University of Delhi 2005-3rd Year B.Com Statistics External

Q. 1. (a) The arithmetic mean of the marks found by 50 students was computed as 44. It was later discovered that a score of 36 was misread as 56. obtain the accurate value of the arithmetic mean of the marks found by the students.

(b) The arithmetic mean and standard deviation of 2 brands of light bulbs are provided below:
Brand I - Brand II
Arithmetic mean - 800 hours - 770 hours
Standard deviation - 100 hours - 60 hours

compute coefficient of variation for the 2 brands.

© In a moderately asymmetrical distribution, the mode and mean are 32.1 and 35.4 respectively. obtain the value of median.

(d) “An index number is a specialised kind of avg..” discuss.

(e) Distinguish ranging from positive and negative correlation,


Q. 2. (a) What is statistics ? explain its importance in business.

(b) From the subsequent data, compute Karl Pearson’s coefficient
of correlation.

Height of Fathers (inches) - Height of Sons (inches)

66 - 65
68 - 64
69 - 67
72 - 69
65 - 64
59 - 60
62 - 59
67 - 68
61 - 60
71 - 64

© From the subsequent data, compute Bowley’s coefficient of
skewness.
No. of Children per Family - No. of Families

0 - 7
1 - 10
2- 16
3 - 25
4 - 18
5 - 11
6 - 8


Q. 3. (a) discuss the different methods of collecting primary data ind point out their relative merits and demerits. 6

(b) From the subsequent data, compute standard deviation: 8
x - f
10 - 2
11 - 7
12 - 10
13 - 12
14 - 15
15 - 11
16 - 10
17 - 6
18 - 3

© Represent the subsequent data by a sub-divided bar diagram.

Years - 1998 - 1999 - 2000- 2001- 2002
,
No. of
government
companies- 322- 674 - 867 - 1034 - 1170

No. of non government
companies - 31- 45 - 66 - 133 - 223

Total - 353 - 719 - 933 - 1167 - 1393


Q. 4. (a) What is a sample survey ? explain its merits and demerits.

(b) Fit a straight line pattern to the subsequent data and estimate the likely profit for the year 2003. Also compute the pattern values. 10

Year - Profit
(in lakhs of Rs.)
1994 - 60
1995 - 72
1996 - 75
1997 - 65
1998 - 80
1999 - 85
2000 - 95

© The population of a country increased by 20% in the 1st decade, 30% in the 2nd decade and 45% in the 3rd decade. obtain the avg. rate of increase in population per decade.


Q. 5. (a) discuss the meaning and objectives of time series analysis.

(b) From the subsequent data, prove that Fisher’s ideal index satisfies the time reversal test and the factor reversal test:

Base Year_____________Current Year

Commodity - Price - volume - Price - volume
A- six - 50 - 10 - 60
B - two - 100 - two - 120
C_-_________ 4__-___0 - _ __6__-_____60

© From the subsequent data, compute Spearman’s coefficient of correlation:

Sales Advertisement
(in lakhs of Rs.) Expenditure
(in lakhs of Rs.)-
56 - 40
56 - 36
39 - 30
54 - 44
45 - 36
40 - 32
56 - 45
60 - 42
30 - 20
36 - 36

Earning:   Approval pending.