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st. joseph’s college of commerce (autonomous)

END SEMESTER EXAMINATION – MARCH/APRIL 2016

B.com – iV semester

C1 11 402: BUSINESS STATISTICS & RESEARCH TECHNIQUES

Duration: 3 Hours Max. Marks: 100

SECTION – A

Answer ALL the questions. Each carries 2 marks. (10×2=20)

Mention any four limitations of statistics.

Define Correlation.

What are the components of Time Series Analysis?

Two coins are tossed. Find the probability of getting either heads or both tails.

What is a null hypothesis?

What is meant by an Index Number? State any two problems in construction of an Index Number?

State any 2 differences between Classification and Tabulation?

What is meant by Range? State any two uses of Range?

Define secondary data. What are its chief sources?

10.

Arithmetic mean= 26.8, Median= 27.9. What is the value of Mode?

SECTION – B

II)

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

11.

What is a pie diagram? Construct a pie chart for the following data:

Principal Exporting countries of cotton

U.S.A	INDIA	EGYPT	BRAZIL	ARGENTINA
6,367	2,999	1,688	650	202

12.

What do you mean by a questionnaire? State the essential points in drafting a good questionnaire.

13.

In a singing competition 7 candidates were ranked by judges A and B as follows:

Candidate:	I	II	III	IV	V	VI	VII
Rank by A:	3	4	5	6	1	2	7
Rank by B:	2	1	7	5	3	4	6

Compute the coefficient of rank correlation.

14.

From the following data calculate Fishers index number.

	Price		Quantity
Commodity	2010	2015	2010	2015
Rice	9.3	4.5	100	90
Wheat	6.4	3.7	11	10
Jowar	5.1	2.7	5	3

15.

Prepare a blank table showing the average wages of males and females, classified into two age-groups of eighteen and over, and under eighteen years in five industries at two different dates.

16.

Calculate 3 yearly moving average for the following data:

Year	2008	2009	2010	2011	2012	2013	2014	2015
Price (Rs.)	100	107	109	111	110	112	114	113

SECTION – C

III)

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

17.

Following data are available in respect of sales and advertisement expenditure:

Statistical Details

Sales

(in Rs.)

Advertisement Expenditure

(in Rs.)

Mean

Standard Deviation

70,000

15,000

3,000

Co-efficient of correlation

+0.8

Find out:

(a) Two regression equations;

(b) If the company desires to achieve the target sales of Rs.1,00,000 then how much should be the advertisement budget?

(c) If the company has budget for advertisement expenditure limited to Rs.10,000, then what would be the expected sales in Rs.?

18.

The Aravind Store has its head office at Ahmedabad, Gujarat. It has a textile showroom in Karnataka. The following table shows daily sales of the branch during January and February 2016 (Totally 50 days excluding holidays):

Branch	Daily Sales (Rs. in thousands)
Jayanagar Branch, Bangalore	42	53	65	63	61	47	56	60	64	45
	55	57	82	42	39	51	65	55	33	70
	50	52	53	45	45	25	36	59	63	39
	65	30	45	35	49	15	54	48	64	26
	75	20	42	40	41	55	52	46	35	18

As a Marketing Manager of Aravind Store,

(a) Calculate the frequency distribution table for sales figure using continuous series (0-10, 10-20, and so on)

(b) Provide the data on Mean, Standard deviation and Coefficient of variation of sales to the Head Office of Aravind Store, Ahmedabad, Gujarat.

(5+10)

19.

a. Calculate the expected frequencies for the following data presuming the two attributes, i.e, conditions of home and condition of child as independent.

Condition of Home
Clean Dirty
Condition of Child	Clean	70	50
	Fairly clean	80	20
	Dirty	35	45
	Total	185	115

Use chi-square test at 5% level of significance to state whether the two attributes are independent.

b) A sample of 400 male students of a college is found to have a mean height of 171.38 cm. Can it be regarded as a sample from a large population with mean height 171.17 cm and standard deviation 3.30 cm? Test at 5% level of significance.

(10+5)

20.

a) The monthly profits in Rupees of 100 textile shops in Bangalore City are distributed as follows:

Profits

(Rs. in ‘000s)

No. of Shops

Profits

(Rs. in ‘000s)

No. of Shops

0-100

100-200

200-300

300-400

400-500

500-600

Find the value of mode by drawing histogram of the given data. Check this value by the calculation, using formula.

b) A box contains 25 balls numbered 1 to 25. Two balls are drawn from the box with replacement. Find the probability of selecting:

Both odd numbers
One odd and one even number
Atleast one odd number

(10+5)

21.

Given below are the figures of sales (‘000 rupees) of a certain shop:

Year	2009	2010	2011	2012	2013	2014	2015
Sales	125	128	133	135	140	141	143

a) Fit a straight line by the method of least squares and show the trend values

b) Estimate the trend value for the year 2016.

SECTION – D

IV)

Case Study (1×15=15)

22.

a. Discuss the scope of statistics in detail.

b. Calculate the mean of the following distribution using short cut method

Class-interval	50-60	60-70	70-80	80-90	90-100	100-110	110-120
Frequency	8	12	13	15	10	11	6

(7+8)

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