# Dibrugarh University Question Paper: Business Statistics (Nov' 2014)

2014 (November)
COMMERCE
(General / Speciality)

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