Loyola College B.Com April 2008 Business Statistics Question Paper PDF Download

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Com. DEGREE EXAMINATION – COMMERCE

NO 3

 

SECOND SEMESTER – APRIL 2008

ST 2102 – BUSINESS STATISTICS

(Also Equal ST 2101/3101/3104)

 

 

Date : 25/04/2008                Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION A

Answer ALL questions.                                                                       (10 x 2 =20 marks)

 

  1. State the applications of statistics.
  2. What are the advantages of diagrammatic presentation of data?
  3. An automobile driver travels 240 kms. at speed of 40 km per hr and 20 kms at a speed of  10 km per hr. Calculate the average speed.
  4. What do you mean by skewness?
  5. What is the use of a scatter diagram?
  6. The lines of regression of a bivariate distribution are as follows: 5X – 145 = -10Y,       14Y -208 = -8X. Find the means of X and Y.
  7. Define time series.
  8. What are the uses of index numbers?
  9. Define objective function in a Linear Programming Problem.
  10. What is simplex method?

 

SECTION B

 

Answer any FIVE questions.                                                               (5 x 8 =40 marks)

 

  1. Discuss the scope and limitations of statistics.

 

  1. Find the mode for the following data:

 

X 5 10 11 12 13 14 15 16 18 20
Freq. 4 6 5 10 20 22 23 6 2 1

 

  1. Calculate mean deviation from median and its coefficient from the following data:

 

Marks 10-20 20-30 30-40 40-50 50-60 60-70 70-80
No. of students 4 6 10 20 10 6 4

 

  1. Draw less than and more than ogives for the data given below:

 

Value 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90
Freq. 9 42 61 140 250 102 71 23 2

 

  1. Calculate 5-yearly and 7-yearly moving average for the following data of a number of commercial industrial failures during 1992-2007.

 

Year 1992 ‘93 ‘94 ‘95 ‘96 ‘97 ‘98 ‘99
No. of failures 23 26 28 32 20 12 12 10
Year 2000 ‘01 ‘02 ‘03 ‘04 ‘05 ‘06 ‘07
No. of failures 9 13 11 14 12 9 3 1

 

  1. Calculate fixed base indices and chain base indices with 2000 as the base for the following data:
Average wholesale prices (Rs.)
Commodities 2000 2001 2002 2003 2004
A 20 25 30 45 63
B 30 36 45 63 126
C 40 34 51 102 51

 

 

 

 

 

 

 

 

 

  1. Calculate Karl Pearson’s coefficient of correlation between per capita national income(X) and per capita consumer expenditure(Y)(for 10 consecutive years) from the data given below:
X 249 251 248 252 258 269 271 272 280 275
Y 237 238 236 240 245 255 254 252 258 251

 

 

 

 

  1. A company manufactures 2 models of voltage stabilizers A and B. All components of the stabilizers are purchased from outside and only assembling and testing is carried out at the company. The assembly and testing time required for the two models are 0.8 hours each for A and 1.2 hours for B. manufacturing capacity of 720 hours at present is available per week.

The market for the 2 models has been surveyed which suggests maximum weekly sales of 600 units of A and 400 units of B. Profit per unit for A and B models has been estimated at Rs.100 and Rs.150 respectively. Find the optimum product mix using graphical method.

 

SECTION C

 

Answer any TWO questions.                                                               (2 x 20 =40 marks)

 

  1. The following table gives the profits (Rs.’000s) of two companies for the last 10 years. Which of the two companies has greater consistency in profits?
Profit of Co.X 700 625 725 625 650 700 650 700 600 650
Profit of Co.Y 550 600 575 550 650 600 550 525 625 600

 

 

 

 

  1. Price index of cotton and wool are given below for the 12 months of a year. Obtain both the lines of regression, Also find the correlation coefficient.

 

Index of cotton 78 77 85 88 87 82 81 77 76 83 97 93
Index of wool 84 82 82 85 89 90 88 92 93 89 98 99

 

 

  1. Calculate seasonal variations given the average quarterly price of a commodity for 5 years by ratio to trend method.

 

Year I Quarter II Quarter III Quarter IV Quarter
2001 28 22 22 28
2002 35 28 25 36
2003 33 34 30 35
2004 31 31 27 35
2005 37 36 31 36

 

  1. (i) There are three sources A, B, C which store a given product. These sources supply these products to four dealers D, E, F, G. The cost (Rs.) of transporting the products from various sources to various dealers, the capacities of the sources and the demands of the dealers are given below.

 

D E F G Supply
A 6 8 8 5 30
B 5 11 9 7 40
C 8 9 7 13 50
Demand 35 28 32 25 120

 

Find out the solution for transporting the products at a minimum cost by using Vogel’s Approximation Method.

 

(ii) Determine the least cost allocation of the available machines M1, M2, M3, Mand M5,  to 5 jobs A, B, C, D and E.

A B C D E
M1 25 29 31 42 37
M2 22 19 35 18 26
M3 39 38 26 20 33
M4 34 27 28 40 32
M5 24 42 36 23 45

 

 

 

 

 

 

 

 

 

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