LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.COM. DEGREE EXAMINATION – COMMERCE

SECOND SEMESTER – APRIL 2011

ST 2102/2101 – BUSINESS STATISTICS

 

 

Date : 09-04-2011              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer all the questions:                                                                                                         ( 10 X 2 = 20)

 

1. State any two measures of dispersion
2. State the formula for computing Karl Pearson coefficient of correlation
3. State the formula for computing Spearman’s Rank correlation
4. Determine mean and median for the for the following observations 12,10,5,8,9
5. State the components of a time series
6. State the methods of estimating trend
7. The fitted regression equation is Sales=0.3+3.2Advertisement_Expense. Determine Sales when Advertisement Expense is Rs.2,00,000
8. Define Index number
9. Current year price ( P₁) = 187, base year price (P­₀ ) = 167 determine the price index
10. State the methods of determining the Initial Basic Feasible Solution(IBFS) for a transportation problem

                                                                      SECTION- B

Answer any five questions:                                                                                                      ( 5 X 8 = 40)

 

11. Explain the Scope and Limitation of Statistics

 

1. Construct a Histogram and Frequency polygon for the data given below

Income(in 000s)	0-5	5-10	10-15	15-20	20-25	25-30
Number of Employees	5	20	25	40	50	20

 

13. Explain the different types of bar charts with examples

 

Judge I	1	5	4	8	9	6	10	7	3	2
Judge II	4	8	7	6	5	9	10	3	2	1

14. Determine Spearman’s Rank Correlation

 

 

 

 

15. State the differences between Correlation and Regression

 

16. Explain the components of Time series

 

 

17. Determine Price index number by the method of Laspere, Paasche, Bowley, and Fisher for the data given below

Commodity	2009		2010
	Price (p0)	Quantity(q0)	Price (p1)	Quantity(q1)
A	15	12	16	15
B	12	8	10	10
C	8	5	7	10
D	10	15	15	20
E	14	4	13	5

 

18. The estimated time taken for each person in completing different jobs is given below. Determine the optimum solution of the assignment problem by Hungarian method

	Job
Person	I	II	III	IV
A	14	5	8	7
B	2	12	6	5
C	7	8	3	9
D	2	4	6	10

 

 

 

 

 

 

 

 

 

SECTION- C

Answer any two questions:                                                                                                     ( 2 X 20 = 40)

 

19. (i) Determine Mean deviation and Standard deviation for the data given below                 (10)

Mark(X)	0-10	10-20	20-30	30-40	40-50	50-60
Frequency(f)	10	20	30	50	40	30

 

(ii) Determine Mean , Median and Mode for the data given below                              (10)

Mark(X)	0-10	10-20	20-30	30-40	40-50	50-60
Frequency(f)	10	20	30	50	40	30

 

20. Data on Advertisement Expense and Sales are given below

Advertisement Expense(in lakhs) (X)	1	2	3	4	5
Sales(in lakhs) (Y)	10	20	30	50	40

1. i) Construct a Regression model of Y on X (7)
2. ii) Construct a Regression model of X on Y (7)

iii) Estimate Sales when Advertisement expense equal to 5.2                                      (3)

1. iv) Etimate the advertisement expense required to get a sales of 70 lakhs (3)

 

21. Fit a straight line and a second degree parabola for the given data and estimate sales for the

year 2011

Year	2006	2007	2008	2009	2010
Sales(000s)	23	45	56	62	68

 

 

 

 

22.(i) Determine the optimum solution for the given LPP problem by Graphical method           (10)

Maximize:   Z = 45x₁ + 55x₂

Subject to:    6x₁+3x₂   120

4x₁+10x₂  180

 

 

(ii)  Determine Initial Basic Feasible Solution(IBFS) for the following transportation problem

by the method of  a) North west corner rule  b)Vogel’s  approximation method  (10)

	Demand
Supply	D1	D2	D3	D4	AVAILABILITY
A1	1	2	1	4	30
A2	3	3	2	1	50
A3	4	2	5	9	20
DEMAND	20	40	30	10	100

 

 

 

 

 

 

 

 

 

 

 

 

 

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