Punjabi University 2007 B.Com Business Statistics - Question Paper

B.Com Business Statistics (Compulsory) ques. paper

Business Statistics (Compulsory)

Seat No:


Time : three Hours] [Max. Marks : 70

Instructions : (1)
All ques. carry equal marks.
(2) The use of simple calculator is allowed.
(3) Graph paper will be supplied on request.

1. (a) discuss Rank method to obtain coefficient of correlation. 04

(b)
From the subsequent data, obtain the coefficient of correlation ranging from Father’s
06
height (x) and their Son’s height (y) by product moment method.

Father’s height (x) 65 66 67 67 68 69 70 72
Son’s height (y) 67 68 65 68 72 72 69 71

(c) obtain Yule’s coefficient of association from the subsequent data. 04
N = 200, (A) = 80, ( ? ) = 120 and (AB2) = 20
OR15

1. (a) State the properties of coefficients of regression. 04


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

(i) means of x and y
(ii) 2 coefficients of regression and
(iii) coefficient of correlation.

y + 19 , obtain 06

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

2.
(a)
What is time series ? discuss the different components of it.
04
(b) From the subsequent data, find short term variations by using 3 yearly moving 06
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


(c) compute seasonal Indices from the subsequent data.

OR 04
2. (a) What is Business forecasting ? discuss its importances. 04
(b) The technology matrix for 2 industries A and B are as follows. 06

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 data. Estimate the sales for the year 2005.

04

3.

(a)

What is Interpolation and Extrapolation ? discuss its importance.

04
(b) From the subsequent data, find the value of log 45 by using improper method of 06
interpolation.
log 40 = 1.6021, log 48 = 1.6812 and log 50 = 1.6990
(c) The population of city is 3,00,000 and of them 40% are females. 45% females of total 04
females are in child bearing age. If the birth rate of that city is 32, estimate the number
of children that will born during the next year.
OR

3. (a) discuss registration method to find vital statistics. 04
(b) From the subsequent data, obtain crude and standarised death rates of 2 cities and 06
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

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



4. (a) find an formula of a straight line AB joining the points A (x1, y1) and B (x2, y2). 04

(b)
Attempt any 2 :
06
(i) Prove that the straight lines 4x + 3y + 12 = 0 and 6x – 8y + one = 0 are perpendiculars to every other.

(ii) find an formula of a straight line passing through the point of intersection of
x + y + one = 0 and 3x + y – five = 0 and having a slope 2.

(iii) find an formula of a straight line passing through (–2, 3) and making intercepts on 2 axes equal in magnitude but opposite in sign.


(c) 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.

OR 04
4. (a) What is Linear Programming ? State its assumptions. 04

(b)
Maximize an objective function z = 20x + 30y under the subsequent constraints.
06
(i) 3x + 3y ? 36
(ii) 5x + 2y ? 50
(iii) 2x + 6y ? 60
(iv) x ? 0, y ? 0

(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. 35. Represent the above issue in the mathematical
form of linear programming.

5.
(a)
Define,
Zero matrix, Diagonal matrix, Symmetric matrix and Skew Symmetric matrix. 04

(b)
Solve the subsequent equations by inverse matrix.
06
(i) x + y + z = 8
(ii) 2x + 3y – z = 15 (iii) 3x – 5y + z = 6


(c) If A =

? two 1
? three 2
???1 0

? 2? ? ?
1 ??



and B =

?1
?2
??3

?1 3?
1 ?
?1 4??



obtain 2A + B and A – 2B. 04

OR

5.
(a) In usual notations, write formulae of nth term and the sum of n terms of A.P. and G.P.
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.