In this post, I am going to discuss Business Statistics Solved Paper FBISE 2012 ICOM II, MCQS, Short Questions, Extensive Questions of the topics of Introduction to Statistics, Averages, Index Numbers and Probability is discussed and solved. Business Statistics Solved Paper 2013 is also posted.
Solved by Iftikhar Ali, M.Sc Economics, MCOM Finance Lecturer Statistics, Finance and Accounting
Table of Contents
Business Statistics Solved Paper FBISE 2012 ICOM II, MCQS, Short Questions, Extensive Questions
MCQS
Q.1 Circle the Correct Option i.e. A/B/C/D. Each Part Carries 1 Mark.  
(i)  The Word Statistics may have been derived from the German Word:  
A. Status  B. Statistik  C. Statistique  D. Statista  
(ii)  The data, which have not undergone any statistical treatment are:  
A. Primary Data  B. Secondary Data  C. Discrete Data  D. Continuous Data  
(iii)  If the data are classified according to their time of occurrence then this procedure is called:  
A. Multiway Classification  B. Chronological Classification  C. Geographical Classification  D. Spatial Classification  
(iv)  The total of relative frequencies is always equal to:  
A. – 1  B. 0.5  C. 1  D. 100  
(v)  In a symmetrical distribution mean, median and mode are always:  
A. Negative  B. Zero  C. Different  D. Equal  
(vi)  Median is a/an:  
A. Calculating average  B. Positional Average  C. Exact Average  D. None of these  
(vii)  The most suitable average for index number is:  
A. Arithmetic Mean  B. Geometric Mean  C. Median  D. Mode  
(viii)  The index number is called?  
A. Economic Barometer  B. Statistical Barometer  C. Mathematical Barometer  D. Physical Barometer  
(ix)  The probability of an event always lies between:  
A. 1 and 0  B. 1 and 1  C. 0 and +1  D. 0.5 and 0.5  
(x)  The probability of drawing red card out of 52 cards is:  
A.1/2  B. 1/4  C. 1/13  D. None of these 
Short Questions
SECTIONB (Marks 24)
Q.2 Attempt any eight parts. The answer to each part should not exceed 3 to 4 lines. (8 x 3 = 24)
(i) Write down the applications of Statistics in Business.
Answer:
Statistics is applied in several areas of business given below:
 Decision Analysis
 Descriptive Analysis
 Predictive Analysis
 Management Analysis
 Production Analysis
 Risk Analysis
 Sales Analysis
 Quality Assurance Analysis
 Financial Analysis
 & many others.
(ii) Differentiate between Primary & secondary data.
Answer:
First hand, newly collected, ungrouped data is called primary data or data which is not collected by someone previously is called primary data.
Second hand, previously collected, grouped data is called secondary data or data which is collected by someone previously is called secondary data.
(iii) The following data show the number of absent students during the month of November 2011 from I COM class:
3, 4, 5, 6, 7, 1, 0, 2, 3, 4, 5, 7, 8, 7, 2, 1, 5, 6, 7, 8, 9, 10, 6, 7, 3 Make a frequency distribution taking class intervals as one.
Solution
X  0  1  2  3  4  5  6  7  8  9  10 
f  1  2  2  3  2  3  3  5  2  1  1 
(iv) What is meant by graph?
Solution
A diagram which shows the relationship of normally two variables is called graph. For example Bar graph, Line graph, Pie Chart, Histogram are common examples of graphs.
(v) The following data indicate the size of shoes sold at a store during the given week. Find model size of shoes:
Size of Shoes  4.5  5  5.5  6  6.5  7  7.5  8 
No. of Pairs Sold  2  5  7  20  25  17  15  4 
Solution
X  f  fX 
4.5  2  9 
5  5  25 
5.5  7  38.5 
6  20  120 
6.5  25  162.5 
7  17  119 
7.5  15  112.5 
8  4  32 
∑f = 95  ∑fX = 618.5 
(vi) Write down the desirable qualities of a good average.
Answer
(1) It should be easy to calculate and simple to understand.
(2) It should be clearly defined by a mathematical formula.
(3) It should not be affected by extreme values.
(4) It should be based on all the observations.
(5) It should be capable of further mathematical treatment.
(6) It should have sample stability.
(vii) In a certain distribution mean is 45 and median is 50 then find mode. Also give the assumption you take regarding the shape of distribution.
Solution
Mode = 3 Median – 2 Mean
Mode = 3(50) – 2(45)
Mode = 150 – 90
Mode = 60
So Mean = 45, Median = 50 and Mode = 60
Mean < Median < Mode
It is negatively Skewed distribution
(viii)Differentiate between Fixed base & Chain Base method.
Answer
In fixed base method, base period remains fixed whereas in chain base method base period does not remain fixed. On the other hand in fixed base method, we calculate price relative whereas in chain base method, we calculate link relative and then we calculate chain index.
(ix) Find Price Relatives for the data given below using average of last three years as base:
Year  1990  1991  1992  1993  1994  1995  1996  1997  1998 
Price  15  16  20  22  24  23  25  15  20 
Solution
Years  Prices 

1990  15  =75 
1991  16  =80 
1992  20  =100 
1993  22  =110 
1994  24  =120 
1995  23  =115 
1996  25  =125 
1997  15  =75 
1998  20  =100 
(x) Two unbiased coins are tossed once. Find the following.
(a) Make a sample space (b) Probability that two head appears
(c) Probability that exact one head appeared
Solution
All possible outcomes
HH  HT  TH  TT 
(xi) A fair cubical die is rolled once. What is the probability of obtaining?
(a) Six (b) An even number (c) The number greater than 4
Solution
All possible outcomes = 1, 2, 3, 4, 5, 6
Events
Section C (Marks 16)
Extensive Questions
Note: Attempt any two questions. All questions carry equal marks. (2×8=16)
Q.3 Calculate Arithmetic Mean, Median Mode from the following data:
Groups  Frequency 
0–4  20 
5–9  23 
10–14  30 
15–19  21 
20–24  17 
25–29  19 
Solution
Groups  Frequency  Class Boundaries  X  fX  C.f 
0–4  20  0.5 – 4.5  2  40  20 
5–9  23  4.5 – 9.5  7  161  43 
10–14  30  9.5 – 14.5  12  360  73 
15–19  21  14.5 – 19.5  17  357  94 
20–24  17  19.5 – 24.5  22  374  111 
25–29  19  24.5 – 29.5  27  513  130 
130  1805  
∑f=  ∑fX= 
Model Class = n/2 = 130/2 = 65 falls in C.f of 73 so data is:
L = 9.5, h = 5, f = 30, n/2 =130/2 = 65 & C = 43
Model Class: Maximum frequency is 30 so data for model class is:
L = 9.5, fm = 30, f1 = 23, f2 = 21 & h = 5
Q.4 Construct Index number for 1995 from the following data taking 1990 as base.
(i) Laspeyre’s Method
(ii) Paasche’s method
(iii) Fisher Ideal Method
Items  1990  1995  
Price  Quantity  Price  Quantity  
A  10  120  12  100 
B  8  150  10  130 
C  12  80  13  70 
D  15  60  20  50 
Solution
Article  1990  1995  
Price (Po)  Quantity (qo)  Price (P1)  Quantity (q1)  poqo  p1qo  p1q1  poq1  
A  10  120  12  100  1200  1440  1200  1000 
B  8  150  10  130  1200  1500  1300  1040 
C  12  80  13  70  960  1040  910  840 
D  15  60  20  50  900  1200  1000  750 
Sum  4260  5180  4410  3630  
∑poqo =  ∑p1qo =  ∑p1q1 =  ∑poq1 = 
Q.5 A marble is drawn at random from a box containing 10 red and 30 white, 20 blue and 15 orange marbles. What is the probability that it is: (i) White (ii) Orange or Red (iii) Not red or blue (iv) Red, White or blue
Solution
Red marbles = 10
White marbles = 30
Blue marbles = 20
Orange marbles = 15
Total marbels = 10 + 30 + 20 + 15 = 75
Events:
Probabilities
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