1. JOSEPH’S COLLEGE OF COMMERCE (AUTONOMOUS)

END SEMESTER EXAMINATION – APRIL 2014

B.COM (TRAVEL & TOURISM) – IV SEMESTER

BUSINESS STATISTICS

Time: 3 Hrs.                                                                                                                                              Max. Marks : 100

SECTION – A

1. Answer ALL the Each carries 2 marks.                (10 x 2 =20)

 

1. Mention the differences between  the two types of class intervals.
2. A reporter has an average speed of taking 160 words per minute. A typed page takes an average of 200 words . How many sheets of paper will be needed to type out the speech that lasted half an hour assuming that typing is done on both sides of
3. Differentiate between absolute measure of dispersion and relative measure of dispersion. Give examples.
4. Define regression. Why the regression lines cannot be used interchangeably. Is it possible to have only one regression line?
5. State the empirical relation between Mean, Median and Mode. If Mean=120, Mode=135  a moderately asymmetrical distribution, what would be its most probable median value?
6. Calculate mean, median and mode of the following numbers

3, 2, 0, 4, 2, 4, 5, 4, 6, 5

7. What are Pictograms and Cartograms?
8. Why are index numbers called economic barometers?
9. Fisher’s index number is the ideal index number- give reasons.
10. What do you mean by irregular variations in Time series?

SECTION- B

II   Answer any FOUR questions. Each carries 5 marks.                                               (4 x 5 = 20)

 

11. A study conducted for 500 tourists in India revealed the following data regarding the favorite tourist place. The Four tourist spots considered were beaches & Resorts , Historical places, Religious places and Heritage Hotels. Among the respondents 150 were foreigners and the rest were Indians. The number of tourists who liked beachs & resorts and Historical Places were 25% each. The number of people who liked religious places is 50 more than the people who liked Beaches & resorts. 49 Indians liked Heritage hotels and Foreigners who liked beaches & Resorts and  Historical places are 60 and 33 respectively.  Present the above data in an appropriate table.
12. The following table shows religiosity and death anxiety  scores of 10 people. High score implies greater religiosity or greater death anxiety resp.  Find  correlation coefficient using con-current deviation method. What does the statistics indicate?

 

Religiosity	4	3	11	5	9	6	14	9	10
Death Anxiety	38	42	29	31	28	15	24	17	19

 

13. Apply 3 yearly moving averages method and determine the trend for the following data.

Year	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010
Sales (in lakhs)	500	520	550	470	510	540	560	570	590	610

14. The following information is obtained through a middle class family budget enquiry of Bombay. Calculate consumer price index number by family budget method. What changes have taken place in 2010 compared to 2006?

 

Items	Food	Rent	Clothing	Fuel	Miscellaneous
% Expenditure	35	15	20	10	20
Price (Rs)  2006	150	50	100	20	60
Price (Rs) 2010	174	60	125	25	90

 

15. Write a short note on importance of Index numbers.

 

16. Explain the different positional averages and their uses.

 

SECTION- C

III)   Answer any THREE questions. Each carries 15  marks.                                         ( 3×15 =  45)

 

17. The following table shows annual profits ( Rs. In crore) of two investment companies  A and B during the given five years. Find the mean and  standard deviation of profits for both the companies A and B. Which company is better?  Which company ensures consistent profit?

Year Company	2009	2010	2011	2012	2013
A	70	60	70	60	70
B	60	50	60	80	80

                      

18. a) The following results are given. The co-efficient of correlation between X and Y is

r= +0.66. Find the two regression lines and estimate the value of X when Y=75.

	X	Y
Arithmetic Mean	36	85
Standard deviation	11	8

 

1. b) Identify the regression equations and find the means of variables X and Y and the correlation co-efficient   2Y – X – 50 =0,  3Y – 2X – 10=0

(8 +7)

19. a) From the following data fit a straight line trend through the method of least square. Calculate the trend values.

Year	2005	2006	2007	2008	2009	2010	2011	2012
Expenditure (Rs. In ‘000)	43	49	54	62	71	75	78	80

 

1. b) Calculate Arithmetic mean by step deviation method

Production In tonnes	0- 100	100- 200	200- 300	300- 400	400- 500	500- 600	600- 700	700- 800	800- 900	900- 1000
No of factories	7	15	10	9	10	12	8	13	9	7

(8+7)

20. For the following data calculate Laspeyre’s, Paasche’s and Fisher’s Index Numbers. Also prove that Fisher’s Index number satisfies Time Reversal Test and Factor Reversal Test.

Commodity	2005		2012
	Price (Rs)	Quantity (Kg)	Price (Rs)	Quantity (Kg)
I	6	50	10	56
II	2	100	2	120
III	4	60	6	60
IV	10	30	12	24
V	8	40	12	36

 

21. a ) Present the following data using sub divided bar diagram and percentage bar diagram.

Subject	No. of Students
	2010-11	2011-12	2012-13
Science	240	280	340
Humanities	560	610	570
Commercw	220	280	370

 

1. b) Prepare Histogram for the following data and find mode graphically. Also support the value using calculation method.

Wages (Rs)	325-350	350-375	375-400	400-425	425-450
Frequency	30	45	75	60	35

(8 + 7)

 

 

 

 

 

 

SECTION- D

1. IV) Compulsory Question                                                     (1x 15 =  15)

 

22. A tour operator during a survey asks three families to rank the ten different places visited in Rajasthan in the order of their preference. The data is presented in the table below. Use the method of Rank Correlation  to determine to what extent the families match in their choices?  Interpret the result.

 

Places	A	B	C	D	E	F	G	H	I	J
Family I	1	6	5	10	3	2	4	9	7	8
Family II	3	5	8	4	7	10	2	1	6	9
Family III	6	4	9	8	1	2	3	10	5	7

 

 

 

 

 

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