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

 

22. (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, M_2, M_3, M₄  and 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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