BACHELOR'S DEGREE PROGRAMME
Term-End Examination: June, 2010
ELECTIVE COURSE: COMMERCE
ECO-7: ELEMENTS OF STATISTICS
Time: 2 hours Maximum Marks: 50
Note: Attempt any four questions. All questions carry equal marks.
1. (a) Fill in the blanks with the appropriate word given in the brackets: 8+4½
(i) In construction of Index numbers Weighted mean is specially used. (weighted / unweighted)
(ii) It takes Less time to collect secondary data compared to primary data. (less / more)
(iii) Use of Correspondents is an appropriate method of data collection when the information is to be obtained at regular intervals over a wide area. (Interview / correspondents)
(iv) Data array does not provide any information regarding the range of data. (does / does not)
(v) It is not always necessary that the magnitude of different classes must be equal. (unequal / equal)
(vi) Mode and Median are positional measures . (calculative / positional)
(vii) For a moderately skewed distribution, the empirical relation is given as 3Me - 2 Mean. (3Me - 2 Mean /2Me-3Mean)
(viii) The title given to rows of a table is called a Caption. (stub / caption)
(b) State any four limitations of statistics.
Ans: 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.
2. (a) The median, mean and coefficient of skewness for a certain distribution are 80, 86 and 0.42 respectively. Calculate coefficient of variation. 6+6½
Ans: Given,
Median = 80
Mean = 86
Coefficient of Skewness = 0.42
Now,
=> 3 Median = 2 Mean + mode
=> 3 x 80 = 2 x 86 + Mode
=> 240 = 172 + Mode
=> Mode = 240 – 172 = 68
Again, Coefficient of Skewness
Therefore, Coefficient of variation
(b) The mean and standard deviation of 100 items are 50 and 5 respectively. The mean and standard deviation of another 150 items are 40 and 6 respectively. Find the standard deviation of all the 250 items taken together.
Q. 2 (b) Given
Now, 
Now, 
3. Explain the methods of collecting primary data. 12½
Ans: Methods of Collection:
Following are the important methods of collecting primary data:
(a) Observation Method: It is the most commonly used method especially in studies relating to behavioural science. In this method information are sought by way of investigator’s own direct observation without asking from the respondent. For instant, in study relating to consumer bahaviour, the investigator instead of asking the brand of wrist watch used by the respondent may himself look at the watch.
Advantage of Observation Method: Following are the advantages of observation method:
- Subjected bias is eliminated, if observation is done correctly.
- The information obtained under this method relates to what is currently happening, it is not complicated by either the past behaviour or future intentions or attitudes.
- This method is independent of respondent’s willingness to respond and as such is relatively less demanding of active cooperation on be part of respondents as happen to be the case in the interview or the questionnaire method.
- This method is particularly suitable in studies which deal with subject, i. e. respondents who are not capable of giving verbal report of their feelings for one reason or the other.
Disadvantage: However observation method has various disadvantages:
- It is an expensive method.
- Information provided by this method is very limited.
- Sometimes unforeseen factors may interfere with the observational task. At times, the fact that some people are rarely accessible to direct observation creates obstacles for this method to collect data effectively.
(b) Interview Method: There are two types of interview method:
(i) Personal Interview: In this method of data collection, there is a face-to-face contact with persons from whom the information is to be obtained. The interviewer asks them questions pertaining to the survey and collects the desired information. The information thus obtained is original in character.
Advantage: The advantages of personal interview method are as follows:
- More information and too in greater depth can be obtained.
- Interviewer by his own skill can overcome the resistance, if any, of the respondents.
- There is a greater flexibility under this method as the opportunity to restructure questions is always there, especially in the case of unstructured interviews.
- Observation method can also be applied to recording verbal answers to various questions.
- Personal information can as be obtained easily under this method.
- Sample can be controlled more effectively as there arises no difficulty of missing return, non-response generally remains very low.
Disadvantages: There are certain weaknesses of personal interview method:
- It is very expensive method, especially when large and wide spread geographical sample is taken.
- There remains the possibility of the bias of interviewer as well as that of the respondents.
- This method is more time consuming, especially when the sample is large and recalls upon the respondents are necessary.
- Interview at times may also introduce systemic errors.
- Effective interviews pre-suppose proper rapport with respondents that would facilitate free and frank response.
(ii) Telephone Interview: This method of collecting information consists in contacting respondents on telephone itself. It is not a very widely used method, but plays important part in industrial surveys, particularly in developed regions.
Merits: The chief merits of such systems are:
- It is more flexible in comparison to mailing method.
- It is faster than other methods.
- It is cheaper than personal interviewing method.
- Recall is easy, callback are simple and economical.
- There is a higher rate of response than what we have in mailing method.
Demerits: It is not free from demerits:
- Surveys are restricted to respondents who have telephone facilities.
- Extensive geographical coverage may get restricted by cost consideration.
- It is not suitable for intensive surveys where comprehensive answers are required to various questions.
- Possibility of bias of the interviewer is relatively more.
- Questions have to be short and to the point, probes are difficult to handle.
(c) Questionnaire Method: In this method a list of questions pertaining to the survey is prepared and sent to the various informants by post. The questionnaire contains questions and provides space for answers. A request is made to the informants through a covering letter to fill up the questionnaire and send it back within a specified time. This method is adapted by private individuals, research workers, private and public organisations and even by govt.
Merits: This method is most extensively employed in various economic and business surveys. The main merits are as follows:
- There is low cost even when the universe is large and is widely spread geographically.
- It is free from the bias of the interviewer; answers are in respondent’s own words.
- Respondents have adequate time to give well out answers.
- Respondents who are not easily approachable can also be reached conveniently.
- Large sample can be made use of and thus the results can be more dependable and reliable.
Demerits: It is not free from demerits:
- Low rate of return of the duly filled in questionnaires, bias due to no-response is often indeterminate.
- It can be used only when respondents are educated and cooperating.
- There is inbuilt inflexibility because of the difficulty of amending the approach once questionnaires have been sent.
- The control over questionnaire may be lost once it is sent.
- There is also the possibility of ambiguous replies or omission of replies altogether to certain questions, interpretation of omission is difficult.
- It is difficult to know whether willing respondents are truly representative.
- This method is likely to be the slowest of all.
(d) Schedule Method: This method of data collection is very much like questionnaire method, with a little difference which lies in the fact that schedules are being filled in by the numerators who are specially appointed for this purpose. These numerators along with schedules go to respondents put to them the questions from the Performa in the order questions are listed and record the replies in the space provided. Numerators explains them the object of the investigation and also removes the difficulties felt by the respondents. The numerators should train to perform their job well and the nature and scope of the investigation should be explained to them thoroughly. The numerators should be intelligent and must posses the capacity of cross examination in order to find out the truth. This method of data collection is very useful in extensive enquiries and can lead to fairly reliable results. It is, however very expensive and is usually adopted in investigations conducted by governmental agencies or by some big organisations. Population census all over the world is conducted through this method.
(e) Other methods Of collecting Data: There are some other methods of data collection particularly used by big business houses I modern time:
- Warranty cards
- Distributor or store audits
- Pantry audits
- Consumer panel
- Use of mechanical device
- Project techniques
- Depth interviews
- Contact analysis
4. Find the mode of the following data graphically. 12½
x :
|
0-10
|
10-20
|
20-30
|
30-40
|
40-50
|
50-60
|
60-70
|
f :
|
1
|
6
|
15
|
20
|
15
|
6
|
1
|
5. (a) Calculate mean deviation about median. 10+2½
x :
|
20
|
30
|
40
|
50
|
60
|
70
|
f :
|
8
|
12
|
20
|
10
|
6
|
4
|
(b) What is spurious accuracy?
Ans: Spurious Accuracy: This is a form of innumeracy in calculations and computers. It consists of claiming a greater accuracy than is justified, and usually arises when numbers are being combined (arithmetically) to produce an answer to a problem. As an example, consider the arithmetic used in working out the circumference of a circle.
6. (a) Calculate geometric mean from the following data: 8+4½
Marks :
|
5
|
15
|
25
|
35
|
45
|
No. of students :
|
5
|
7
|
15
|
25
|
8
|
(b) State any four seasons of non – sampling errors.
Ans: Non-sampling error is caused due to the following reasons:
- Coverage error: This occurs when a unit in the sample is incorrectly excluded or included, or is duplicated in the sample.
- Non-response error: this refers to the failure to obtain a response from some unit because of absence, non-contact, refusal, or some other reason.
- Response error: this refers to a type of error caused by respondents intentionally or accidentally providing inaccurate responses.
- Processing error: this refers to errors that occur in the process of data collection, data entry, coding, editing and output.
7. Draw a pie diagram to represent the following information: 12½
Items
|
Amount
|
Food
Clothing
Rent
Other Expenses
|
800
200
300
500
|
