LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034

B.com. DEGREE EXAMINATION – COMMERCE

THIRD SEMESTER – NOVEMBER 2003

ST – 3101/STA101 – BUSINESS STATISTICS

06.11.2003                                                                                                           Max:100 marks

9.00 – 12.00

SECTION-A

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

1. Define statistic and state any two misuses.
2. Mention any four one-dimensional diagrams.
3. State a merit and a demerit of median.
4. Provide any two properties of Arithmetic mean.
5. For a moderately asymmetric distribution, find median when mean and mode are respectively 48 and 60.
6. Depict ‘skewness’ and ‘kurtosis’ with the help of diagrams.
7. If the regression coefficient of Y on X an X on Y are respectively 0.58 and0.65, Calculate the coefficient of correlation.
8. From the following index number of prices, shift the base from 1987 to 1993 and recast the index numbers.

Year:   1987    1988    1989    1990    1991    1992    1993    1994

Index:  100      110      120      200      400      410      400      380

9. Construct 5-yearly moving average:

Year:   1988    1989    1990    1991    1992    1993    1994    1995

No. of:   332    317      357      392      402      405      410      417

students

10. Express an mxn transportation problem as a Linear programming Problem (L.P.P).

SECTION-B

Answer any FIVE  questions.                                                                          (5×8=40 marks)

11. For the following data on heights of 150 students, construct Histogram and locate the mode from it:

Height (In cm): 120-130  130-140    140-150     150-160      160-170    170-180

No. of students:     18            30            40               33               17              12

12. Find Geometric mean and Harmonic mean of the following frequency distribution:

C.I:      0-4       4-8       8-12     12-16   16-20

F:           6        10         16         10         8

13. Compute rank correlation coefficient between Debenture price and share price of a company given the following data:

Debentures

Price:         79       81        83        85        87        87        89        92

Share

Price:           67      65        66        64        64        64        63        62

14. The first four moments of a distribution about the value 3 are 2, 20, 40, 50. Find the first four central moments, b₁ and b₂ .
15. Fit the equation Y = a + bX to the following data:

Year(x) :    1990    1991    1992    1993    1994    1995    1996

Sales(y):      32        47         65       88      132     190       275

Estimate sales for 1997.

16. Explain the four components of a time series.
17. a) Find Fisher’s Price index number given the following data:

Item           Price (1985)     Price (1986)     Quantity (1985)          Quantity (1986)

A                       1                      5                          40                                30

B                       1                     2                          20                                25

C                       8                    20                          50                                60

D                       2                      5                          10                                  8

E                        2                     6                          15                                10

(b) Verify that Time Reversal Test is satisfied by Fisher’s index.                          (4+4)

18. Solve Graphically:

Minimize         Z = 20x₁+ 40x₂

subject to the constraints:       36x₁ + 6x₂ ³ 108

3x₁ + 12x₂ ³ 36

20x₁ + 10x₂ ³ 100

x₁, x₂ ³ 0

SECTION-C

Answer any TWO questions.                                                                           (2×20=40 marks)

19. a) From the data given below, find which series is more consistent:

X                     Series A                       Series B

F_A                                  F_B

10-20                   20                                  13

20-30                  18                                   22

30-40                  32                                   40

40-50                  40                                   32

50-60                  22                                   18

60-70                  18                                   10

1. Calculate Bowley’s coefficient of skewness for the following frequency distribution:

X:     0-10   10-20   20-30   30-40   40-50   50-60   60-70   70-80

f:     10         25        20         15        10        35        25         10                       (12+8)

20. a) The following data relates to the intelligence test scores and the weekly sales of 9

salesmen.

Intelligence

Test Score (X):      70     40      80        50      80          60        50   60    50

Weekly sales

(Y):             60    50      70          30      60       50        40     60    30

Obtain the regression line of Y on X and estimate Y when X = 65.                          (12+8)

1. b) Explain the problems involved in the construction of index numbers.
2. Find the seasonal indices by Ratio to Trend method:

Year                I           II         III        IV

1993                30        40        36        34

1994                34        52        50        44

1995                40        58        54        48

1996                54        76        68        62

1997                80        92        86        82

22. a) Solve the following Transportation problem:

Destination

Source             1          2          3          4          Availability

1                      21        16        25        13             11

2                      17        18        14        23             13

3                      32        27        18        41             19

Requirement:   6          10        12        15             43

1. b) These are 4 jobs A, B, C,D and these are to be performed on 4 machine centres I, II,

III,IV.  One job is to be allocated to a machine centre, though each machine is capable of

doing any job, at different costs given by the matrix below:

I      II     III   IV

Find the allocation of jobs to the machine centres so that the total cost of processing

is minimum.                                                                                                      (10+10)

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             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034  B.Com DEGREE EXAMINATION – COMMERCE

THIRD SEMESTER – NOV 2006

ST 3101 – BUSINESS STATISTICS

(Also equivalent to STA 101)

Date & Time : 08-11-2006/1.00-4.00           Dept. No.                                                       Max. : 100 Marks

SECTION-A     (10 x 2 = 20)

Answer All the questions. Each question carries 2 marks.

1. What are the different levels of measurements?
2. Create your own example and draw histogram.
3. Distinguish between symmetric and asymmetric distributions.
4. When do you prefer median as compared to arithmetic mean?
5. What do you understand by Kurtosis?
6. Explain briefly any two properties of Regression coefficients.
7. Write the normal equations for fitting Quadratic model.
8. Give the meaning of “Splicing the index numbers”.
9. Distinguish between slack and surplus variables.
10. Define a Transportation problem.

SECTION-B    (5 x 8 = 40)

Answer any 5 questions.  Each question carries 8 marks.

11. Draw ogive curve for the following data and locate D₃₉ and P₆₃.

Also, verify it using the formula.

12. The wage distribution of employees working in two different IT

industries are given below:

1. Calculate the combined mean and combined standard deviation.
2. b) Which industry is consistent in wage distribution? (4+4)

13. Calculate the Bowley’s coefficient of skewness for the following

data:

14. Calculate the rank correlation coefficient for the following data:

15. a) What is the purpose of constructing index numbers?
16. b) Distinguish between weighted and unweighted index numbers.
17. Calculate the cost of living index using the Family Budget method for the following data:

17. Product A offers a profit of Rs.25/- per unit and Product B yields a profit of Rs. 40/- per unit. To manufacture the products—leather, wood and glue are required in the amount shown below:

Available resources include 2,200 kg. of leather; 28,000 square metres of wood and 1,400 litres of glue.  Formulate the problem as an LPP.

18. What do you mean by unbounded solution in LPP? Does

unboundedness implies no solution to the Problem?  Explain in

detail.

SECTION-C  (2 x 20 = 40)

Answer any 2 questions.  Each question carries 20 marks.

19. a) What are the scope and limitations of Statistics? (4+4)
20. b) Distinguish between sample surveys and Census. Explain the

     merits and demerits of both. (12)

20. Consider the following data:

1. Fit a regression line of Y on X
2. Estimate profit for 2006
3. Obtain the standard error of the estimate
4. Draw the original and trend lines on the graph. (10+2+4+4)

1.   a) Explain in detail the major components of Time series. (8)

1. b) Calculate the seasonal indices for the following data using the

ratio to moving average method:

(12)

• a) Solve the following LPP by Simplex method:

Max. Z = 3 X + 2 Y

S.to

X + Y ≤  4

X – Y ≤ 2

X,  Y  ≥ 0           (12)

1. MCS Inc. is a Software company that has three projects with the departments of health, education and housing. Based on the background and experiences of the project leaders, they differ in terms of their performance at various projects.  The performance score matrix is given below:

Help the management by determining the optimal assignment that

maximize the total performance score.              (8)

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Com. DEGREE EXAMINATION – COMMERCE

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:

1. Calculate mean deviation from median and its coefficient from the following data:

1. Draw less than and more than ogives for the data given below:

1. Calculate 5-yearly and 7-yearly moving average for the following data of a number of commercial industrial failures during 1992-2007.

1. Calculate fixed base indices and chain base indices with 2000 as the base for the following data:

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:

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?

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.

1. Calculate seasonal variations given the average quarterly price of a commodity for 5 years by ratio to trend method.

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.

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.

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     LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.COM. DEGREE EXAMINATION – COMMERCE

SECOND SEMESTER – April 2009

ST 2102 / 2101 / 3104 / 3101 – BUSINESS STATISTICS

Date & Time: 25/04/2009 / 1:00 – 4:00  Dept. No.                                                  Max. : 100 Marks

SECTION – A                    

Answer ALL the questions.                                                                              (10 x 2 = 20)

1. Clarify the difference between exclusive and inclusive class interval.
2. What are the advantages of diagrammatic representation of the data?
3. For what type of values harmonic mean is suitable?
4. How will you calculate median in case of ungrouped data?
5. What is a scatter diagram?
6. Define correlation.
7. Define regression.
8. What are the important properties of regression coefficient?
9. Define index number.
10. Define time series and write its components.

SECTION – B

Answer any FIVE questions.                                                                                               ( 5 x 8 = 40)

11. Draw the histogram, frequency curve and frequency polygon for the following data.

12. The average score of girls in class X examination in a school is 67 and that of boys is 63. The average score for the whole class is 64.5, find the percentage of girls and boys in the class.

13. The following are the run scored by two batsman A and B in ten innings.

Who is more consistent?

14. Calculate the Karl Pearson’s coefficient correlation between the marks in English and Hindi obtained by 10 students.

15. Construct a 4 – year centered moving average from the following data.

16. Compute Laspeyre’s, Paasche’s, Fisher’s and Kelly’s Price index numbers for 2005 for the following data.

17. Explain the components of time series.

18. Find the minimum value of

z = –  x₁ + x₂

subject to the constraints

–  x₁ + 3 x₂  ≤ 10

x₁ +  x₂    ≤ 6

x₁ –  x₂   ≤ 10

x₁ , x₂  ≥ 0.

SECTION –C

Answer any TWO questions.                                                                            ( 2 x 20 =40)

19. Find the median, lower quartile, 7^th decile and 85^th percentile of the frequency distribution given below.

20 a). Ten competitors in a beauty contest are ranked by three judges in the following  orders:

Use the correlation coefficient to determine which pair of judges has the nearest approach to common

taste in beauty.

b). From the following data, obtain two regression equations:

21). Find the seasonal variations by Ratio Trend method from the data given below.

22). Obtain an initial basic feasible solution to the following transportation problem by

(i). North-west corner rule          (ii) Least cost  method

(iii). Vogel’s approximation methods.

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