# Dibrugarh University - Business Statistics 2009

1.       (a)  Mention at least five characteristics of a good measure of dispersion.
(b)  Calculate Mean and Variance from the following data :
 X 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79 Y 3 61 223 137 53 19 4

Or

(c)   From the following data find the value of X, if A.M. is 17.
 Age 8 20 26 29 No. Of Persons 3 2 X 1

(d)  Discuss any five essential qualities of an ideal measure of central tendency and state the Advantages of sample survey of collecting data.

2.       (a)  What is regression line ? Why there are two lines of regression ?
(b)  Calculate Karl Pearson’s coefficient of correlation from the data given below :

 X: 39 65 62 90 82 75 25 98 36 78 Y: 47 53 58 86 62 68 60 91 51 84
Or
(c)   What is coefficient of correlation ? What is its range ?
(d)  From the following data obtain the two regression equations :
 X: 6 2 10 4 8 Y: 9 11 5 8 7
3.       (a) Mention five different uses of Index Number in the study of Economics and Commerce.
(b) Calculate price indices for the year 1993 from the following using (i) Laspeyre’s method               And (ii) Fisher’s Method.

 Commodity 1990 1993 Price Quantity Price Quantity A B C D 6 2 4 10 50 100 60 3 10 2 6 12 56 120 60 24

Or
c)    Why Fisher Index Number is called Ideal Index ?
d)    Distinguish between Price and Quantity Index number’s . Also mention five limitations of Index Number.

4.       (a) Using the least square principle find the trend values from the following data:
 Year: 1990 1991 1992 1993 1994 1995 1996 Production: 83 60 54 21 22 13 23

(b) Expalin the components of a time series. Write down any two models used for time series analysis.
Or
(c) Find the trend values by 3-yearly moving average method from the following data:
 Year: 1990 1991 1992 1993 1994 1995 1996 1997 1998 Sales(In lakhs) 5 7 9 12 11 10 8 12 13

(d) Write short notes on : (any three)
(i) Trend
(ii) Seasonal fluctuations
(iii) Cyclical fluctuations
(iv) Irregular fluctuations.

5.       (a) State the Additive and Multiplicative Laws of Probability:
(b) Discuss any three methods of forecasting.
Or
(c) State five objectives of Business Forecasting.
(d) Explain Sales forecasting and Demand forecasting.