Loyola College Business Statistics Question Papers

Loyola College B.Sc. Statistics April 2012 Business Statistics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – APRIL 2012

ST 3104/3101 – BUSINESS STATISTICS

 

 

Date : 28-04-2012              Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

 

 

SECTION A

 

Answer ALL questions.                                                                                    (10 x 2 =20)

  1. Define median. Give an example.
  2. Write any two applications of statistics in business.
  3. Find the  mode: 3,5,6,5,6,7,2,8,9,6,7,8,10,6.
  4. Write down the formulae for Regression equations X on Y and Y on X.
  5. Define correlation.
  6. Mention any two uses of Index numbers.
  1. What is Time Series?
  1. Write down the formula for Karl Pearson’s coefficient of Skewness
  2. Define Transportation Problem.
  3. List out Methods of finding an Initial Basic Feasible Solution (IBFS).

 

SECTION B

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

  1. Draw a Histogram and Frequency Polygon for the following data:
Class interval 500-509 510-519 520-529 530-539 540-549 550-559 560-569
Frequency 8 18 23 37 47 26 16

 

  1. Write down the merits and demerits of statistics.
  2. Calculate Q.D and coefficient of Q.D for the given data:
X 10 20 30 40 50 80 90
F 4 7 15 18 7 2 5

 

 

 

  1. Find coefficient of rank correlation between the variables X and Y.
Weight of fathers 65 66 67 68 69 70 71
Weight of mothers 67 68 66 69 72 72 69

 

 

 

 

 

 

  1. Construct the Price index numbers to the following data by using the method of

(i) Laspeyre’s (ii).Paasche’s (iii). Marshall-Edgeworth (iv). Fisher’s Ideal index number

 

Commodities

           2010

  P0               Q0

           2011

  P1               Q1
A 10 6 15 5
B 12 10 15 10
C 18 5 27 3
D 8 5 12 4

 

 

 

 

 

 

 

 

  1. Calculate Karl Pearson’s Coefficient of Skewness:
Size 1 2 3 4 5 6 7
Frequency 10 18 30 25 12 3 2

 

 

 

  1. Solve the following Assignment Problem, given the cost involved for each machine.
Works Machines
M1 M2 M3 M4
W1 15 6 7 8
 W2 3 13 7 6
 W3 8 9 4 10
W4 3 5 7 11

 

  1. Fit a Straight line to the following data.
X 2 4 6 8 10
Y 4 3 5 3 6

 

 

 

SECTION C

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

  1. (i) Find the Mean and Standard Deviation from the following data:
Class interval 20-30 30-40 40-50 50-60 60-70 70-80 80-90
frequency 3 61 132 153 140 51 2

 

 

 

 

(ii) Two cricketer scored the following runs in seven matches. Find who is more consistent                 player.

M.Hussey 67 29 95 83 44 101 72
V.Kholi 35 71 108 40 64 94 88

 

 

 

 

  1. Obtain the Initial Basic Feasible Solution and the cost of the Transportation Problem by        Using (i) North-West Corner Rule, (ii) Least Cost method and (iii) Vogel’s Approximation Method.
 

 

 

 

Origin

 Destination
D1 D2 D3 Supply
O1 4 9 6 8
O2 5 5 3 11
O3 7 6 10 7
O4 3 8 4 17
Demand 10 12 21 43

 

 

 

 

 

 

 

 

 

  1. The following table gives the age of cars of a certain make and annual maintenance costs.
Age of cars in years 2 4 6 8 10 12
Maintenance cost in Rs.(’00) 10 20 30 50 62 74

 

 

 

(i)  Find the two Regression Equations.

(ii) Estimate the likely Age of cars in years when Maintenance cost in Rs 2500

(iii) Calculate the correlation between Age of cars in years and Maintenance cost.

 

  1. Find the seasonal variations by the Link Relative Method to the following data
YEAR
QUARTER 2007 2008 2009 2010 2011
I 30 35 31 31 34
II 26 28 29 31 36
III 22 22 28 25 26
IV 31 36 32 35 33

 

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Loyola College B.Sc. Commerce Nov 2008 Business Statistics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – COMMERCE

 

BA 04

 

THIRD SEMESTER – November 2008

ST 3104/ST 3101/ST 2101 – BUSINESS STATISTICS

 

 

 

Date : 11-11-08                     Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

SECTION A

 

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

  1. Define statistics.
  2. Differentiate between primary and secondary data.
  3. What is the mode of 110, 120, 130, 120, 110, 140, 130, 120, 140.
  4. If the mode and mean of a moderately asymmetrical distribution are 80 and 68, what is the median?
  5. If Q1 = 30 and Q3 = 50, what is the coefficient of quartile deviation?
  6. Define skewness.
  7. Define correlation.
  8. Find the mean value of X and Y, from the following regression equations:

4 X – 5 Y + 33 = 0, 20 X – 9 Y – 107 = 0.

  1. What are the uses of index numbers?
  2. Define time series data.

SECTION B

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

  1. Explain the scope and limitations of statistics.
  2. Draw a histogram and frequency polygon for the following data:
Length of leaves(cms.) 6-7 7-8 8-9 9-10 10-11 11-12 12-13
No. of leaves 5 12 25 48 32 6 1

 

 

  1. Calculate Karl Pearsons’ coefficient of skewness:
X 6 12 18 24 30 36 42
f 4 7 9 18 15 10 5

 

 

                                                                                  

E1 E2 E3
No. of employees 20 25 40
Avg. daily salaries 305 300 340
Standard deviation 50 40 45
  1. A company has 3 establishments E1, E2, E3 in 3 cities. Analysis of the daily   salaries (Rs.) paid

to the employees is given below:

 

 

 

 

Find the average and standard deviation of the monthly salaries of all the 85 employees.

  1. Analyze the following frequency distribution by the method of moments, find β 2 and interpret the result.
X 2 3 4 5 6
f 1 3 7 3 1

 

 

 

  1. From the following data, calculate coefficient of rank correlation.
X 33 56 50 65 44 38 44 50 15 26
Y 50 35 70 25 35 58 75 60 55 26

 

 

 

 

  1. Calculate fixed base and chain base index numbers for the following data.
Average wholesale prices (Rs.)
Commodities 2003 2004 2005 2006 2007
A 2 3 5 7 8
B 8 10 12 4 18
C 4 5 7 9 12

 

 

 

 

  1. Solve the following Linear Programming Problem: Max z = 22 x + 18 y subject to the constraints, 360 x + 240 y ≤ 5760, x + y ≤ 20, x, y ≥ 0.

 

SECTION C

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

  1. From the prices of shares of company X and Y given below, state which share prices are more stable in value, using coefficient of variation.
X 35 54 52 53 56 58 52 50 51 49
Y 108 107 105 105 106 107 104 103 104 101

 

 

  1. From the following data of sales and purchases (Rs. crores), obtain the two regression equations, and find the estimated sales when the purchase is Rs. 100 Crores.
Sales 91 97 108 121 67 124 51 73 111 57
Purchases 71 75 69 97 70 91 39 61 80 47

 

 

 

  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

 

  1. 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 3 7 6 4 5
B 2 4 3 2 2
C 4 3 8 5 3
Demand 3 3 2 2  

 

Find out the initial solution for transporting the products by using  (i) North-West Corner Rule, (ii) Least Cost method and (iii) Vogel’s Approximation Method. Compare the costs and write down the best initial solution.

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Loyola College B.Sc. Commerce Nov 2012 Business Statistics Question Paper PDF Download

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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – COMMERCE

THIRD SEMESTER – NOVEMBER 2012

ST 3104/3101 – BUSINESS STATISTICS

 

 

Date : 07/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 9:00 – 12:00

                        

SECTION – A

 

Answer All the Questions:                                                                                                        ( 10 x 2 =20)

 

  1. Define the term Statistics
  2. How are statistics being mis-used? Give anyone mis-interpretation of statistics.
  3. Define Weighted Arithmetic Mean.
  4. Why is median called a positional average?
  5. State the properties of Pearson’s correlation coefficient.
  6. What is meant by regression analysis?
  7. What is the scatter diagram?
  8. What are the uses of index numbers?
  9. Define trend and seasonal variation.
  10. State the components of time series.

 

SECTION – B

Answer any five questions:                                                                                                      ( 5 x 8 =40 )

 

  1. Explain the scope and limitation of statistics.

 

  1. Draw a histogram and frequency polygon for the following data:

 

Class 0-10 10-20 20-30 30-40 40-50 50-60 60-70
Frequency 4 6 7 14 16 14 8

 

  1. Find coefficient of correlation between the costs and sales for the following data:

 

Cost 39 65 62 90 82 75 25 98 36 78
Sales 47 53 58 86 62 68 60 91 51 84

 

  1. An analysis of the weekly wages paid to workers in two firms, A and B belonging

to the same industry give the following results.

  Firm A Firm B
No. of wage earners 586 648
Avg. Weekly wage Rs. 52.5 Rs. 47.5
Variance of the distribution of  wage 100 121

Find the average weekly wage and the standard deviation of the wage of all the workers in two firms, A and B taken together.

 

  1. Find the coefficient of skewness from the following data:

 

Value 6 12 18 24 30 36 42
Frequency 4 7 9 18 15 10 5

 

  1. Analyse the following frequency distribution by the method of moments, find β2 and interpret your results.
X 2 3 4 5 6
F 1 3 7 3 1

 

  1. Calculate Laspeyre’s, Paashe’s, and Fisher’s index numbers for the data given below
   Commodity Base  year Current year
Price Expenditure Price Expenditure
A 5 50 6 72
B 7 84 10 80
C 10 80 12 96
D 4 20 5 30
E 8 56 8 64

 

  1. Solve (using graphical method)

 

Max  Z  =  3X1  + 4 X2

 

Subject to the constraints  4X1 + 2X2  80

2X1 + 5X2  180

and X1, X2  0.

 

SECTION –C

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

 

  1. a)  From the following data, calculate mean  and  mode                   (7)

 

Maks 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60
No. of students 10 20 30 50 40 30

 

  1. b) From the marks given below obtained by two students taking the same course,

find out who is more consistent.                                                                  (13)

A 58 59 66 65 66 52 75 31 46 48
B 56 87 89 46 93 65 44 54 78 68

 

 

 

 

 

 

 

 

 

  1. The following table represents aptitude test scores and productivity indices of 10 workers selected at random.

 

Aptitude test scores 60 62 65 70 72 48 53 73 65 82
Productivity indices 68 60 62 80 85 40 52 62 60 81

 

Calculate two regression equations and estimate the productivity index of a worker

whose test score is 92.

  1. From the following data, calculate seasonal indices by Ratio to trend method.
Year                               QUARTERLY SALES (Rs. Lakhs)
I II III IV
A 8 16 24 32
B 48 36 24 12
C 48 16 32 64
D 72 108 144 36
E 56 28 84 112

 

  1. 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.

 

  Destination    
origin D E F G Availability
A 11 13 17 14 250
B 16 18 14 10 300
C 21 24 13 10 400
Requirement 200 225 275 250  

 

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Loyola College B.Com Nov 2004 Business Statistics Question Paper PDF Download

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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

  1. 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

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

 

SECTION-B

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

 

  1. 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

  1. 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

  1. 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

  1. 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 .
  2. 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.

  1. Explain the four components of a time series.
  2. 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)

  1. 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)

 

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

X                     Series A                       Series B

FA                                  FB

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)

 

 

 

  1. 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

 

  1. 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 B.Com Nov 2006 Business Statistics Question Paper PDF Download

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

AB 04

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.

 

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

Also, verify it using the formula.

 

 

Electricity consumption per month 0-100     100-500      500-1000    1000-1500        1500-2000

 

 
No. of  families 26                     148                  296                    185               70

 

 

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

industries are given below:

 

 

              Particulars IT-1 IT-2
No. of  Employees 800 550
Average Salary per month (in Rs.) 16,500 21,300
Standard Deviation (in Rs.) 1,900 2,600

 

 

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

 

 

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

data:

 

Processing time (in min.) 0- 5        5-10      10-15    15-20    20-25
No. of  Operators  8             24           58         31         14

 

 

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

 

                                Awarded Scores out of 20
Judge-1 8      14           16         19         20       10          5       7     3       14
Judge-2 6      10            18        20         20        14          4       6      4      13

 

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

 

Particulars Food Rent Fuel &Elect. Education Medical Misc.
Weights 4 4 1 2 2 3
Base year expenses (in Rs.) 2500 3000 600 900 800 1700
Current year (in Rs.) expenses 3000 3250 700 950 700 2200

 

  1. 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:

 

 

          RESOURCES REQUIRED FOR ONE UNIT
Product Leather(in kg.) Woods                 (in sq.metres) Glue(in litres)
A 0.5 4 0.2
B 0.25 7 0.3

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.

 

  1. 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.

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

     merits and demerits of both. (12)

 

  1. Consider the following data:
  Year (X) 2001     2002         2003       2004     2005
Profit in lakhs (Y)  12.3     16.8          21.5         26.4      30.2

 

  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:

 

 

           Quarterly Cement Production ( in lakh tons)
YEAR I II III IV
2003 48.3 62.1 36.1 41.2
2004 69.7 79.4 29.4 56.9
2005 84.1 96.3 59.1 62.8

 

(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:

 

 

                    Projects
Project leaders Health Education Housing
P1 20 26 42
P2 24 32 50
P3 32 34 44

 

Help the management by determining the optimal assignment that

maximize the total performance score.              (8)

 

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Loyola College B.Com April 2008 Business Statistics Question Paper PDF Download

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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

 

  1. (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, M2, M3, 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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Loyola College B.Com April 2009 Business Statistics Question Paper PDF Download

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     LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

YB 03

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)

 

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

 

Weekly wages( in Rs.) No. of workers
10 – 15 7
15 – 20 19
20 – 25 27
25 – 30 15
30 – 35 12
35 – 40 12
40 – 45 10
45 – 50 8

 

  1. 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.

 

 

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

 

A 101 27 0 36 82 45 7 13 65 14
B 97 12 40 96 13 8 85 8 56 15

Who is more consistent?

 

 

  1. Calculate the Karl Pearson’s coefficient correlation between the marks in English and Hindi obtained by 10 students.
Marks in English 10 25 13 25 22 11 12 25 21 20
Marks in Hindi 12 22 16 15 18 18. 17 23 24 17

 

 

  1. Construct a 4 – year centered moving average from the following data.
Year 1940 1950 1960 1970 1980 1990 2000
Imported cotton consumption

(in India ‘000 bales)

 129 131 106 91 95 84 93

 

 

 

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

 

Commodity 2000 2005
Price Rs. Quantity Price Quantity
A

B

C

 15

20

4

 15

5

10

 22

27

7

 12

4

5

 

  1. Explain the components of time series.

 

  1. 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)

 

  1. Find the median, lower quartile, 7th decile and 85th percentile of the frequency distribution given below.
Marks in statistics Below 10 10-20 20-30 30-40 40-50 50-60 60-70 Above70
No. of students 8 12 20 32 30 28 12 4

 

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

 

1st  Judge 1 6 5 10 3 2 4 9 7 8
2nd Judge 3 5 8 4 7 10 2 1 6 9
3rd Judge 6 4 9 8 1 2 3 10 5 7

 

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:

 

Sales 91 97 108 121 67 124 51 73 111 57
Purchases 71 75 69 97 70 91 39 61 80 47

 

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

Year 1st Quarter 2nd  Quarter 3rd  Quarter 4th  Quarter
1987 34 54 38 38
1988 36 60 52 48
1989 40 58 56 52
1990 52 76 64 58
1991 70 90 88 84

 

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.

 

Destination/

origin

 D E F G Availability

 
A 11 13 17 14 250
B 16 18 14 10 300
C 21 24 13 10 400
Requirement 200 225 275 250

 

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Loyola College B.Com April 2011 Business Statistics Question Paper PDF Download

by

LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.COM. DEGREE EXAMINATION – COMMERCE

SECOND SEMESTER – APRIL 2011

ST 2102/2101 – BUSINESS STATISTICS

 

 

Date : 09-04-2011              Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

SECTION – A

Answer all the questions:                                                                                                         ( 10 X 2 = 20)

 

  1. State any two measures of dispersion
  2. State the formula for computing Karl Pearson coefficient of correlation
  3. State the formula for computing Spearman’s Rank correlation
  4. Determine mean and median for the for the following observations 12,10,5,8,9
  5. State the components of a time series
  6. State the methods of estimating trend
  7. The fitted regression equation is Sales=0.3+3.2Advertisement_Expense. Determine Sales when Advertisement Expense is Rs.2,00,000
  8. Define Index number
  9. Current year price ( P1) = 187, base year price (P­0 ) = 167 determine the price index
  10. State the methods of determining the Initial Basic Feasible Solution(IBFS) for a transportation problem

                                                                      SECTION- B

Answer any five questions:                                                                                                      ( 5 X 8 = 40)

 

  1. Explain the Scope and Limitation of Statistics

 

  1. Construct a Histogram and Frequency polygon for the data given below
Income(in 000s) 0-5 5-10 10-15 15-20 20-25 25-30
Number of Employees 5 20 25 40 50 20

 

  1. Explain the different types of bar charts with examples

 

Judge I 1 5 4 8 9 6 10 7 3 2
Judge II 4 8 7 6 5 9 10 3 2 1
  1. Determine Spearman’s Rank Correlation

 

 

 

 

  1. State the differences between Correlation and Regression

 

  1. Explain the components of Time series

 

 

  1. Determine Price index number by the method of Laspere, Paasche, Bowley, and Fisher for the data given below
Commodity 2009 2010
Price (p0) Quantity(q0) Price (p1) Quantity(q1)
A 15 12 16 15
B 12 8 10 10
C 8 5 7 10
D 10 15 15 20
E 14 4 13 5

 

  1. The estimated time taken for each person in completing different jobs is given below. Determine the optimum solution of the assignment problem by Hungarian method
  Job
Person I II III IV
A 14 5 8 7
B 2 12 6 5
C 7 8 3 9
D 2 4 6 10

 

 

 

 

 

 

 

 

 

SECTION- C

Answer any two questions:                                                                                                     ( 2 X 20 = 40)

 

  1. (i) Determine Mean deviation and Standard deviation for the data given below                 (10)
Mark(X) 0-10 10-20 20-30 30-40 40-50 50-60
Frequency(f) 10 20 30 50 40 30

 

(ii) Determine Mean , Median and Mode for the data given below                              (10)

Mark(X) 0-10 10-20 20-30 30-40 40-50 50-60
Frequency(f) 10 20 30 50 40 30

 

  1. Data on Advertisement Expense and Sales are given below
Advertisement Expense(in lakhs) (X) 1 2 3 4 5
Sales(in lakhs) (Y) 10 20 30 50 40
  1. i) Construct a Regression model of Y on X (7)
  2. ii) Construct a Regression model of X on Y (7)

iii) Estimate Sales when Advertisement expense equal to 5.2                                      (3)

  1. iv) Etimate the advertisement expense required to get a sales of 70 lakhs (3)

 

  1. Fit a straight line and a second degree parabola for the given data and estimate sales for the

year 2011

Year 2006 2007 2008 2009 2010
Sales(000s) 23 45 56 62 68

 

 

 

 

22.(i) Determine the optimum solution for the given LPP problem by Graphical method           (10)

Maximize:   Z = 45x1 + 55x2

Subject to:    6x1+3x2   120

4x1+10x2  180

 

 

(ii)  Determine Initial Basic Feasible Solution(IBFS) for the following transportation problem

by the method of  a) North west corner rule  b)Vogel’s  approximation method  (10)

  Demand  
Supply D1 D2 D3 D4 AVAILABILITY
A1 1 2 1 4 30
A2 3 3 2 1 50
A3 4 2 5 9 20
DEMAND 20 40 30 10 100

 

 

 

 

 

 

 

 

 

 

 

 

 

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