Business Statistics & Research Techniques

St. Joseph’s college of Commerce (Autonomous)

END SEMESTER EXAMINATION – march / APRIL 2014

 B.Com – IV SemESTER

            BUSINESS STATISTICS & RESEARCH TECHNIQUES.

Duration: 3 Hours                                                                                              Max Marks: 100

                                                                 Section – A

1. Answer any ten   Each carries 2 marks.                                    (10 X 2=20)

• Find the arithmetic mean and median for the following scores

15, 30, 40, 60, 32

• Describe the essence of standard deviation while calculating averages.
• Define Statistics.
• Mention any 4 applications of statistics.
• Describe Spearman’s rank correlation with a suitable example.
• If Mode=50 and Median=45 Calculate the mean.
• Describe the demerits of quartile deviation.
• Define Probable Error.
• If the mean score of Rahul in a cricket tournament if 15 and variance is 100 and for Robin the mean score is 40 and the variance 160. Discuss who is a more consistent batsman.
• How is the value of r in Karl Pearson’s coefficient of correlation interpreted?

 

Section – B

1. Answer any four   Each carries 5 marks.                                     (4X5=20)

 

• Describe the characteristics of statistics?
• Explain the limitations and scope of Statistics?
• The following are heights in centimetres of 40 students. Form the frequency distribution with appropriate class interval. 163.3, 155.0, 163.9, 163.9, 148.2, 151.5, 178.9, 155, 146.1, 145.2, 156.6, 159.9, 158.0, 153.4, 160.0, 149.3, 154.2, 164.7, 0, 160.8, 157.1, 176, 164.4, 170.0, 152.9, 169.3, 159.5, 162.4, 173.6, 154.8, 158.3, 172.5, 158.0, 154.0, 172.2, 148.0, 152.4, 156.6, 157.7, 165.3

 

• Locate the Median and Quartiles from the following data.

Size of shoes	Frequencies
4	20
4.5	36
5	44
5.5	50
6	80
6.5	30
7	30
7.5	16
8	14

 

• Calculate from the following data the Fisher’s index number. Verify whether it satisfies the Factor reversal test and the time Reversal Test.

Items	1975(p0)	1983(p1)	1975(q0)	1983(q1)
A	16	40	100	120
B	4	12	30	20
C	2	4	40	50
D	4	10	20	16
E	2	10	80	60

 

• Draw a histogram from the following and locate the mode. Verify it by actual calculations.

Class Interval	Frequencies
0-10	14
10-20	23
20-30	35
30-40	20
40-50	8
50-60	5

                                     

Section – C

• Answer any three   Each carries 15 marks.                               (3X15=45)

 

•   Explain the functions of Statistics?

1. Describe the distrust of Statistics?

(8+7)

18)    a. Following are the runs scored by 2 batsmen in 10 innings. Find who is a better scorer and who is more consistent.

Player1-101, 22, 0, 36, 82, 45,7,13, 65, 14

Player2- 97, 12, 40, 96, 13,8, 85 ,8, 56,16.

1. Draw Ogives from the following data and measure the median value. Verify it by actual calculations.

Mid point:   5    15    25     35    45.

Frequency:   5    11    21    16   10.

(8+7)

19) The life of 2 types of tyres in a sample survey is given below.

Life (kms)	Number of Tyres of Type A	Number of Tyres of Type B
5000-10000	10	18
10000-15000	18	22
15000-20000	32	40
20000-25000	40	32
25000-30000	22	18
30000-35000	18	10

 

1. Which of the 2 makes has a higher average life?
2. If prices are same for both the types, which type would you prefer and why?

 

20) The competitors of a beauty contest were ranked by 3 judges as follows:

Judge A: 3       5       4   10     8    8     1   6     8        2

Judge B: 5.5    5.5   1    8.5    4    10   2    7    8.5     3

Judge c:  9       9       7     5    2    2      2    5    5        9

Which pair of judges has the nearest approach to common taste in beauty?

 

21)  a. The following data relates to the ages of husbands and wives.

Age of the

Husband :    25   28   30   32     35   36   38     39     42   55

Age of wife: 20   26   29   30     25   18    26    35     35   46.

Obtain the two regression equations and determine the most likely age of husband for the age of wife of 25 years.

1. Hinton press hypothesizes that the average life of its largest web press is 14,500 hours. They know that the standard deviation of press life is 2,100 hours. From a sample of 25 presses, the company finds a sample mean of 13,000 hours. At a 1% level of significance, should the company  conclude that the average life of the presses is less than the hypothesized 14,500 hours?

(9+6)

22) a.  Compute the mean runs scored by a batsman from the following data using all the 3 methods.

Runs Scored: 10    20   30   40   50   60    70   80    90

Number of  :   7     8    15   25  30     20    16    7      2.

Batsmen

 

1. b) Represent the following data in a suitable diagram.

Newspaper	Daily Sales
Times of India	1432000
Deccan Herald	1431000
Indian Express	1327000
Asian Age	1119000
Hindustan times	894000

(9+6)

 

Section – D

 

1. IV) Compulsory question.                                            (1X15=15)

          23.

1. a) Compute the Karl Pearson’s coefficient of correlation between per capita national income and per capita consumer expenditure from the data given below.

Year	Per capita National Income	Per capita consumer expenditure
1978	249	237
1979	251	238
1980	248	236
1981	252	240
1982	258	245
1983	269	255
1984	271	254
1985	272	252
1986	280	258
1987	275	251

(8 marks)

1. A bag contains 5 black and 7 white balls. A ball is drawn out of it and replaced in the bag. Then a ball is draw again. What is the probability that
2. Both the balls drawn are black (2 marks)
3. Both are white                                                                               (2 marks)

• The first ball was white and the second black                          (2 marks)

1. The first ball was black and the second white                           (1 mark)

 

 

 

 

st. joseph’s college of commerce (autonomous)
END SEMESTER EXAMINATION – MARCH /APRIL 2015
B.Com – IV SEMESTER
C1 12 402: BUSINESS STATISTICS & RESEARCH TECHNIQUES
Duration: 3 Hours                                                                                             Max. Marks: 100
SECTION – A
I)	Answer ALL the questions.  Each carries 2 marks.                                        (10×2=20)
	1.	Is there any difference between Statistics and Mathematics? Justify your answer.
	2.	Raju finds the mean score of 10 batsmen to be 50 and median to be 25. Help him assess the distribution of the scores?
	3.	Differentiate between Type one and Type two error with a suitable example.
	4.	Consider a series-0, 12, 13, 15, 67, 90.  Find the range and coefficient of range for the series?
	5.	It is 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against a person now 50 living till he is 80. Find the probability that at least one of these persons would be alive 30 years hence?
	6.	Coefficient of correlation between two variables X and Y is 0.8. The covariance is 20. The variance is 16? Find the standard deviation of Y series?
	7.	Differentiate among various Graphs strictly based on dimensions.
	8.	Explain the reason for taking a factor of 0.6745 while evaluating probable error.
	9.	The regression coefficient of x on y is 0.5 and y on x is 3.5.  Evaluate the correlation coefficient and comment on the regression coefficients.
	10.	Mention any four problems that need a careful thought before constructing Index numbers.
SECTION – B
II)	Answer any FOUR questions.  Each carries 5 marks.                                      (4×5=20)
	11.	From the following marks of 100 students compute the mean deviation from median and its coefficient. Marks:      20-25    25-30    30-35    35-40    40-45    45-50    50-55   55-60    60-65 Students:     6           12        17          28         12          10          8           5          2
	12.	Construct Fisher’s index number for the following data and prove that it satisfies reversibility tests; Commodity Price (Base Year) Value (Base Year) Quantity (Current Year) Value (Current Year) A 2 10 4 20 B 3 12 5 30 C 1 8 2 16 D 4 20 8 24
	13.	From the following data compute the Regression Coefficients: X : 8    9    10   10   11   13   14   16 Y : 4    6    8     12   13   15   17   28
	14.	State the differences between Correlation and Regression.
	15.	Find the Mean and Median from the following: X F Less than 5 7 Less than 10 20 5-15 38 15 and above 55 20-25 20 25 and above 5 30 and above 1
	16.	Draw Ogives from the following data and measure the median value. Verify it  by actual calculations. Central size : 5       15      25       35       45 Frequency   : 5        11     21        16      10
SECTION – C
III)	Answer any THREE questions.  Each carries 15 marks.                                (3×15=45)
	17.	Amith, Balu and Chandrashekar ranked students. Comment on their compatibility in ranking students : Amith :                   3      5      4  10     8   8     1  6    8     2 Balu    :                   5.5   5.5   1   8.5   4   10   2   7   8.5   3 Chandrashekar:    9       9     7   5      2   2     2   5   5      9
	18.	What do you mean by a questionnaire?  State the essential points in drafting a good questionnaire.  Make a questionnaire for conducting a study on importance of different facilities available in college.  Make a questionnaire for conducting a study on importance of different facilities available in college.
	19.	Calculate the trend values for the production figures by least squares method in Alka textile Pvt. Ltd Year Production in tons 1977 12.7 1978 10.1 1979 13 1980 13.2 1981 12.6 1982 14.2 1983 13.7
	20.	a) A company is engaged in making brake systems for cars. A car running at a speed of 50 kmph comes to a halt after covering a distance of 24 feet on the average when the brake already in use is applied. Recently the company has developed a new brake system which when applied 80 times to cars running at 50 kmph, gave a mean distance of 23.2 feet, with a standard deviation of 2.8 feet, for the cars to come to a halt. Test at 1 percent Level of significance whether the new brake system is superior to the existing one?   b)  Mean height of 50 students is 5’-8”.  The height of 10 students are given below: 5’-6”, 5’-2”, 5’-4”, 5’-0”, 4’-10”, 4’-8”, 6’-2”,5’-8”, 5’-9”,5’-3”.Find the mean height of remaining students?                                                             (10+5) )
	21.	a) By using the simultaneous equations method find out the most probable value of y when x=15?   X 1 2 3 4 5 Y 2 5 3 8 7     b)  The salary for IT managers in state A and state B are shown below: State A: 3.2   4.8   5.3   2.2   2.7   6.2   3.4   3.7   4.1   4.2   5.7   2.5 State B: 1.5   2.6   2.8   4.6   3.6   6.2   6.8   1.3   2.1   1.5 Test at 2% Level of significance whether the difference between mean incomes of two states is equal.                                                                                  (7+8)
SECTION – D
IV)	Case Study                                                                                                              (1×15=15)
	22.	An agent obtained samples of bulbs from the 2 companies. He had them tested for durability and got the following results:   Durability in ‘00’ hr. Company A Company B 17-19 100 30 19-21 160 420 21-23 260 120 23-25 80 30   Which company bulbs are uniform?

 

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