FIA Test Preparation Lecture #9
Basic Probability, Mean, Median, Mode, Standard Deviation & Charts
Top MCQs with Proper Lecture Notes
1. Basic Probability
Probability means the chance of an event happening.
Formula
Probability = Favourable outcomes ÷ Total outcomes
Example:
A coin has 2 sides: Head and Tail.
Probability of Head = 1/2
MCQs: Probability
1. A coin is tossed once. Probability of getting head is:
A) 1
B) 1/2
C) 1/3
D) 0
Answer: B) 1/2
2. A dice is rolled once. Probability of getting 6 is:
A) 1/2
B) 1/3
C) 1/6
D) 1/4
Answer: C) 1/6
3. A dice is rolled once. Probability of getting an even number is:
A) 1/6
B) 1/3
C) 1/2
D) 2/3
Answer: C) 1/2
Reason: Even numbers are 2, 4, 6. Total outcomes = 6. Probability = 3/6 = 1/2.
4. Probability value always lies between:
A) 0 and 1
B) 1 and 2
C) 2 and 3
D) 5 and 10
Answer: A) 0 and 1
5. Probability of an impossible event is:
A) 0
B) 1
C) 1/2
D) 2
Answer: A) 0
6. Probability of a sure event is:
A) 0
B) 1
C) 1/2
D) 1/6
Answer: B) 1
7. A bag has 3 red balls and 2 blue balls. Probability of red ball is:
A) 2/5
B) 3/5
C) 1/5
D) 5/3
Answer: B) 3/5
8. A bag has 4 black balls and 6 white balls. Probability of white ball is:
A) 2/5
B) 3/5
C) 4/5
D) 1/5
Answer: B) 3/5
Reason: Total balls = 10. White balls = 6. Probability = 6/10 = 3/5.
2. Mean
Mean is also called average.
Formula
Mean = Sum of values ÷ Number of values
Example:
Values: 2, 4, 6
Mean = 2 + 4 + 6 ÷ 3 = 12 ÷ 3 = 4
MCQs: Mean
9. Mean of 2, 4, 6 is:
A) 2
B) 3
C) 4
D) 6
Answer: C) 4
10. Mean of 5, 10, 15 is:
A) 5
B) 10
C) 15
D) 20
Answer: B) 10
11. Mean of 10, 20, 30, 40 is:
A) 20
B) 25
C) 30
D) 35
Answer: B) 25
12. Average marks of 4 students are 20. Total marks are:
A) 60
B) 70
C) 80
D) 90
Answer: C) 80
Reason: Total = Average × Number = 20 × 4 = 80.
13. Mean of 3, 7, 8, 10 is:
A) 6
B) 7
C) 8
D) 9
Answer: B) 7
Reason: Sum = 28. Number of values = 4. Mean = 28/4 = 7.
3. Median
Median is the middle value after arranging data in order.
Rule
First arrange values from smallest to largest.
If number of values is odd, median is the middle value.
If number of values is even, median is average of two middle values.
MCQs: Median
14. Median of 3, 5, 7 is:
A) 3
B) 5
C) 7
D) 15
Answer: B) 5
15. Median of 2, 4, 6, 8 is:
A) 4
B) 5
C) 6
D) 7
Answer: B) 5
Reason: Middle values are 4 and 6. Median = 5.
16. Median of 9, 3, 5 is:
A) 3
B) 5
C) 9
D) 17
Answer: B) 5
Reason: Arrange: 3, 5, 9. Middle value = 5.
17. Median of 10, 20, 30, 40, 50 is:
A) 20
B) 25
C) 30
D) 40
Answer: C) 30
18. Median of 1, 3, 5, 7, 9, 11 is:
A) 5
B) 6
C) 7
D) 8
Answer: B) 6
Reason: Middle values are 5 and 7. Median = 6.
4. Mode
Mode is the value that appears most frequently.
Example:
2, 3, 3, 5
Mode = 3
MCQs: Mode
19. Mode of 2, 3, 3, 5 is:
A) 2
B) 3
C) 5
D) 13
Answer: B) 3
20. Mode of 4, 4, 5, 6, 7 is:
A) 4
B) 5
C) 6
D) 7
Answer: A) 4
21. Mode of 1, 2, 2, 3, 3, 3 is:
A) 1
B) 2
C) 3
D) 6
Answer: C) 3
22. In 10, 20, 30, 40, there is:
A) One mode
B) Two modes
C) No mode
D) Three modes
Answer: C) No mode
5. Standard Deviation
Standard deviation shows how much values are spread out from the mean.
Simple Meaning
If standard deviation is small, values are close to mean.
If standard deviation is large, values are far from mean.
For FIA basic test, mostly concept-based questions are expected.
MCQs: Standard Deviation
23. Standard deviation measures:
A) Central value
B) Spread of data
C) Total number
D) Highest value only
Answer: B) Spread of data
24. If standard deviation is zero, all values are:
A) Different
B) Equal
C) Negative
D) Very large
Answer: B) Equal
25. Small standard deviation means:
A) Data values are close to mean
B) Data values are very far
C) Mean is always zero
D) Data is wrong
Answer: A) Data values are close to mean
26. Large standard deviation means:
A) Less variation
B) More variation
C) No variation
D) No data
Answer: B) More variation
27. Which data has zero standard deviation?
A) 2, 4, 6
B) 5, 5, 5
C) 1, 2, 3
D) 10, 20, 30
Answer: B) 5, 5, 5
6. Interpreting Data from Charts
Charts are used to present data clearly.
Common Charts
| Chart Type | Use |
|---|---|
| Bar chart | Compare categories |
| Pie chart | Show parts of a whole |
| Line chart | Show trend over time |
| Table | Show exact values |
How to Solve Chart Questions
- Read the title of chart.
- Check labels and units.
- Find the required value.
- Compare carefully.
- For percentage, use:
Part ÷ Total × 100
Example Chart Data
Marks of students:
| Student | Marks |
|---|---|
| Ali | 60 |
| Bilal | 70 |
| Hamza | 80 |
| Sara | 90 |
MCQs: Chart Interpretation
28. Who got the highest marks?
A) Ali
B) Bilal
C) Hamza
D) Sara
Answer: D) Sara
29. Who got the lowest marks?
A) Ali
B) Bilal
C) Hamza
D) Sara
Answer: A) Ali
30. Difference between Sara and Ali’s marks is:
A) 20
B) 25
C) 30
D) 35
Answer: C) 30
31. Total marks of all students are:
A) 250
B) 280
C) 300
D) 320
Answer: C) 300
32. Average marks are:
A) 70
B) 75
C) 80
D) 85
Answer: B) 75
Reason: Total = 300. Students = 4. Average = 75.
Example Pie Chart Data
Monthly expenses:
| Expense | Percentage |
|---|---|
| Food | 40% |
| Rent | 30% |
| Transport | 20% |
| Others | 10% |
33. Highest expense is on:
A) Food
B) Rent
C) Transport
D) Others
Answer: A) Food
34. Lowest expense is on:
A) Food
B) Rent
C) Transport
D) Others
Answer: D) Others
35. If total expense is Rs. 10,000, food expense is:
A) Rs. 2,000
B) Rs. 3,000
C) Rs. 4,000
D) Rs. 5,000
Answer: C) Rs. 4,000
36. If total expense is Rs. 10,000, rent expense is:
A) Rs. 2,000
B) Rs. 3,000
C) Rs. 4,000
D) Rs. 5,000
Answer: B) Rs. 3,000
37. Food and rent together are:
A) 50%
B) 60%
C) 70%
D) 80%
Answer: C) 70%
Example Line Chart Data
Sales of a shop:
| Month | Sales |
|---|---|
| January | 100 |
| February | 150 |
| March | 120 |
| April | 180 |
38. Sales were highest in:
A) January
B) February
C) March
D) April
Answer: D) April
39. Sales were lowest in:
A) January
B) February
C) March
D) April
Answer: A) January
40. Increase from January to February is:
A) 30
B) 40
C) 50
D) 60
Answer: C) 50
41. Difference between April and March sales is:
A) 40
B) 50
C) 60
D) 70
Answer: C) 60
42. Total sales from January to April are:
A) 450
B) 500
C) 550
D) 600
Answer: C) 550
7. Mixed Important MCQs
43. Mean is also called:
A) Average
B) Mode
C) Median
D) Range
Answer: A) Average
44. Median means:
A) Most repeated value
B) Middle value
C) Highest value
D) Lowest value
Answer: B) Middle value
45. Mode means:
A) Average value
B) Middle value
C) Most repeated value
D) Total value
Answer: C) Most repeated value
46. Probability of getting tail on a coin is:
A) 1/2
B) 1/3
C) 1/4
D) 1
Answer: A) 1/2
47. In a pie chart, total percentage is:
A) 50%
B) 75%
C) 100%
D) 120%
Answer: C) 100%
48. Bar chart is mainly used for:
A) Comparing categories
B) Writing essays
C) Measuring temperature
D) Solving grammar
Answer: A) Comparing categories
49. Line chart is mainly used to show:
A) Trend over time
B) Parts of whole
C) Dictionary meanings
D) Nouns and verbs
Answer: A) Trend over time
50. Pie chart is mainly used to show:
A) Parts of a whole
B) Only time
C) Alphabet order
D) Grammar rules
Answer: A) Parts of a whole
Quick Revision Table
| Topic | Meaning / Formula |
|---|---|
| Probability | Favourable outcomes ÷ Total outcomes |
| Mean | Sum ÷ Number |
| Median | Middle value after arranging |
| Mode | Most repeated value |
| Standard Deviation | Spread of data |
| Bar Chart | Compare categories |
| Pie Chart | Parts of whole |
| Line Chart | Trend over time |
Common Mistakes
| Mistake | Correct Method |
|---|---|
| Finding median without arranging data | Arrange data first |
| Confusing mean and mode | Mean = average, Mode = repeated value |
| Taking pie chart total as more than 100% | Pie chart total is always 100% |
| Adding probabilities without checking event | First find favourable and total outcomes |
| Ignoring units in chart | Always check units and labels |
Homework MCQs
1. Mean of 4, 6, 8 is:
A) 4
B) 5
C) 6
D) 8
Answer: C) 6
2. Median of 2, 8, 4 is:
A) 2
B) 4
C) 8
D) 14
Answer: B) 4
3. Mode of 5, 6, 6, 7 is:
A) 5
B) 6
C) 7
D) No mode
Answer: B) 6
4. Probability of getting 1 on a dice is:
A) 1/2
B) 1/3
C) 1/6
D) 1
Answer: C) 1/6
5. Standard deviation shows:
A) Spread of data
B) Name of data
C) Only total
D) Only percentage
Answer: A) Spread of data
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