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Table of Contents
Business Statistics Solved Paper FBISE 2018 2nd Annual ICOM II, MCQS, Short Questions, Extensive Questions
Solved by Iftikhar Ali, M.Sc Economics, M.Com Finance Lecture Statistics, Finance & Accounting
MCQS
Q.1 Circle the Correct Option i.e. A/B/C/D. Each Part Carries 1 Mark.  
(i)  The data which have not undergone through any statistical process are called:  
A. Primary Data  B. Discrete Data  C. Secondary Data  D. Qualitative Data  
(ii)  A measure computed from sample data is called:  
A. Parameter  B. Statistic  C. Statistics  D. Data  
(iii)  Cumulative frequency distribution is graphically presented by:  
A. Ogive  B. Histogram  C. Bar Chart  D. Pie Chart  
(iv)  The number of observations falling in a particular class is known as:  
A. 𝐶𝑙𝑎𝑠𝑠 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦  B. Class Mark  C. Class Limit  D. Mid Point  
(v)  If ∑(X11)=6, ∑(X30)=19 & ∑(X17)=0 then mean of X is:  
A. 11  B. 30  C. 17  D. 19  
(vi)  Sum of deviations taken from mean is:  
A. Positive  B. Zero  C. Negative  D. Minimum  
(vii)  If Laspayr’s index = 116 & Paasche’s index = 110 then Fisher’s index is=?  
A. 110.96  B. 116.00  C. 113.69  D. 112.96  
(viii)  In chain base method the base period is:  
A. Fixed  B. Constant  C. Not Fixed  D. Zero  
(ix)  n(n1)(n2)……3.2.1 is equal to:  
A. ∑n  B. ∑(n)(n1)  C. 𝑛!  D. n(n1)  
(x)  Probability of a sure event is equal to:  
A.0  B. 1  C. 1  D. 0.5 
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) Define sample and population.
Answer:
Whole group under discussion is called population for example the whole strength of college student or whole population of a certain district etc.
Whereas part of population is called sample for example 30 students out of 100 students or 300 persons out of district population etc.
(ii) Define descriptive and inferential statistics.
Answer
Descriptive statistics deals with collection and presentation of data in various forms, such as tables, graphs and diagrams and findings averages and other measures of data.
Inferential statistics deals with the testing of hypothesis and inference about population parameter is called Inferential Statistics.
(iii) Define histogram and historigram.
Answer
Histogram
Histogram is a graph of frequency distribution in which class boundaries with suitable width is taken on Xaxis whereas respective frequencies are taken on Yaxis. In Histogram relative frequencies are shown in the shape of adjacent rectangular bars.
Historigram
Histogram is a graph of frequency distribution in which class boundaries with suitable width is taken on Xaxis whereas respective frequencies are taken on Yaxis. In Histogram relative frequencies are shown in the shape of adjacent rectangular bars. Whereas graph of Time Series or historical series is called historigram.
(iv) Describe any three qualities of a good statistical table.
Answer
A good statistical table must contain at least the following components:
i Table Number ii Title of the Table iii Caption iv Stub v Body vi Head Note vii Footnote
(v) Find arithmetic mean given that x=10 +5U; ∑fu = 40; ∑f=125
Solution
Here ∑fU = 40, ∑f = 125, A = 10 & h = 5
(vi) For a moderately skewed distribution mode = 60 and median = 30. Find mean.
Solution
Mode = 3 Median – 2 Mean
60 = 3(30) – 2(Mean)
60 = 90 – 2(Mean)
2(Mean) = 90 – 60
2(Mean) = 30
Mean = 30/2
Mean = 15
(vii) The logarithm of five values of x are: 1.8062, 1.2304, 1.6532, 1.5798, 1.4314. Find X̄.
Solution
Log of X  Antilog Value of X or X 
1.8062  64 
1.2304  17 
1.6532  45 
1.5798  38 
1.4314  27 
∑X =191 
(viii) Define price relative and link relative.
Answer
Price Relative is used in fixed base method of Index Number in which each current price is divided by base period price which remains fixed. The formula for price relative is given below:
where Pn is current period price & Po is base period price.
Link Relative is used in chain index in which each period price is divided by previous time period price. The formula for Link relative is given below:
(ix) For the given link relatives 100, 120, 102, 118 & 112, find chain indices.
Solution
Years  L.R 

1  100  100 
2  120 

3  102 

4  118 

5  112 

(x) Define simple event and composite event.
Answer
Simple Event
An event of sample space contains only one outcome is called simple event. For example getting 6 or 5 or 3 in a throwing of single die is a simple event.
Compound Event
An event of sample space contains at least two outcomes is called compound event these may be denoted by any letter A to Z except S. For example If event consists of the sum of two dice is ‘’5’’ than it consists of four outcomes i.e., (1, 4), (2, 3), (3, 2), (4, 1) and this is considered to be a compound event
(xi) A pair of dice is rolled find the probability that both faces are same:
Solution
Event:
Same Faces η(A) = 6
All Possible Outcomes
1, 1  2, 1  3, 1  4, 1  5, 1  6, 1 
1, 2  2, 2  3, 2  4, 2  5, 2  6, 2 
1, 3  2, 3  3, 3  4, 3  5, 3  6, 3 
1, 4  2, 4  3, 4  4, 4  5, 4  6, 4 
1, 5  2, 5  3, 5  4, 5  5, 5  6, 5 
1, 6  2, 6  3, 6  4, 6  5, 6  6, 6 
Probabilities
Extensive Questions
Section C (Marks 16)
Note: Attempt any two questions. All questions carry equal marks. (2×8=16)
Q.3 Find mean, median and mode for the following data:
Weight  35–39  40–44  45–49  50–54  55–59  60–64 
Frequency  3  10  21  15  1  4 
Solution
Marks  f  Class Boundaries  X  fX  C.F 
35–39  3  34.5—39.5  37  111  3 
40–44  10  39.5—44.5  42  420  13 
45–49  21  44.5—49.5  47  987  34 
50–54  15  49.5—54.5  52  780  49 
55–59  1  54.5—59.5  57  57  50 
60–64  4  59.5—64.5  62  248  54 
∑f=54  ∑fx=2603 
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 Three coins are tossed. Find the following probabilities:
(a) At most one head appear
(b) Same faces appear
(c) Head on the first coin
Solution:
All possible outcomes
HHH  HHT  HTH  THH 
TTT  TTH  THT  HTT 
Events:
Probability:
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