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Table of Contents
Business Statistics Solved Paper FBISE 2018 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)  Statistics is always:  
A. Fixed  B. Aggregate of Facts and Figures  C. Always Continuous  D. Always True  
(ii)  The data which have not undergone and statistical treatments are:  
A. Discrete data  B. Secondary Data  C. Primary Data  D. Qualitative Data  
(iii)  The number of observations falling in a particular class is known as:  
A. Midpoint  B. Class mark  C. Class Interval  D. Class Frequency  
(iv)  In a pie chart, angle of a sector is:  
A. (Component Part/Total) x 100  B. (Component Part/Total) x 360⁰  C. (Total/Component Part) x 100  D. (Total/Component Part) x 360⁰  
(v)  The sum of square deviations from mean is:  
A. Zero  B. Minimum  C. Negative  D. Maximum  
(vi)  The empirical relationship among mean, median and mode is:  
A. Mode=3Mean – 2 Median  B. Mode = 3Median – 2 Mean  C. Mode = 3Median – 3Mean  D. Mode = 2Mean – 3Median  
(vii)  If all the values are not of equal importance, the index number is called:  
A. Simple  B. Composite  C. UnWeighted  D. Weighted  
(viii)  Imports and exports of Pakistan is an example of:  
A. Composite Index Number  B. Wholesale price Index Number  C. Volume Index Number  D. Simple Index Number  
(ix)  The probability of an event always lies between:  
A. 0 and 1  B. 1 and 1  C. 1 and 0  D. 1 and 2  
(x)  The probability of sure event is:  
A.
 B.
 C.
 D.

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) Differentiate between 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.
(ii) Define discrete variable by giving examples.
Answer
In discrete variable, data has some specific value within a given range for example Number of persons, Number of Cars, Number of Students in a class etc.
(iii) Define Histogram.
Answer
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.
(iv) Define classification and tabulation.
Answer
The process of classifying data into groups is called classification whereas to present data in the form of table or to present into rows and columns is called tabulation.
(v) A student obtained 40, 50, 60, 80 and 45 marks in the subjects of English, Urdu, Maths, Stats and Pakistan Studies, respectively, assuming weights 5, 2, 4, 3 and 1 respectively for above mentioned subjects. Find weighted AM for subjects.
Answer
Subjects  Marks (X)  Weights (W)  WX 
English  40  5  200 
Urdu  50  2  100 
Maths  60  4  240 
Statistics  80  3  240 
Pak. Studies  45  1  45 
∑W=15  ∑WX=825 
(vi) A distribution consists of four components with frequencies 40, 50, 65 and 45 having their means 20, 38, 45 and 52. Find mean of combined distribution.
Solution:
(vii) Define median and also write it’s any two advantages.
Solution
Median is a second type of average. Its formula for ungrouped data is:
In grouped data, the formula for median is:
(viii) Laspeyre’s Index No= 115, Fisher’s Index No=112.98 Paasch’s Index No=?
Answer
(ix) Find Index No. from the following data taking average of all five years as base:
Year  1970  1971  1972  1973  1974 
Price  9  6  9  11  10 
Solution
Years  Prices 

1970  14 

1971  15 

1972  16 

1973  17 

1974  18 

(x) If one card is drawn from 52 playing cards. Find the probability that it is a king of heart.
Solution:
Event
Probability
(xi) In how many ways, the word “Committee” can be arranged?
Solution
In word “Committee”, M, T and E appear 2 times each whereas C, O and I appears one time each and total letters are 9, so the permutation applied:
Extensive Questions
Section C (Marks 16)
Note: Attempt any two questions. All questions carry equal marks. (2×8=16)
Q.3 Calculate arithmetic mean by using:
(a) Direct method
(b) Indirect/Shortcut Method
(b) Stepdeviation/Coding method
Marks  No. of Students 
30–39  1 
40–49  3 
50–59  11 
60–69  21 
70–79  43 
80–89  32 
90–99  9 
Solution
Marks  f  Class Boundaries  X  fX  D=X64.5  fD 
 fU 
30–39  1  29.5–39.5  34.5  34.5  30  30  3  3 
40–49  3  39.5–49.5  44.5  133.5  20  60  2  6 
50–59  11  49.5–59.5  54.5  599.5  10  110  1  11 
60–69  21  59.5–69.5  64.5  1354.5  0  0  0  0 
70–79  43  69.5–79.5  74.5  3203.5  10  430  1  43 
80–89  32  79.5–89.5  84.5  2704  20  640  2  64 
90–99  9  89.5–99.5  94.5  850.5  30  270  3  27 
Sum  120  8880  1140  114  
∑f=  ∑fX=  ∑fD=  ∑fU= 
Q.4 Calculate Chain Index numbers for the following data. Use Median as an average.
Year  A  B  C  D 
1958  94  98  82  122 
1959  98  83  97  105 
1960  96  87  95  107 
1961  94  82  97  112 
Solution
Year  A  B  C  D  Median  Chain Index 
1958  94  98  82  122  (82+94)/2 =88  88 
1959  =104.25  =84.69  =118.29  =86.86  (86.86 + 104.25)/2 =95.555  (88 x 95.555)/100 = 84 
1960  =97.95  =104.81  =97.93  =101.90  (97.95 + 101.90)/2 =99.925  (84 x 99.925)/100 = 83.93 
1961  =97.917  =94.25  =102.10  =104.67  (97.917 + 102.10)/2 =100  (83.93 x 100)/100 = 83.93 
Q.5 From a pack of playing cards, a card is drawn at random, find the probability that the drawn card is:
(i) Ace card
(ii) A red card
(iii) A king or a queen
(iv) A jack of clubs
Solution
Events
Probabilities
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