# Punjabi University 2007 B.Com Business Statistics - Question Paper

Tuesday, 05 February 2013 07:30Web

B.Com Business Statistics (Compulsory) ques. paper

Business Statistics (Compulsory)

Seat No:

**Time :**three Hours] [Ma

**x.**

**Marks :**70

Instructions : (1)

All ques. carry equal marks.

**(**The use of simple calculator is allowed.

**2)****(**Graph paper will be supplied on request.

**3)****1.**

**(**discuss Rank method to obtain coefficient of correlation. 04

**a)**(b)

From the subsequent data, obtain the coefficient of correlation ranging from Father’s

06

height

**(**and their Son’s height (y) by product moment method.

**x)**Father’s height

**(**65 66 67 67 68 69 70 72

**x)**Son’s height (y) 67 68 65 68 72 72 69 71

**(**obtain Yule’s coefficient of association from the subsequent dat

**c)****a.**04

N = 200,

**(**= 80, ( ? ) = 120 and (AB

**A)****2)**= 20

OR15

**1.**

**(**State the properties of coefficients of regression. 04

**a)****(**If the equations of 2 regression lines are y = 4x + 40 and x =

**b)****(**means of x and y

**i)****(**2 coefficients of regression and

**i****i)****(**coefficient of correlation.

**i****i****i)**y + 19 , obtain 06

**(**discuss the meaning of Q = + 1, –1 and 0. 04

**c)**2.

(a)

What is time series ? discuss the different components of it.

04

**(**From the subsequent data, find short term variations by using 3 yearly moving 06

**b)**avg. method.

Year 1984

80 ’ 85

88 ’ 86

98 ’ 87

92 ’ 88

84 ’ 89

88 ’ 90

80 ’ 91

100

Sales

Year ’92

84 ’93

96 ’94

92 ’95

104 ’96

116 ’97

112 ’98

102 ’99

114

Sales

**(**compute seasonal Indices from the subsequent data.

**c)**OR 04

**2.**

**(**What is Business forecasting ? discuss its importances. 04

**a)****(**The technology matrix for 2 industries A and B are as follows. 06

**b)**A B

A 0.2 0.15

B 0.4 0.2

(c)

If the final demands are 740 and 500 respectively, obtain the total production. Fit a straight line to the subsequent dat

**a.**Estimate the sales for the year 2005.

04

3.

(a)

What is Interpolation and Extrapolation ? discuss its importance.

04

**(**From the subsequent data, find the value of log 45 by using improper method of 06

**b)**interpolation.

log 40 = 1.6021, log 48 = 1.6812 and log 50 = 1.6990

**(**The population of city is 3,00,000 and of them 40% are females. 45% females of total 04

**c)**females are in child bearing ag

**e.**If the birth rate of that city is 32, estimate the number

of children that will born during the next year.

OR

**3.**

**(**discuss registration method to find vital statistics. 04

**a)****(**From the subsequent data, obtain crude and standarised death rates of 2 cities and 06

**b)**compare them.

Age

(in Year) City A City B

Population No. of deaths Population No. of deaths

0 - one 0

10 -2 0

20 -6 0

Above 60 6,000

10,000

30,000

4,000 180

50

240

200 4,000

15,000

24,000

7,000 160

60

240

210

**(**If u0 = 8, u1 = 12, u2 = 19, u3 = 29 and u4 = 42, obtain the value of u . 04

**c)****4.**

**(**find an formula of a straight line AB joining the points A (x1, y

**a)****1)**and B (x2, y2). 04

(b)

Attempt any 2 :

06

**(**Prove that the straight lines 4x + 3y + 12 = 0 and 6x – 8y + one = 0 are perpendiculars to every other.

**i)****(**find an formula of a straight line passing through the point of intersection of

**i****i)**x + y + one = 0 and 3x + y – five = 0 and having a slope 2.

**(**find an formula of a straight line passing through (–2,

**i****i****i)****3)**and making intercepts on 2 axes equal in magnitude but opposite in sign.

**(**The cost of manufacturing x units of an item is y. If the cost of manufacturing 400 units is Rs. 1100 and that of manufacturing 600 units is Rs. 1400, obtain fixed cost. Also obtain the profit, if 800 units are sold at Rs. 2.50 every.

**c)**OR 04

**4.**

**(**What is Linear Programming ? State its assumptions. 04

**a)**(b)

Maximize an objective function z = 20x + 30y under the subsequent constraints.

06

**(**3x + 3y ? 36

**i)****(**5x + 2y ? 50

**i****i)****(**2x + 6y ? 60

**i****i****i)****(**x ? 0, y ? 0

**i****v)**(c)

A Producer produces 2 items A and

**B.**It requires 20 minutes for the production

04

process for every unit of A and 15 minutes for the production process for every unit of B.

The maximum time available for the production process is 150 minutes. five kgs of raw

material is needed for the production of A and four kgs of raw material for the production

of

**B.**The total raw material is 850 kgs. If the profit for every unit of A is Rs. 25 and

profit for every unit of B is Rs.

**3**Represent the above issue in the mathematical

**5.**form of linear programming.

5.

(a)

Define,

Zero matrix, Diagonal matrix, Symmetric matrix and Skew Symmetric matr

**i**04

**x.**(b)

Solve the subsequent equations by inverse matrix.

06

**(**x + y + z = 8

**i)****(**2x + 3y – z = 15

**i****i)****(**3x – 5y + z = 6

**i****i****i)****(**If A =

**c)**? two 1

? three 2

???1 0

? 2? ? ?

1 ??

and B =

?1

?2

??3

?1 3?

1 ?

?1 4??

obtain 2A + B and A – 2

**B.**04

OR

5.

**(**In usual notations, write formulae of nth term and the sum of n terms of A.P. and G.P.

**a)**04

(b)

7 + 77 + 777 + ............. find upto n terms and also obtain the sum of 1st n terms

06

from it.

(c)

If the Arithmatic Mean and the Geometric mean of 2 numbers are 26.5 and 14 then

04

obtain these 2 numbers.

Earning: Approval pending. |