BACHELOR'S DEGREE PROGRAMME
TermEnd Examination, December, 2013
ELECTIVE COURSE: COMMERCE
ECO7: ELEMENTS OF STATISTICS
Time: 2 hours Maximum Marks: 50 (Weightage: 70%)
Note: Attempt any four questions. All questions carry equal marks.
1. (a) Fill in the blanks with a suitable word as given in brackets: 8
(i) In Census enquiry the whole group is to be surveyed. (sample/ census)
(ii) When the errors tend to cancel each other, they are called Unbiased errors. (unbiased/biased)
(iii) Arithmetic Mean is unduly affected by extreme values. (Arithmetic mean/ median)
(iv) It takes Less time to collect secondary data compared to primary data. (less/more)
(v) If the data is divided on the basis of similarity, it is called Classification. (Tabulation/ classification)
(vi) Two dimensional diagram indicates Area. (volume/area)
(vii) Dispersion is the degree of variation of the variables about a central value. (Skewness/ Dispersion)
(viii) UShaped data generally has two modes. (Ushaped/Jshaped)
(b) What do you mean by statistical survey? 4½
Ans: Meaning of Statistical Survey: A Statistical Survey is a scientific process of collection and analysis of numerical data. Statistical surveys are used to collect information about units in a population and it involves asking questions to individuals. Surveys of human populations are common in government, health, social science and marketing sectors. Statistical investigation is a long and comprehensive process. It extends over various stages, from initial planning to the preparation of the report. There are mainly two stages involved in statistical survey which are:
 Planning a statistical survey
 Executing a statistical survey
2. (a) Compute standard deviation, mode and median, when mean = 50, coefficient of variation = 40% and skewness = —0.4. 2+2+4
Solution: 2. (a) Given,
(b) State the advantages of collection of data through a questionnaire. 4½
3. (a) Explain the importance of visual presentation of data. 6½
Ans:
(b) What are the sources of secondary data? Explain. 6
Ans: Secondary Data and its sources: Secondary data are second hand information’s. They are not collected from the source as the primary data. In other words, secondary data are those which have already been collected. So they may be relatively less accurate than the primary data. Secondary data are generally used when the time of enquiry is short and the accuracy of the enquiry can be compromised to some extent. Secondary data can be collected from a number of sources which can broadly be classified into two categories.
i) Published sources
ii) Unpublished sources
Published Sources: Mostly secondary data are collected from published sources. Some important sources of published data are the following.
1. Published reports of Central and State Governments and local bodies.
2. Statistical abstracts, census reports and other reports published by different ministries of the Government.
3. Official publications of the foreign Governments.
4. Reports and Publications of trade associations, chambers of commerce, financial institutions etc.
5. Journals, Magazines and periodicals.
6. Periodic Publications of Government organizations like Central Statistical Organization (C. S. O.), National Sample Survey Organization (NSSO).
7. Reports submitted by Economists, Research Scholars, Bureaus etc.
8. Published works of research institutions and Universities etc.
Unpublished Sources: Statistical data can also be collected from various unpublished sources. Some of the important unpublished sources from which secondary data can be collected are:
1. The research works carried out by scholars, teachers and professionals.
2. The records maintained by private firms and business enterprises. They may not like to publish the information considering them as business secret.
3. Records and statistics maintained by various departments and offices of the Central and State Governments, Corporations, Undertakings etc.
4. Compute the coefficient of variation from the data given below: 12½
Marks :

1020

2030

3040

4050

5060

6070

No. of Students:

18

22

40

32

18

10

Solution
Marks

f

X

fx

d=(XA)

d’=d/10

d’2

fd’

fd’2

10 – 20
20 – 30
30 – 40
40 – 50
50 – 60
60 – 70

18
22
40
32
18
10

15
25
35
45
55
65

270
550
1400
1440
990
650

30
20
10
0
+10
+20

3
2
1
0
+1
+2

9
4
1
0
1
4

54
44
40
0
18
20

162
88
40
0
18
40

N = 140

5300

100

348

5. From the following data, draw the "less than" and "more than" curves (ogives) and ascertain the median graphically: 12½
Weight (kgs)

No. of Persons

Weight (kgs)

`No. of Persons

Less than 10

4

More than 0

50

Less than 20

10

More than 10

46

Less than 30

30

More than 20

40

Less than 40

40

More than 30

20

Less than 50

47

More than 40

10

Less than 60

50

More than 50

3

6. (a) Compute Bowley's skewness, when: Q, = 60, Q3 = 96 and median = 80. 6
Solution: Bowley’s coefficient of Skewness
(b) Prepare a blank statistical table to show age, sex, literacy levels and occupation of the residents of Rural and Urban areas during the periods of 19952000, 20002005 and 20052010. 6½
Solution: Blank Table
Rural

Urban

Total
 
Year

Age of Group

Occupation

Literate

Illeterate

Occupation

Literate

Illeterate
 
19952000

Upto 25
 
25 to 50
 
50& above
 
20002005

Upto 25
 
25 to 50
 
50 &
above
 
20052010

Upto 25
 
25 to 50
 
50 & above
 
Total

7. (a) Explain the purpose of percentages and ratios. 6½
(b) One of the properties of Arithmetic mean is E(x—x) is always zero. Explain it with an illustration. 6
Solution: Sum of Deviation of Series from actual mean is always Zero i.e.,
Consider the following example, Wages of workers : 10, 20, 30, 50, 60, 40.
Now, Mean of the given series
Again, taking duration from the actual mean
Wages
 
10
20
30
50
60
40

25
15
5
+15
+25
+5

From the above calculations it is clear that sum of deviation of series from actual mean is always zero.