In this blog post, we delve into the intricacies of the **Business Statistics Solved Paper FBISE 2024 Annual ICOM II, MCQS, Short Questions, Extensive Questions**, providing detailed solutions and explanations. Whether you’re a student looking to ace your exams or simply keen on enhancing your statistical knowledge, this guide will serve as a valuable resource. We’ll cover key topics including: Introduction to Statistics, Graphical Presentation of Data, Averages, Index Numbers & Probability. By the end of this post, you will have a thorough understanding of these essential statistical concepts and be well-prepared to tackle similar problems in your studies or professional work. Join us as we unravel the complexities of business statistics and turn them into manageable, solvable components.

## Business Statistics Solved Paper FBISE 2024 Annual ICOM II, MCQS, Short Questions, Extensive Questions

**For more solved papers of Business Statistics click below links:**

**Solved Papers Business Statistics**

**Solved by Iftikhar Ali, M.Sc Economics, M.Com Finance Lecture Statistics, Economics, Finance & Accounting**

## Table of Contents

## Business Statistics Solved Paper FBISE 2024 Annual ICOM II, MCQS, Short Questions, Extensive Questions

## MCQS

**MCQS will be available soon when available**

## Short Questions

**SECTION — B (Marks 24)**

**Q. 2 Write brief answers of any EIGHT parts. (8 x 3 = 24)**

**(i)** Distinguish between variable and constant.

** Answer** A variable is a data, numbers, figures which does not remain fix for example, income, consumption, saving etc.; whereas constant is a number or figure which remain fix for example, Avogadro number, gravitational force, mass of earth, value of Pi etc.

**(ii)** Give the importance of Statistics in Education.

**Answer:** Statistics can help education in number of ways:

**Assessment and Evaluation:**With the help of statistics, student’s performance can be assessed and evaluated.**Educational Research:**With the help of statistics, educational research about trends can be done.**Policy making & Decisions:**With the help of statistics, decisions and policies about education can be made on time.**Improving Teaching & Learning:**With the help of statistical data analysis, teaching methods and learning process can be developed.**Quality Control:**Quality control of education can be maintained with the help of statistical data analysis and evaluation.**Prediction:**Statistics can predict about future forecast of education and timely decision can be made.

**(iii)** Differentiate between grouped data and ungrouped data.

__Answer__

__Ungrouped Data__

First hand, newly collected, ungrouped data is called primary data or data which is not collected by someone previously is called primary data.

__Grouped Data__

Second hand, previously collected, grouped data is called secondary data or data which is collected by someone previously is called secondary data.

**(iv)** Find [∑f(X – 4)]² given X = 3, 4, 5, 8 and f = 2, 1, 2, 2

**Solution:**

X | f | (X – 4) | f(X – 4) |

3 | 2 | -1 | -2 |

4 | 1 | 0 | 0 |

5 | 2 | 1 | 2 |

8 | 2 | 4 | 8 |

| | ∑f(X – 4)=8 |

**[∑f(X – 4)]² = 8²=64**

**(v)** If sum of 15 values is 300 and by addition of two more values, it becomes 360. Find the new values if the ratio between them is 1:4.

**Solution:**

**∑X1=300, n1 =15, ∑X2=360, n2 = 17**

**Difference = 360 – 300 = 60**

**Sum of the ratio = 1+4=5**

**(vi)** Deviations from 10.5 of ten items are: -1.3, 2.0, 2.9, 7.5, -4.6, -3.4, 8.2, 9.3, -7.4, 5.6. Calculate the arithmetic mean.

**Solution:**

D | -1.3 | 2.0 | 2.9 | 7.5 | -4.6 | -3.4 | 8.2 | 9.3 | -7.4 | 5.6 | ∑D=18.8 |

**(vii)** Give fm = 33, f1=26, f2 =23, h = 10, l =40.5. Find mode.

**Solution:**

**(viii)** If the mode and mean of a moderately asymmetrical series are 16 and 20.2 respectively, compute the value of median.

**Solution:**

**Mode = 3Median – 2Mean**

**16 = 3Median – 2(20.2)**

**3Median = 16 + 40.4**

**3Median = 56.4**

**Median = 56.4/3**

**Median = 18.8**

**(ix)** Compute Fisher’s price index number for the given data: ∑poqo = 35310, ∑p1qo = 41140, ∑p1q1= 46707 and ∑poq1 = 39644.

**Solution:**

**(x) **If W = 20, 25, 30, 40, & I = 100, 105, 110, 120. Find weighted average of relative’s Index No.

**Solution:**

W | I | WI |

20 | 100 | 2000 |

25 | 105 | 2625 |

30 | 110 | 3300 |

40 | 120 | 4800 |

W=115 | | WI=12725 |

**(xi) **Solve: (a) 14P11 (b) 20C5

**Solution:**

**Section-C (Marks 16)**

## Extensive Questions

**Note: Attempt any two questions. All questions carry equal marks.**

**Q.3 **Calculate Mean, Median and Mode from the following frequency distribution.

Class Limits | 3.0—3.9 | 4.0—4.9 | 5.0—5.9 | 6.0—6.9 | 7.0—7.9 | 8.0—8.9 |

Frequency | 13 | 27 | 40 | 30 | 16 | 4 |

**Solution:**

Class Limits | Frequency | C.B | X | fx | C.F |

3.0—3.9 | 13 | 2.95—3.95 | 3.45 | 44.85 | 13 |

4.0—4.9 | 27 | 3.95—4.95 | 4.45 | 120.15 | 40 |

5.0—5.9 | 40 | 4.95—5.95 | 5.45 | 218 | 80 |

6.0—6.9 | 30 | 5.95—6.95 | 6.45 | 193.5 | 110 |

7.0—7.9 | 16 | 6.95—7.95 | 7.45 | 119.2 | 126 |

8.0—8.9 | 4 | 7.95—8.95 | 8.45 | 33.8 | 130 |

| ∑f=n=130 | | | 729.5∑fx= | |

**n/2=130/2=65 falls in c.f of 80 so L = 4.95, h = 1, f = 40 & C = 40**

**Maximum frequency fm is 40 so L = 4.95, h = 1, f1 = 27 & f2 = 30**

**Q.4** Compute index numbers of prices from the following data taking 1981 as base using median as an average: (08)

Year | Price | ||

A | B | C | |

1981 | 18 | 85 | 52 |

1982 | 22 | 76 | 60 |

1983 | 28 | 80 | 66 |

1984 | 31 | 95 | 80 |

**Solution:**

Year | Price Relatives | Median | ||

A | B | C | | |

1981 | 100 | 100 | 100 | 100 |

1982 | (22/18)x100=122.22 | (76/85)x100=89.411 | (60/52)x100=115.38 | 115.38 |

1983 | (28/18)x100=155.55 | (80/85)x100=94.11 | (66/52)x100=126.92 | 126.92 |

1984 | (31/18)x100=172.22 | (95/85)x100=111.76 | (80/52)x100=153.84 | 153.84 |

**Q.5 **Find the probability for each of the following:

**(i)** An even number appears in a single toss of fair die.

**(ii)** The sum of 5 appears in a single toss of a pair of fair dice.

**(iii)** A queen, ace, jack of spades or king of diamonds appears in drawing a single card from a well-shuffled ordinary deck of 52 cards.

**(iv)** Of getting a number less than 7, if a die is rolled one time.

**Solution (i) and (iv):**

**All Possible outcomes: {1, 2, 3, 4, 5, 6}**

**Events**:

**Probability**:

**Solution (ii):**

**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 |

**Sum Table**

2 | 3 | 4 | 5 | 6 | 7 |

3 | 4 | 5 | 6 | 7 | 8 |

4 | 5 | 6 | 7 | 8 | 9 |

5 | 6 | 7 | 8 | 9 | 10 |

6 | 7 | 8 | 9 | 10 | 11 |

7 | 8 | 9 | 10 | 11 | 12 |

**Events**:

**Probability**

**Solution (iii):**

**Events**:

**Probability**:

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