Business Statistics Question Papers
2016 (November)
COMMERCE
(General/Speciality)
Course: 303
(Business Statistics)
The figures in the margin indicate full marks for the questions
(New Course)
Full Marks: 80
Pass Marks: 24
Time: 3 hours
1. Answer any eight questions: 2x8=16
- What do you mean by statistical unit?
- Write one advantage of sampling method and one disadvantage of complete enumeration method.
- If two variables
and
are related as
and
, then what will be the value of
?
- If the coefficient of correlation between
and
is 0.67, then what will be the coefficient of correlation between
and
?
- If the correlation coefficient between two variables
and
is +1 and
, then find the value of
.
- Given the annual trend equation of a company is
(
unit = 1 year), estimate the monthly trend equation of the company.
- Write the multiplication model of time series analysis.
- Define covariance between two variables.
- If the price index number for the year 2016 compared to 2006 is 210 and monthly income of a person in 2006 be Rs. 10,500, then what should be his monthly income in 2016?
- Write the formula for Fisher’s ideal index number.
- If the two regression lines are
and
, then find the arithmetic mean of
and
.
- What do you mean by quantity index number?
2. (a) (i) ____ is regarded as the best measure of dispersion. (Fill up the blank) 1
(ii) In a moderately asymmetrical distribution mode and mean are 32.1 and 35.4 respectively. Find the median. 3
(iii) Find the mean deviation from mean for the following data: 5
(Marks):
|
0 – 10
|
10 – 20
|
20 – 30
|
30 – 40
|
40 – 50
|
50 – 60
|
60 – 70
|
(No. of Students):
|
20
|
25
|
32
|
40
|
42
|
35
|
10
|
(iv) Calculate the coefficient of variation for the following data: 7
(Weight):
|
0 – 10
|
0 – 20
|
0 – 30
|
0 – 40
|
0 – 50
|
0 – 60
|
0 – 70
|
0 – 80
|
(No. of Persons):
|
15
|
30
|
53
|
75
|
100
|
110
|
115
|
125
|
Or
(b) (i) for a symmetrical distribution value of mean, median and mode are ____. (Fill up the blank) 1
(ii) Prove that
3
3
(iii) Calculate quartile deviation for the following data: 5
(Class):
|
5 – 10
|
10 – 15
|
15 – 20
|
20 – 25
|
25 – 30
|
30 – 35
|
35 – 40
|
(Frequency):
|
10
|
15
|
25
|
40
|
35
|
20
|
5
|
(iv) Calculate mean and median for the following distribution: 7
(No. of Firms):
|
10 – 19
|
20 – 29
|
30 – 39
|
40 – 49
|
50 – 59
|
60 – 69
|
70 – 79
|
(Production):
|
3
|
61
|
223
|
137
|
53
|
19
|
14
|
3. (a) (i) What is the range of coefficient of correlation? 1
(ii) Write the properties of coefficient of correlation. 3
(iii) Given the two regression equations
and
, find the coefficient of correlation between
and
. 5
and, find the coefficient of correlation betweenand. 5
(iv) Find the two regression equations from the data given below: 7
(b) (i) When
there is ____ regression equation. (Fill up the blank) 1
there is ____ regression equation. (Fill up the blank) 1
(ii) In a Bivariate data the sum of squares of the differences between the ranks of observed values is 231 and the rank correlation coefficient is – 0.4, find the number of pairs of items. 3
(iii) For a Bivariate data of
and
, variance of
and
are respectively 2.25 and 4.00, 
and
, find the regression equation ofand. 5
and, variance ofandare respectively 2.25 and 4.00, and, find the regression equation ofand. 5
(iv) Calculate coefficient of correlation betweenandfrom the following data: 7
andfrom the following data: 7
4. (a) (i) Fisher’s index number is the ____ mean of Laspeyres and Paasche’s indices. (Fill up the blank) 1
(ii) Write the chief features of index number. 3
(iii) From the data given below, calculate quantity index number by using Laspeyre’s formula: 5
Base Year
|
Current Year
| |||
Items
|
Price (in Rs.)
|
Quantity
|
Price (in Rs.)
|
Quantity
|
A
B
C
D
E
|
5
3
4
11
7
|
50
100
60
30
40
|
10
4
6
14
10
|
56
120
60
24
36
|
(iv) Calculate Fisher’s price index number from the data given below: 7
Base Year
|
Current Year
| |||
Items
|
Price (in Rs.)
|
Quantity
|
Price (in Rs.)
|
Quantity
|
A
B
C
D
E
F
|
10
8
12
20
5
2
|
10
12
12
15
8
10
|
12
8
15
25
8
4
|
8
13
8
10
8
10
|
Or
(b) (i) ____ is regarded as the best measure for the construction of index number. (Fill up the blank) 1
(ii) Discuss why Fisher’s index number is regarded as an ideal index number. 3
(iii) Give a comparative study of fixed base and chain base indices. 5
(iv) Calculate Cost of living index number from the following data: 7
Items
|
Price of the Base Year
|
Price of the Current Year
|
Weight
|
Food
Fuel
Clothing
House Rent
Others
|
30
8
14
22
25
|
47
12
18
15
30
|
4
1
3
2
1
|
5. (a) (i) Continuous price rise is an example of ____ in a time series. (Fill up the blank) 1
(ii) Write a short note on graphic method of measuring trend in a time series. 3
(iii) Write how trends in a time series are measured by the method of moving averages. 5
(iv) Calculate trend values for the data given below by using the method of least squares: 7
(Year):
|
1997
|
1998
|
1999
|
2000
|
2001
|
2002
|
2003
|
(Values):
|
30
|
45
|
39
|
41
|
42
|
46
|
49
|
Or
(b) (i) Give an example of random fluctuations in a time series. 1
(ii) Write a short note on trends in a time series. 3
(iii) Calculate trends by the method of 3 yearly moving averages from the data given below: 5
(Year):
|
1995
|
1996
|
1997
|
1998
|
1999
|
2000
|
2001
|
2002
|
2003
|
2004
|
(Production):
|
52
|
79
|
76
|
66
|
68
|
93
|
87
|
79
|
90
|
95
|
(iv) Fit a straight line trend by the method of least squares and hence find the probable sale for the year 1988:
(Year):
|
1980
|
1981
|
1982
|
1983
|
1984
|
1985
|
1986
|
1987
|
(Sales):
|
12
|
13
|
13
|
16
|
19
|
23
|
21
|
23
|
(Old Course)
Full Marks: 80
Pass Marks: 32
Time: 3 hours
The figures in the margin indicate full marks for the questions
1. (a) (i) Write the definition of statistics given by Prof. H. Secrist. 2
(ii) Discuss any one method of collection of primary data. 3
(iii) Given AM of the following distribution is 67.45, find the value of missing frequency: 4
(Class Interval):
|
60 – 62
|
63 – 65
|
66 – 68
|
69 – 71
|
72 – 74
|
(Frequency):
|
5
|
54
|
?
|
81
|
24
|
(iv) Calculate standard deviation for the data given below: 7
(Class):
|
0 – 10
|
10 – 20
|
20 – 30
|
30 – 40
|
40 – 50
|
50 – 60
|
60 – 70
|
(Frequency):
|
8
|
12
|
17
|
14
|
9
|
7
|
4
|
Or
(b) (i) Calculate AM and HM of 2, 4, 8, and 10. 2
(ii) For any two values prove that
. 3
. 3
(iii) Calculate the mode of the following frequency distribution: 4
(Weight):
|
0 – 10
|
10 – 20
|
20 – 30
|
30 – 40
|
40 – 50
|
(No. of Children):
|
10
|
14
|
19
|
17
|
13
|
(iv) Calculate the values of median and two quartiles for the following data:
Daily Wages (in Rs.):
|
30-32
|
32-34
|
34-36
|
36-38
|
38-40
|
40-42
|
42-44
|
44-46
|
46-48
|
48-50
|
No. of Workers:
|
3
|
8
|
24
|
31
|
50
|
61
|
38
|
21
|
12
|
2
|
2. (a) (i) What are the properties of coefficient of correlation? 2
(ii) If the two regression equations are
and
, what should be the means of
and
?
and, what should be the means ofand?
(iii) What do you mean by Karl Pearson’s coefficient of correlation? What is its range? When does it become positive, negative or zero? 4
(iv) Find the two regression equations from the following data: 7
X:
|
5
|
10
|
15
|
25
|
30
|
35
|
40
|
45
|
Y:
|
25
|
32
|
44
|
32
|
39
|
49
|
55
|
60
|
Or
(b) (i) If the two regression coefficients are 0.8 and 0.12, what will be the value of coefficient of correlation?
(ii) The value of Spearman’s rank correlation coefficient for a certain pair of items is 2/3 and the sum of the squares of differences between corresponding ranks is 55, finds the number of pairs of items. 3
(iii) If the regression equation of Y and X is
, then under what conditions the regression equation of X and Y will be
? 4
, then under what conditions the regression equation of X and Y will be? 4
(iv) From the data given below, find Karl Pearson’s coefficient of correlation: 7
X:
|
3
|
5
|
6
|
7
|
9
|
12
|
Y:
|
20
|
14
|
12
|
10
|
9
|
7
|
3. (a) (i) What are the differences between Laspeyres and Paasche’s indices? 2
(ii) Construct new indices by shifting base year to 1994 from the following data: 3
(Year):
|
1989
|
1990
|
1991
|
1992
|
1993
|
1994
|
1995
|
(Index No.)
|
100
|
120
|
122
|
116
|
120
|
120
|
137
|
(iii) Write why Fisher’s index number is regarded as an ideal index number. 4
(iv) Calculate appropriate index number from the data given below: 7
Base Year
|
Current Year
| |||
Items
|
Price (in Rs.)
|
Quantity
|
Price (in Rs.)
|
Quantity
|
A
B
C
D
E
|
5
3
4
11
7
|
50
100
60
30
40
|
4
10
6
14
10
|
56
120
60
24
36
|
Or
(b) (i) Calculate price relative of 2011 with reference to 2010 from the data given below: 2
Year
|
Price (in Rs.)
|
2010
2011
|
18
15
|
(ii) Write a short note on factor reversal test. 3
(iii) Calculate (1) Laspeyre’s and (2) Paasche’s Price indices from the data given below:
Base Year
|
Current Year
| |||
Items
|
Price (in Rs.)
|
Quantity
|
Price (in Rs.)
|
Quantity
|
A
B
C
D
|
8
12
10
15
|
10
5
12
10
|
15
10
12
20
|
12
7
15
12
|
(iv) Calculate cost of living index number from the data given below: 7
Price
| |||
Items
|
Weight
|
Base Year
|
Current Year
|
Food
Rent
Clothing
Fuel
Others
|
35
20
15
10
20
|
250
60
80
50
200
|
270
80
100
50
250
|
4. (a) (i) If the annual trend line equation be
(
= 1 year, origin 2013), then what will be the annual rate of growth of production? 2
(= 1 year, origin 2013), then what will be the annual rate of growth of production? 2
(ii) Write a short note on seasonal variation in a time series. 3
(iii) Calculate 3 yearly moving average from the data given below: 4
(Year):
|
2005
|
2006
|
2007
|
2008
|
2009
|
2010
|
2011
|
2012
|
(Values):
|
28
|
38
|
46
|
40
|
56
|
40
|
50
|
60
|
(iv) Using the method of least squares, find the trend line equation for the following data and hence estimate the production for the year 2015: 7
(Year):
|
2010
|
2011
|
2012
|
2013
|
2014
|
(Production):
|
28
|
38
|
46
|
40
|
46
|
Or
(b) (i) Write the multiplicative model used in time series analysis. 2
(ii) Write the disadvantages of moving average method of calculating trend values. 3
(iii) Write how trends in a time series are calculated by applying the method of least squares. 4
(iv) Estimate trend values by using 4 yearly moving averages for the following data: 7
Year:
|
2001
|
2002
|
2003
|
2004
|
2005
|
2006
|
2007
|
2008
|
2009
|
2010
|
Sales:
|
60.0
|
46.5
|
53.0
|
54.5
|
48.9
|
48.2
|
42.6
|
51.7
|
51.1
|
43.8
|
5. (a) (i) Write the assumptions for forecasting. 2
(ii) Discuss about the limitations of forecasting. 3
(iii) Write a short note about the barometric techniques used in forecasting. 4
(iv) Write a short note about demand forecasting. 7
Or
(b) (i) Write how the study of regression analysis can help in forecasting. 2
(ii) What precautions are to be taken while forecasting? 3
(iii) Write a short note about the importance of forecasting. 4
(iv) Discuss various steps in the process of forecasting. 7