# Dibrugarh University Question Papers: Business Statistics (November' 2016)

2016 (November)
COMMERCE
(General/Speciality)
Course: 303
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
1. What do you mean by statistical unit?
2. Write one advantage of sampling method and one disadvantage of complete enumeration method.
3. If two variables and are related as and , then what will be the value of ?
4. If the coefficient of correlation between and is 0.67, then what will be the coefficient of correlation between and ?
5. If the correlation coefficient between two variables and is +1 and , then find the value of .
6. Given the annual trend equation of a company is ( unit = 1 year), estimate the monthly trend equation of the company.
7. Write the multiplication model of time series analysis.
8. Define covariance between two variables.
9. 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?
10. Write the formula for Fisher’s ideal index number.
11. If the two regression lines are and , then find the arithmetic mean of and .
12. 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 equations and , find the coefficient of correlation between and . 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
(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 of and . 5
(iv) Calculate coefficient of correlation between and from 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.): 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 ?
(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 46.5 53 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