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 variablesandare related asand, then what will be the value of?
 If the coefficient of correlation betweenandis 0.67, then what will be the coefficient of correlation betweenand?
 If the correlation coefficient between two variablesand 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 areand, then find the arithmetic mean ofand.
 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
(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 equationsand, find the coefficient of correlation betweenand. 5
(iv) Find the two regression equations from the data given below: 7
(b) (i) Whenthere 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 ofand, 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
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
(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.):

3032

3234

3436

3638

3840

4042

4244

4446

4648

4850

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 areand, 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
(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
(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