2012 (November)
Commerce (General/Speciality)
Course: 303
Full Marks: 80
Time: 3 Hours
1. (a) Answer the following question:
(i) What do you mean by sample?
(ii) when are pie charts used to
represent statistical data?
(iii) What do you mean by
frequency distribution?
(iv) Write the relationship
between coefficient of correlation and the two regression coefficients.
(v) Write the additive model used
for time –series analysis.
(b) Fill up the blanks:
(i) Fisher’s index number is the
____ of Laspeyres’ and Paasche’s indices.
(ii) Flood in Assam is an example
of ______ in time series.
(iii)The rang of coefficient of
correlation _______.
2. (a) (i) “Statistics is like a mould of which one can make
a God or a Devil .” Discuss.
(ii) Calculate arithmetic mean
and harmonic mean from the following data:
(iii)Calculate standard deviation
from the data given below:
Wages:
|
120 – 130
|
130 – 140
|
140 – 150
|
150 – 160
|
160 – 170
|
170 – 180
|
180 – 190
|
No of Person:
|
15
|
30
|
44
|
60
|
30
|
14
|
7
|
Or
(b) (i) “ All facts numbercially expressed are
not statistics.” Discuss.
(ii) Prove that for any two
values: AM _> GM_> HM _>
(iii) Calculate the two quartiles, 8th
decile and 57th percentile from the data given below :
Values:
|
15 – 20
|
20 – 25
|
25 – 30
|
30 – 35
|
35 – 40
|
40 – 45
|
45 – 50
|
50 – 55
|
Frequency:
|
30
|
40
|
45
|
50
|
45
|
70
|
40
|
35
|
3. (a) (i) write the
uses of correlation analysis.
(ii) Given the two regression
equation as 8x – 10y + 66 = 0 and 40x – 18y =214, find the coefficient of
correlation between x and y.
(iii) Frome the given data below,
find the coefficient of correlation: N =12, EY = 5, EX2 =598, EY2=285,
EXY = 325
Or
(b) (i) prove that the coefficient of correlation
is the geometric mean of the two regression coefficients
(ii) Prove that coefficient of correlation is
independent of the change of the origin and scale of measurement
(iii) The demand of TV sets as
obtained by a sample survey on the residents of 7 towns is shown below :
Population (in’ 000):
|
11
|
14
|
14
|
17
|
17
|
21
|
25
|
Demand of TV:
|
15
|
27
|
27
|
30
|
34
|
38
|
46
|
Find the linear regression equation of Y on X and also find
the demand of TV sets in a town of population 30 thousand
4. (a) (i) Write a short note on time- reversal test.
(ii) Distinguish fixed based index and chain-
base index.
(iii) Calculate the cost of living index from
the data given below :
Item
|
Cost of Living
|
Weight
|
Food
|
525
|
40
|
Clothing
|
325
|
16
|
Fuel
and Lighting
|
240
|
15
|
House
rent
|
180
|
20
|
Others
|
200
|
9
|
Or
(b) (i) “ The wholesale price index of the year
2010 with the year 2005 as base year is 140.’’ What does the statement tell you
about the price rise ?
(ii)Write Why Fisher index number
is regarded as an ideal index number.
(iii) Construct an appropriate
index number from the data given below :
ITEM
|
2005
|
2010
|
||
Price
|
Quantity
|
Price
|
Quantity
|
|
A
|
4
|
50
|
10
|
40
|
B
|
3
|
10
|
9
|
2
|
C
|
2
|
5
|
4
|
2
|
5. (a) (i)What do you
mean by seasonal variations?
(ii)From the following data,
calculate 3- yearly moving averages :
Year:
|
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
Production:
|
12.7
|
17.3
|
17.7
|
18.9
|
19.2
|
19.3
|
(iii) From the data given, below,
find trend values using the latest squares principle :
Year:
|
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
2007
|
2008
|
2009
|
Sales:
|
38
|
40
|
65
|
72
|
69
|
62
|
67
|
95
|
104
|
Or
(b) (i)Write two models used for time series
analysis.
(ii) What is secular trend? What
are its causes?
(iii) Calculate trends from the
following data using four-yearly moving average:
Year:
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
Sales:
|
464
|
515
|
518
|
467
|
502
|
540
|
557
|
571
|
586
|
612
|
6. (a) (i) What do you mean by forecasting?
(ii) Mention the purposes of
business forecasting.
(iii) What is demand forecasting?
Discuss the necessary steps for demand forecasting.
Or
(b) (i) What are the assumption
of business forecasting?
(ii) Explain time-series analysis
as a tool of forecasting.
(iii) Discuss the steps involved
in business forecasting.