2014 (November)
COMMERCE
(General / Speciality)
(Business Statistics)
Course: 303
Full Marks: 80
Pass Marks: 32
Time: 3 hours
The figures in the margin indicate full marks for the questions.
1. Answer any five questions: 2x5=10
a)
Prove that the correlation coefficient is the
geometric mean of the two regression coefficients
b)
State the limitations of Laspeyres’ formula for
the construction of index numbers.
c)
Calculate AM and HM of 2, 4 and 8.
d)
Write the two models used for the study of time
series.
e)
“The correlation coefficient between two
variables X and Y is r and r2 =0.65,” What can be concluded from
this statement?
f)
What do you mean by business forecasting?
g)
What is the difference between Karl Pearson’s coefficient
of correlation and Spearman’s coefficient of correlation?
h)
Define price index number and quantity index number.
2. (a) (i)
which measures of dispersion is regarded as the best and why? 3
(ii) The
AM of the following distribution is 1.46, find the missing frequencies: 4
No. of Students :
|
0
|
1
|
2
|
3
|
4
|
5
|
Total
|
No. of Days :
|
46
|
25
|
10
|
5
|
200
|
(iii) Calculate the standard deviation for the following
data: 7
Wages in (Rs.)
|
No. of Men
|
O and above
20 and above
40 and above
60 and above
80 and above
100 and above
|
50
45
34
16
6
0
|
Or
2. (b) (i) For any two values, prove that AM>GM>HM 3
(ii) The mean,
median and mode of a group of 25 observations are 143, 144 and 147. A set of 6 observations
is added to this data with values132, 125,130,160,165 and 157. Find the mean
and median for the combined group of 31 observations. 4
(iii)
Calculate AM and SD for the following Data: 7
Midpoint :
|
15
|
20
|
25
|
30
|
35
|
40
|
45
|
50
|
55
|
Frequency :
|
2
|
22
|
19
|
14
|
3
|
4
|
6
|
1
|
1
|
3. (a) (i) Define Karl Pearson’s Coefficient of
correlation. 3
(ii) Discuss
the uses of regression analysis. 4
(iii) From
the following data, find the two regression lines: 7
Mean for
X=90, Mean for Y=70, N=10, Sum of X square = 6360, Sum of Y square = 2860, Sum
of Product of X and Y = 3900.
Or
(b) (i) The correlation coefficient of two
variables X and Y is r = 0.60, variance of X and Y are respectively 2.25and 4.00;
Mean for X =10, Mean for Y=20. From the above data, find the regression
equation of X on Y. 3
(ii)
Calculate Spearman’s rank correlation coefficient from the data given below: 4
X :
|
11
|
12
|
13
|
14
|
18
|
15
|
Y :
|
13
|
12
|
15
|
14
|
16
|
11
|
(iii) Find the value of the
coefficient of correlation from the data given below: 7
Income :
|
46
|
54
|
56
|
56
|
58
|
60
|
62
|
Expenditure :
|
36
|
40
|
44
|
54
|
42
|
58
|
54
|
4. (a) (i) Write the differences between chain base
index and fixed base index. 3
(ii) Prove
that Fisher’s index number satisfies time reversal test.
4
(iii) Find
the quantity index number from the following data using Paasche’s and Laspeyres
index:
Items
|
Base
year
|
Current
year
|
||
Price
(in Rs.)
|
Quantity
|
Price (in
Rs.)
|
Quantity
|
|
A
B
C
|
4
6
8
|
10
15
15
|
6
4
10
|
15
20
4
|
Or
(b) (i)
What is cost of living index? How does it help in policy formulation by the
Government? 3
(ii) Why
Fisher’s index number is regarded as an ideal index number? 4
(iii) From
the following data, prove that Fisher’s Index number satisfies (1) time reversal
test and (2) factor reversal test: 7
Items
|
Q0
|
Q1
|
P0
|
P1
|
A
B
C
D
E
|
4
5
2
1
3
|
20
15
30
50
25
|
6
6
3
1
5
|
18
12
30
60
28
|
5. (a) (i) Discuss the uses of studying time series. 3
(ii) What
is trend in a time series? State the factors responsible for trend in a time
series. 4
(iii)
Calculate trend values by using the method of least squares from the data given
below: 7
Year :
|
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
Values :
|
101
|
107
|
113
|
121
|
136
|
148
|
(b) (i) The trend equation for publicity cost (Rs. In’ 000) of a
company is YC
=20.2 – 0.8t. Origin 2001 (1st July), t unit = 1 year, Y unit =
yearly cost. Shift the origin to 2010. 3
(ii) Calculate 3 yearly moving averages
from the following data: 4
Year :
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
Profit: (in Rs.)
|
20
|
21
|
23
|
22
|
25
|
24
|
27
|
26
|
28
|
30
|
(iii) Fit
a straight line trend to the following data and estimate the profit for the
year 2010: 7
Year:
|
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
2007
|
Profit: (‘000 Rs.)
|
60
|
72
|
75
|
65
|
80
|
85
|
90
|
6. (a) (i) Discuss about demand forecasting. 5
(ii)
Discuss the limitations of business forecasting. 9
Or
(b) (i) Discuss the factors of a good forecasting. 5
(ii) Discuss the steps for
forecasting. 9
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