# Dibrugarh University Question Paper - Business Statistics (Nov' 2013)

2013 (November)
Commerce (General/Speciality)
Course: 303
Full Marks: 80
Pass Marks: 32

1. (a) Answer the following questions:                                   1x5=5
(i)      Which average is considered to be best for the construction of index numbers?
(ii)    Which is the GM of 5, 10, 20, 0 and 100?
(iii)   Write the relationship among AM, GM, and HM.
(iv)  When rank correlation used?
(v)    Write the relationship among Fisher’s index, Laspeyre’s index and Paasche’s index.

(b) Fill up the blanks:                                      1x3=3
(i)      The index number for the base year is taken as _______.

(ii)    When r = ± 1, the number of regression line is _____.
(iii)   Flood in Assam is an Example of ______ in time series.

2. (a) (i) State the features of a good measure of average.                                           3
(ii) If the AM of the following distributions is 67.45, find the value of the missing frequency:                        5
 Height Frequency 60-62 5 63-65 54 66-68 ---- 69-71 81 72-74 24

(iii) Calculate the coefficient of variation of the following data:                                   5+2=7
 Weight No. of persons 155-125 4 125-135 5 135-145 6 145-155 3 155-165 1 165-175 1

Or
(b) (i)   For any two values, prove that AM≥GM≥HM.                                      3
(ii) Calculate mode and median for the data given below:                             5
 Marks Less than (No. of students) 10 15 20 35 30 60 40 100 50 150 60 220 70 245 80 270

(iii) An analysis of the monthly wages paid to the works in two departments A and B f a company gave the following result. Find the combined standard deviation of the wages of the workers of the company as a whole:                                7
 Department A Department B No. of persons 60 20 Average wages Rs. 648 Rs. 584 Standard deviation 4 5

3. (a) (i) Prove that the correlation coefficient is the GM of the two regression coefficients.                         3
(ii) Explain why there should be two lines of regression.                                                5
(iii) Calculate the coefficient of correlation from the following data:                                         7
­­∑X = 125, ∑Y= 100, ∑X2 =650, ∑Y2 =460, ∑XY =508, N=25.

Or

(b) (i) Write the two regression equations.                                          3
(ii) Regression equations of two correlated variables X and Y are 5X – 6Y + 90=0 and 15X – 8Y – 130=0. Find which equation is the regression equation of Y on X and Which one is for X on Y. Also find means of X and Y.                            5
(iii) Find out the value of Y when X = 36 from the data given below:                                          7
 X Y Mean Standard Deviation 30 4 45 10 Correlation coefficient = +0.8

4. (a) (i) Discuss the relative merits and demerits of Laspeyre’s and Paasche’s indices.                                    3
(ii) During a certain period when the cost of living index goes up from 110 to 200, the dearness allowance of an employee was also increased from Rs.325 to Rs.500. Does the worker really gain? If so, by how much?                        4
(iii) Using Fisher’s formula, calculate price index number from the data given below:                                       7
 2005 2012 Items Price Quantity Price Quantity A B C D 12 18 21 25 5 4 3 2 15 22 18 20 6 5 4 3

Or

(b) (i) Describe the various types of Index numbers.                                       3
(ii) The following series of index numbers were constructed with the year 2000 as base year. Form a new set of index number with the year 2005 as base year:                                                              4
 Year 2001 2002 2003 2004 2005 2006 Index No. 105 118 125 130 150 156

(iii) Calculate Cost of Living Index number from the data given below and hence suggest what should be the salary of a person whose salary in the base year was Rs.500 to maintain his living status:                                     5+2=7
 Items Index No. Weight Food Clothing Fuel and lighting House Rent Miscellaneous 360 295 287 110 315 60 5 7 8 20

5. (a) (i) Discuss the uses of studying time series.                                              3
(ii) From the following data, calculate trend values by using the method of 3-yearly moving averages:                     4
 Year 2001 2002 2003 2004 2005 2006 2007 Production 100 120 95 105 108 110 120

(iii) What do you mean by trends in a time-series analysis? What are the factors responsible for the occurrence of trends? What are the uses of studying trends?                                   7

Or

(b) (i) Write the two models used for analysis of time series.                                       3
(ii) What is seasonal variation in a time series? Discuss the uses of studying seasonal variation in business.            4
(iii) Using the method of least squares, find the trend values for the following data:                                        7
 Year 2001 2002 2003 2004 2005 2006 2007 Income 67 53 43 61 56 79 58

6. (a) (i) State the assumptions under which business forecasting is carried out.                                 3
(ii) Discuss how forecasting is done by regression analysis method.                                                          4
(iii) Prepare a note why a business manager should use forecasting methods.                                    7

Or

(b) (i) Discuss the limitations of business forecasting.                                                      3
(ii) Discuss the economic models of business forecasting.                                             4
(iii) Discuss the qualities of a good method of forecasting.                                            7