on Construction: Such series can be univariate where frequencies mined on the basis of one variable of bivariate where data is classified with reference to two are determined on the hasis of one variah bases. Univariate series can be:

(a) Individual Series: When the observations are expressed individually, the value of each and every item can be observed separately.

(b) Discrete Series: The data are presented in a way that exact measurements of units are clearly 1 indicated.

(C) Continuous Series: The data is further simplified for the purpose of analysis by presenting it in the form of continuous series. Continuous series can be cumulative (derived by the cumulation of the frequencies of successive values) or open end classes series (lower limit of the first class interval and the upper limit of the last class interval are not specified.) Q.20. Write a short note on frequency distribution.

Ans. The arrangement in which the data is distributed into classes and the number of individuals belonging to each class are determined is called the frequency distribution. It is a table in which the variables are given on one side and the number of items related to each variable are recorded on the. other side.

‘Frequency distribution is a statistical table in which different values of variable are shown in the sequence of magnitude along with the corresponding frequencies.

Two elements are necessary for the construction of frequency distribution-Variable and Frequency. Variable are the facts that can be measured directly in quantitative terms and that varies in amount or magnitude. The value of the fact if remains fixed is called as constant. Frequency distribution may be of two types:

1. Discrete Frequency Distribution: It is a discontinuous frequency distribution where the observations are independent from each other. Data is presented as it is in the universe along with its frequency of occurrence.

2. Continuous Frequency Distribution: In it, observations are expressed in small groups called as class intervals with certain limits. Here, the frequencies refer to the group but not to the individual items.

There is also a cumulative frequency distribution where the cumulative frequencies are obtained by successively adding the frequencies in the distribution.

Q.21. What is tabulation? Give its objectives.

Ans. Tabulation is an orderly arrangement of data in columns and rows.

“Tabulation involves the orderly and systematic presentation of numerical data in a form designed so as to elucidate the problem that is under consideration.’ –Conner

In it, table is prepared by presenting data in a simple and condensed form in framework of rows and columns

The objective of tabulation is to systematise data and to make them simple and comparable. Some of the main objectives are:

1. To Simplify Complex Data: Tabulation avoids unnecessary and irrelevant details and data is presented in columns and rows.

2. To Facilitate Comparison: Tabulation facilitates comparison of data so that data may be understood easily.

3. To provide Consistency: The errors can be checked easily on the basis of totals, sub-totals and grand totals in the table.

4. To Facilitate Presentation: Tabulation facilitates presentation of data-diagrammatic and graphic representation of data.

5. To Economic Space: Data is presented in minimum space without sacrificing the quality and utility of data.

6. To Clarify Data Characteristics: The headings and sub-headings clarify the data characteristics that help in problems analysis.

7. To Facilitate Statistical Analysis: Properly tabulated data facilitate the analysis of statistical measures like average, dispersion, correlation, etc.

8. To Help in References: Data arranged in tables can be used easily as source reference for further studies.