## Tuesday, February 14, 2017

### AHSEC - Class 11: Commercial Mathematics and Statistics Selected Questions for Feb' 2017 Exam

Part 1 – 25 Marks Expected (Long Questions and Answers)
Part 2 – 55 Marks Expected (Practical Problems)
Part 3 – 20 Marks Expected (Multiple Choice and short answer type Questions)
Q.1. Define the term Statistics. What are its Characteristics? Mention its Functions and Limitations.
Ans: Statistics: The word Statistics seems to have been derived from the Latin word “status” or the Italian word Statista. All word means a political state. In early year “statistics” equipped a collection of facts about the people in the state for administration or political purpose.
A comprehensive definition was given by Prof. Horace Secrist, which is a follows:  “By Statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standards of accuracy, collected in a systematic manner for a predetermined purpose and placed in relation to each other.”
Characteristics of Statistics:
(i) Statistics are aggregates of facts. Single and isolated figures are not statistics because they cannot be compared.
(ii) Statistics must be numerically expressed. Statistical methods are applicable only to those data which can be numerically expressed.
(iii) Statistics should be capable of comparison and connected to each other.
(iv) Statistics should be collected in a systematic manner.
(v) Statistics should be collected for a definite purpose: The purpose should be specific and well defined.

Functions and Limitations of Statistics:
The functions of statistics are as follows:
(i) It presents fact in a definite form. Numerical expressions of data are convincing.
(ii) It simplifies mass of figures. The data presented in the form of table, graph or diagram, average or coefficients are simple to understand.
(iii) It facilitates comparison. Once the data are simplified they can be compared with other similar data.
(iv) It helps in prediction. Plans and policies of organisations are invariably formulated in advance at the time of their implementation.
(v) It helps in the formulation of suitable policies. Statistics provide the basic material for framing suitable policies.
Limitations of statistics are as follows:
(i) Statistics deals only with quantitative characteristics. Data Which cannot be expressed in numbers are incapable of statistical analysis. Qualitative characteristics like honesty, efficiency, intelligence etc. cannot be studied directly.
(ii) Statistics deals with aggregates not with individuals.
(iii) Statistical laws are not perfectly accurate.
(iv) Statistical results are only an average. Statistical results reveal only the average behavior.
(v) Statistics is only one of the methods of studying a problem. Statistical tools do not provide the best solution under all circumstances.
(vi) Statistics can be misused. The data placed to an inexperienced person may reveal wrong results. Only persons having fundamental knowledge of statistical methods can handle the data properly.

Q.2. What are various types of Statistical Data? Mention their merits and demerits.
Ans: Statistical data are of two types
(a) Primary data
(b) Secondary data.
Primary Data: Data which are collected for the first time for a specific purpose are known as Primary data. For example: Population census, National income collected by government, Textile Bulletin (Monthly), Reserve bank of India Bulletin (Monthly) etc.
Secondary Data: Data which are collected by someone else, used in investigation are knows as Secondary data. Data are primary to the collector, but secondary to the user. For example: Statistical abstract of the Indian Union, Monthly abstract of statistics, Monthly statistical digest, International Labour Bulletin (Monthly).
Merits and Demerits of Primary Data:
Merits:
(a) They are reliable and accurate.
(b) If during collection, the Data are wrong they can be checked again by cross examination.
(c)  It is more suitable if the field of enquiry is small.
Demerits:
(a) It the field of enquiry is too wide, it is not suitable.
(b) Collection of primary data is costly and time consuming.
(c) Personal Bias, prejudice and whims may affect the data.

Merits and Demerits of Secondary Data:
Merits:
(a) While using secondary data, time and labour are saved.
(b) It may also be collected from unpublished form.
(c) If secondary Data are available, they are much quicker to obtain than primary data.

Demerits:
(a) Degree of accuracy may not be acceptable.
(b) Secondary Data may or may not fit the need of the project.
(c) Data may be influenced by personal bias of investigator.

Q.3. Distinguish between Primary data and Secondary data.
Ans: Difference between Primary Data and Secondary Data:
(a) Primary data are those which are collected for the first time and thus original in character. While Secondary data are those which are already collected by someone else.
(b) Primary data are in the form of raw-material, whereas Secondary data are in the form of finished products.
(c) Primary data are collected directly from the people related to enquiry while Secondary data are collected from published materials.
(d) Data are primary in the hands of institutions collecting it while they are secondary for all others.

Q.4. What are various sources of Secondary Data? Mention the points which should be considered before using secondary data.
Ans: Sources of Secondary Data:
(a) Official publication by the central and state governments, district Boards.
(b) Publication by research institutions, Universities etc.
(c) Economic Journals.
(d) Commercial Journals.
(e) Reports of Committees, commissions.
(f) Publications of trade associations, Chamber of Commerce etc.

Precautions in the use of Secondary Data:
The following aspects should be considered before use of secondary data:
(i) Suitability: The investigator must check before using secondary data that whether they are suitable for the present purpose or not.
(ii) Adequacy: The investigator has to determine whether they are adequate for the present purpose of investigators.
(iii) Dependability: Dependability of secondary data is determined by the following factors:-
(a) The authority which collected the data.
(b) Procedure of Sampling followed.
(c) Status of Investigator.
(iv) Units in which data are available.

Q.5. What are various essential qualities of Secondary data? Explain some effective methods of collecting primary data.
Ans: Qualities of Secondary Data:
(a) Data should be reliable
(b) Data should be suitable for the purpose of investigator.
(d) Data should be collected by trained investigator.

Methods of collecting primary Data
(a)  Direct Personal Observation: Under this method, the investigator collects the data personally from the persons concerned. The information obtained under this method is original in nature. This method is suitable when the field of enquiry is small.
(b) Indirect Oral Investigation: - Under this method, the investigator collects the data from third parties capable of supplying the necessary information. This method is suitable where the information to be obtained is of a complex nature and informants cannot be approached directly.
(c) Schedule and questionnaire: - A list of question regarding the enquiry is prepared and printed. Data are collected in any of the following ways:-
(i) By sending the questionnaire to the persons concerned with a request to answer the question and return the questionnaire.
(ii) By sending the questionnaire through enumerators for helping the informants.
(d) Local reports: - This method gives only approximate results at a low cost.

Q.6. What are various stages involved in statistical investigation? Explain them briefly.
Ans: Various stages in statistical investigation: There are five stages in a statistical investigation which are given below:
(i) Collection of Data: Utmost care must be exercised in collecting data as they are the foundation of statistical analysis. If the data are faulty, the conclusions drawn can never be reliable.
(ii) Organisation of Data: Data collected from published sources are generally in organised form but data collected from a survey frequently needs organisation. Organising of data involves three steps which are:
(a) Editing of data
(b) Classification of data according to some common characteristics
(c) Tabulation.
(iii) Presentation of Data: Organised data can be further presented in the form of Diagrams and Graphs.
(iv) Analysis: After collection, organisation and presentation, data are analysed by adopting various statistical methods such as measure of central tendency, measure of variation, correlation, regression etc. to dig out information useful for decision-making.
(v) Interpretation: The last stage is interpretation which is a difficult task and requires a high degree of skill, care and experience. If the data have been analysed and not properly interpreted, the whole object of investigation may be defeated and wrong conclusion be drawn.

Q.7. What is Questionnaire? What are its essential characteristics?
Ans: Questionnaire: A Questionnaire is simply a list of questions in a printed sheet relating to survey which the investigators asks to the informants and the answers of the informants are noted down against the respective questions on the sheet. Choice of questions is a very important parts of the enquiry whatever its nature.
Characteristics of an ideal Questionnaire:
(i) The Schedule of question must not be lengthy.
(ii) It should be clear and simple.
(iii) Questions should be arranged in a logical sequence.
(iv) Each question should be brief and must aim to some particular information necessary for the    investigation.
(v) Questions of personal matter like income of property should be avoided.
(vi) The Units of information should be Cleary shown in the sheet.

Q.8. What is Tabulation? Mention its Objectives. What are its importance and limitations?
Ans: Tabulation: Tabulation refers to the systematic arrangement of the information in rows and columns. Rows are the horizontal arrangement. In simple words, tabulation is a layout of figures in rectangular form with appropriate headings to explain different rows and columns. The main purpose of the table is to simplify the presentation and to facilitate comparisons.
According to Neiswanger, "A statistical table is a systematic organisation of data in columns and rows."
The principal objectives of tabulation are stated below:
(i) To make complex data simple: When data are arranged systematically in a table, such data become more meaningful and can be easily understood.
(ii) To facilitate comparison: When different data sets are presented in tables it becomes possible to compare them.
(iii) To economize space: A statistical table furnishes maximum information relating to the study in minimum space.
(iv) To make data fit for analysis and interpretation.
(v) To provide reference: A statistical table can be used as a source of reference for other studies of similar nature.
Importance of Tabulation:
a) Tabulation makes the data brief. Therefore, it can be easily presented in the form of graphs.
b) Tabulation presents the numerical figures in an attractive form.
c) Tabulation makes complex data simple and as a result of this, it becomes easy to understand the data.
d) This form of the presentation of data is helpful in finding mistakes.
e) Tabulation is useful in condensing the collected data.
f) Tabulation makes it easy to analyze the data from tables.
g) Tabulation is a very cheap mode to present the data. It saves time as well as space.
h) Tabulation is a device to summaries the large scattered data. So, the maximum information may be collected from these tables.

Limitations of Tabulation
a) Tables contain only numerical data. They do not contain details.
b) Qualitative expression is not possible through tables.
c) Tables can be used by experts only to draw conclusions. Common men do not understand them properly.

Q.9. What do you mean by Classification of Data? Mention its essential features.
Ans: Classification of Data:
The process of arranging the data in groups or classes according to their common characteristics is technically known as classification. Classification is the grouping of related facts into classes. It is the first step in tabulation.
In the words of Secrist, "Classification is the process of arranging data into sequences and groups according to their common characteristics or separating them into different but related parts."
Essentials of classification
a) The classification must be exhaustive so that every unit of the distribution may find place in one group or another.
b) Classification must conform to the objects of investigation.
c) All the items constituting a group must be homogeneous.
d) Classification should be elastic so that new facts and figures may easily be adjusted.
e) Classification should be stable. If it is not so and is changed for every enquiry then the data would not fit for an enquiry.
f) The data must not overlap. Each item of the data must be found in one class.

Q.10. Define the term population and sample. What is sample and census survey? Distinguish between them.
Ans: Population and Sample
Population: Statistics is taken in relation to a large data. Single and unconnected data is not statistics. In the field of a statistical enquiry there may be persons, items or any other similar units. The aggregate of all such units under consideration is called “Universe or Population”.
Sample: If a part is selected out of the universe then the selected part or portion is known as sample. Sample is only a part of the universe.
Sample survey and Census Survey:
Sample survey: It is a survey under which only a part taken out of the universe is investigated. It is not essential to investigate every individual item of the Universe.
Census survey and complete enumeration: Under Census survey detail information regarding every individual person or item of a given universe is collected.
Difference between Census and Sample survey:
The following are the differences between Census and Sample method of investigation:
(a) Under Census method, each and every individual item is investigated whereas under sample survey only a part of universe is investigated.
(b) There is no chance of sampling error in census survey whereas sampling error cannot be avoided under sample survey.
(c) Large number of enumerators is required in census whereas less number of enumerators is required in sample survey.
(d) Census survey is more time consuming and costly as compared to sample survey.
(e) Census survey is an old method and it less systematic than the sample survey.

Q.11. Mention the Merits and Demerits of Census and Sample Survey.
Ans: Merits and Demerits of Census:
Merits:
(a) Since all the individuals of the universe are investigated, highest degree of accuracy is obtained.
(b) Since there is no possibility of personal bias affecting investigation, this method is free from sampling error.
(c)  It is more suitable if the field of enquiry is small.
(d) Since all the items of the universe are taken into consideration, all the characteristics of the universe

Demerits:
(a) It the field of enquiry is too wide, it is not suitable.
(b) Collection of primary data is costly and time consuming.
(c) Personal Bias, prejudice and whims may affect the data.

Merits and Demerits of sample survey:
Merits:
(a) While using secondary data, time and labour are saved.
(b) It may also be collected from unpublished form.
(c) If secondary Data are available, they are much quicker to obtain than primary data.

Demerits:
(a) Degree of accuracy may not be acceptable.
(b) Secondary Data may or may not fit the need of the project.
(c) Data may be influenced by personal bias of investigator.

Q.12. What are various types of diagrams and graphs? Distinguish between diagrams and graphs.
Ans: Types of diagrams and Graphs:
One of the most effective and interesting alternative way in which a statistical data may be presented is through diagrams and graphs. There are several ways in which statistical data may be displayed pictorially such as different types of graphs and diagrams. The commonly used diagrams and graphs to be discussed in subsequent paragraphs are given as under:
Types of Diagrams/Charts:
a)      Simple Bar Chart
b)      Multiple Bar Chart or Cluster Chart
c)       Staked Bar Chart or Sub-Divided Bar Chart or Component Bar Chart
d)      Simple Component Bar Chart
e)      Percentage Component Bar Chart
f)       Sub-Divided Rectangular Bar Chart
g)      Pie Chart

Types of Diagrams/Charts:
a)      Histogram
b)      Frequency Curve and Polygon
c)       Lorenz Curve
d)      Histogram

Difference Between Diagrams And Graphs
There is no clear-cut line of demarcation between a diagram and a graph yet:
a)      A graph needs a graph paper but a diagram can be drawn on a plain paper.
b)      As diagrams are attractive to look at, they are used for. Graphs on the other hand are more useful to statisticians and research workers for the purpose of further analysis.
c)       For representing frequency distribution, diagrams are rarely used when compared with graphs. For example, for the time series graphs are more appropriate than diagrams.

Q.13. Compare between Tabular and Diagrammatical Presentation of Data? Mention the uses and Limitations of diagrams and graphs.
Ans: Comparison Between Tabular And Diagrammatic Presentation
 Serial No: Diagrams and Graphs Tabulation 1. Diagrams and Graphs are meant for a lay man. Tables are meant for statisticians for the purpose of further analysis. 2. Diagrams give only an approximate idea. Tables contain precise figures. Exact values can be read from tables. 3. Diagrams can be more easily compared, and can be interpreted by a layman. Comparison and interpretations of tables can only be done by statisticians and it is a difficult task. 4. Diagrams and graphs cannot present much information. Tables can present more information. 5. Diagrams are more attractive and have a visual appeal. Tables are dry for a layman (may be attractive to a statistician.)

Uses of Diagrams and Graphs:
Diagrams and graphs are extremely useful due to the following reasons:
(i) Information presented though diagrams and graphs can be understood easily just in a bird’s eye view.
(ii) These are appealing and fascinating to the eyes; Scholars take greater interest in presenting data through these devices.
(iii) Diagrams and graphs produce a greater lasting impression on the mind of the readers than the figures presented in a table.
(iv) They facilitate ready comparison of data over time and space. Graphs study economic relationship between two variables.
However, graphic and diagrammatic presentations have some limitations:
(i)      Unlike a table a diagram or a graph does not show the exact value of a variable.
(ii)    Further, a limited set of facts can be presented through such devices like diagram and graph.

Q.14. What are the points that should be kept in mind while constructing a diagram or graph?
Ans: General Rules for Drawing Graphs and Diagrams
Following points must be kept in mind while constructing a diagram or graph. Every diagram or graph must have a serial number. It is necessary to distinguish one from the other.
1. Serial number: Every diagram or graph must have a serial number. It is necessary to distinguish one from the other.
2. Title: Title must be given to every diagram or graph. From the title one can know the idea contained in it. The title should be brief and self-explanatory. It is usually placed at the top.
3. Proper size and scale: A diagram or graph should be of normal size and drawn with proper scale. The scale in a graph specifies the size of the unit.
4. Cleanliness: Diagrams must be as simple as possible. Further they must be quite neat and clean. They should also be descent to look at.
5. Index: Every diagram or graph must be accompanied by an index. This illustrates different types of lines, shades or colors used in the diagram.

6. Footnote: Foot notes may be given at the bottom of a diagram if necessary. It clarifies certain points in the diagram.