Decoding Data Handling for Class 8: Important Questions and Answers

Data Handling Class 8 Important Questions are available in this Maths article. Data Handling Class 8 Important Questions are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Data Handling. Data handling organizes, displays and interprets data using graphs. Our subject experts have provided detailed solutions for these problems based on the old CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination. 

Table of Contents

• Exercise 5.1: Introduction to Data and Data Collection
• Exercise 5.2: Frequency Distribution and Data Representation
• Exercise 5.3: Bar Graphs
• Exercise 5.4: Pie Charts
• Exercise 5.5: Probability
• Tips for Understanding Data Handling
• Most Common Examination Questions (Board Exams)

Exercise 5.1: Introduction to Data and Data Collection

Question 1: What is Data?

Answer: Data is information collected about something or someone. It can be numbers, colors, names, or any facts that we gather.

Examples of data:

• Heights of students in your class (numbers)

• Colors of cars parked in a street (colors)

• Marks obtained by students in a test (numbers)

• Favorite fruits of your classmates (names)

• Temperature readings for 7 days (numbers)

• Number of books borrowed from library each day (numbers)

When we collect many such pieces of information, we call it a dataset.

Question 2: What is the Difference Between Raw Data and Organized Data?

Answer: Raw data is information in its original form, just as collected. It has no order and can be confusing.

Example of raw data: Marks of 10 students: 45, 78, 82, 45, 92, 78, 56, 78, 82, 45

Organized data is the same information arranged in an order that makes sense and is easy to understand.

Example of organized data: Marks in order: 45, 45, 45, 56, 78, 78, 78, 82, 82, 92

Or shown in a table:

Marks	Count (Frequency)
45	3
56	1
78	3
82	2
92	1

Organized data is much easier to understand and use.

Question 3: What is Frequency? How is it Calculated?

Answer: Frequency is the number of times something appears in a dataset. It tells us how often something happens.

How to calculate frequency:

1. Count how many times each item appears

2. Write down the number of times it appears

Example: If we ask 20 students their favorite color:

• Red: 7 students like red

• Blue: 8 students like blue

• Green: 5 students like green

Frequency of Red = 7 Frequency of Blue = 8 Frequency of Green = 5

Total = 7 + 8 + 5 = 20 

Question 4: Make a Frequency Table for the Following Data: 2, 3, 2, 4, 3, 2, 5, 3, 2, 4

Solution: First, count how many times each number appears:

• 2 appears 4 times

• 3 appears 3 times

• 4 appears 2 times

• 5 appears 1 time

Frequency table:

Number | Tally Marks | Frequency

-------|-------------|----------

2      | |||| (4)    | 4

3      | ||| (3)     | 3

4      | || (2)      | 2

5      | | (1)       | 1

-------|-------------|----------

Total  |             | 10

Question 5: What are Tally Marks? How are They Used?

Answer: Tally marks are a quick way to count and record data. Each group of tally marks represents 5 items.

How tally marks work:

• One mark | = 1

• Two marks || = 2

• Three marks ||| = 3

• Four marks |||| = 4

• Five marks |||| (crossed line) = 5

Example: If you see |||| |||| ||| it means 5 + 5 + 3 = 13 items

When used in frequency table:

Item    | Tally Marks      | Frequency

--------|------------------|----------

Apple   | |||| |||| ||||   | 14

Banana  | |||| |||         | 8

Orange  | |||| |           | 6

--------|------------------|----------

Total   |                  | 28

Question 6: Collect Data About the Number of Hours 10 Students Study Daily. Organize It

Answer: This is a real-life example. Let's say we ask 10 students:

Raw data collected: 2, 3, 2, 4, 1, 2, 3, 4, 2, 3 hours per day

Organized in frequency table:

Study Hours | Tally Marks | Frequency

------------|-------------|----------

1 hour      | |           | 1

2 hours     | ||||        | 4

3 hours     | |||         | 3

4 hours     | ||          | 2

------------|-------------|----------

Total       |             | 10

Conclusion: Most students (4) study for 2 hours daily.

Exercise 5.2: Frequency Distribution and Data Representation

This exercise teaches students to organize large amounts of data using frequency tables and understand what the numbers mean.

Question 7: What is a Frequency Table? Why Do We Use It?

Answer: A frequency table is a way to organize data so we can see which items appear most and least often.

Why we use frequency tables:

1. It makes data easy to understand

2. We can quickly see patterns

3. It saves space compared to listing raw data

4. It helps us calculate totals and percentages

5. It is easy to make charts from frequency tables

Question 8: Create a Frequency Table for Daily Temperature: 25°C, 26°C, 25°C, 24°C, 26°C, 25°C, 27°C, 26°C, 25°C, 24°C

Solution:

Temperature	Frequency
24°C	2
25°C	4
26°C	3
27°C	1
Total	10 days

 From this table we can see:

• Most common temperature: 25°C (4 days)

• Least common temperature: 27°C (1 day)

• Temperature range: 24°C to 27°C (difference of 3°C)

Question 9: What is the Mode of Data? Find the Mode of: 2, 5, 3, 2, 4, 2, 3, 5, 2

Answer: Mode is the item that appears most frequently in a dataset. It is the most common value.

For the given data: 2, 5, 3, 2, 4, 2, 3, 5, 2

Frequency count:

• 2 appears 4 times (most frequent)

• 3 appears 2 times

• 4 appears 1 time

• 5 appears 2 times

Mode = 2 (because it appears 4 times, which is more than any other number)

Question 10: Find the Range of the Following Data: 12, 25, 8, 42, 15, 33, 20

Answer: Range tells us how spread out the data is. It is calculated as: Range = Highest Value - Lowest Value

For the given data: 12, 25, 8, 42, 15, 33, 20

• Highest value = 42

• Lowest value = 8

• Range = 42 - 8 = 34

A range of 34 means the data is spread across 34 units.

Question 11: Calculate Mean (Average) of: 10, 15, 20, 25, 30

Answer: Mean is the average value. To find it: Mean = Sum of all values ÷ Number of values

Sum = 10 + 15 + 20 + 25 + 30 = 100 Number of values = 5 Mean = 100 ÷ 5 = 20

The average is 20.

Question 12: Find the Median of: 3, 7, 2, 9, 5, 1, 8

Answer: Median is the middle value when data is arranged in order.

Step 1: Arrange in ascending order: 1, 2, 3, 5, 7, 8, 9

Step 2: Find the middle position Since there are 7 values (odd number), the middle is at position (7+1)÷2 = 4th position

Step 3: Identify the middle value 1, 2, 3, 5, 7, 8, 9 (4th position)

Median = 5

Exercise 5.3: Bar Graphs

Bar graphs are a simple way to show data using rectangles of different heights. This exercise teaches how to read and create bar graphs.

Question 13: What is a Bar Graph? When Do We Use It?

Answer: A bar graph uses rectangles (bars) to show data. The height or length of each bar shows how many items there are.

When we use bar graphs:

• To compare amounts of different items

• To show changes over time (like daily sales)

• To display survey results clearly

• To make data easy to understand at a glance

Question 14: The Following Table Shows Favorite Sports of 50 Students. Draw a Bar Graph

Sport	Number of Students
Cricket	15
Football	12
Basketball	10
Tennis	8
Badminton	5
Total	50

Solution - Bar Graph:

 Observations from the graph:

• Cricket is most popular (15 students)

• Badminton is least popular (5 students)

• Football is second most popular (12 students)

• Total students = 50

Question 15: Read the Following Bar Graph and Answer Questions

Monthly Rainfall in mm

Questions: (a) In which month was rainfall maximum? (b) What was the rainfall in March? (c) Find the difference between maximum and minimum rainfall

Answers: (a) February had maximum rainfall (400 mm) (b) March had 300 mm of rainfall (c) Maximum (400 mm) - Minimum (50 mm) = 350 mm difference

Question 16: 30 Students Were Asked: How Many Books Do You Read in a Month?

Results: 1, 2, 0, 3, 1, 2, 2, 1, 0, 1, 3, 2, 1, 2, 0, 1, 2, 3, 1, 2, 1, 0, 2, 1, 3, 2, 1, 2, 0, 1

Create a frequency table and bar graph

Solution:

Frequency Table:

Books Read	Frequency
0 books	5
1 book	10
2 books	10
3 books	5
Total	30

 Bar Graph:

Observations:

• 10 students read 1 book per month (most)

• 10 students read 2 books per month (most)

• 5 students read 0 books per month

• 5 students read 3 books per month

Exercise 5.4: Pie Charts

Pie charts show how a whole amount is divided into parts. They look like a circle cut into slices.

Question 17: What is a Pie Chart? 

Answer: A pie chart is a circle divided into slices. Each slice represents a part of the total.

Advantages of pie charts:

• Shows parts of a whole clearly

• Easy to see which part is biggest

• Good for showing percentages

• Makes data look interesting and visual

When we use pie charts:

• To show how a budget is divided

• To show percentages of different items

• To compare parts of a total

• To show market share

Question 18: Calculate Degrees for Each Category: 50% Cricket, 30% Football, 20% Tennis

Answer: In a pie chart, the whole circle = 360°

Formula: Degrees for each item = (Percentage ÷ 100) × 360°

Or: Degrees for each item = (Frequency ÷ Total) × 360°

Calculation:

Cricket: 50% of 360° = (50 ÷ 100) × 360° = 180° Football: 30% of 360° = (30 ÷ 100) × 360° = 108° Tennis: 20% of 360° = (20 ÷ 100) × 360° = 72°

Verification: 180° + 108° + 72° = 360°

Question 19: 120 Students Prefer: 40 Cricket, 30 Football, 25 Basketball, 25 Badminton. Draw a Pie Chart

Solution:

Step 1: Convert to fractions

• Cricket: 40 ÷ 120 = 1/3

• Football: 30 ÷ 120 = 1/4

• Basketball: 25 ÷ 120 = 5/24

• Badminton: 25 ÷ 120 = 5/24

Step 2: Convert to degrees

• Cricket: (40 ÷ 120) × 360° = 120°

• Football: (30 ÷ 120) × 360° = 90°

• Basketball: (25 ÷ 120) × 360° = 75°

• Badminton: (25 ÷ 120) × 360° = 75°

Pie Chart:

Reading the pie chart:

• Cricket takes up exactly 1/3 of the circle

• Football takes up 1/4 of the circle

• Basketball and Badminton each take up 5/24 of the circle

• Cricket is the most popular sport

Question 20: The Pie Chart Shows a Budget. Calculate the Amount for Each Category if Total is Rs. 1200

Budget Distribution

• Housing:   45%
• Food:      30%
• Transport: 15%
• Others:    10%

Solution:

Step 1: Calculate percentage of each category (Already given as percentages)

Step 2: Calculate amount for each category Amount = (Percentage ÷ 100) × Total

Calculations:

Housing: (45 ÷ 100) × 1200 = 0.45 × 1200 = Rs. 540 Food: (30 ÷ 100) × 1200 = 0.30 × 1200 = Rs. 360 Transport: (15 ÷ 100) × 1200 = 0.15 × 1200 = Rs. 180 Others: (10 ÷ 100) × 1200 = 0.10 × 1200 = Rs. 120

Verification: 540 + 360 + 180 + 120 = 1200 

Summary:

Category	Percentage	Amount
Housing	45%	Rs. 540
Food	30%	Rs. 360
Transport	15%	Rs. 180
Others	10%	Rs. 120
Total	100%	Rs. 1200

Probability tells us how likely something is to happen. It helps us understand chances and predict outcomes.

Question 21: What is Probability? Give Simple Examples

Answer: Probability is the chance that something will happen. It is a number between 0 and 1 (or between 0% and 100%).

Probability scale:

0 -------- 0.5 -------- 1

(Impossible) (50-50)  (Certain)

0% ------- 50% ------- 100%

 Examples:

1. Tossing a coin: Probability of getting heads = 1/2 = 0.5 = 50% (Equally likely to get heads or tails)

2. Rolling a dice: Probability of getting a 6 = 1/6 ≈ 16.7% (Any number from 1 to 6 is equally likely)

3. Picking a card: Probability of picking an ace from a deck = 4/52 ≈ 7.7% (There are 4 aces in 52 cards)

Question 22: A Bag Contains 3 Red, 2 Blue, and 5 Green Balls. What is the Probability of Picking Red?

Answer: Formula: Probability = Number of favorable outcomes ÷ Total number of outcomes

Given:

• Red balls = 3

• Blue balls = 2

• Green balls = 5

• Total balls = 3 + 2 + 5 = 10

Calculation: Probability of picking red = 3 ÷ 10 = 3/10 = 0.3 = 30%

Question 23: What is the Probability of Rolling a Number Greater Than 4 on a Dice?

Answer: A dice has 6 faces: 1, 2, 3, 4, 5, 6

Numbers greater than 4: 5, 6 (2 numbers)

Calculation: Probability = 2 ÷ 6 = 1/3 ≈ 0.333 ≈ 33.3%

Question 24: Draw a Spinner with 4 Equal Sections: Red, Blue, Green, Yellow. Find Probability of Getting Green

    Circle divided into 4 equal parts

        North: Red (R)

        East:  Blue (B)

        South: Green (G)

        West:  Yellow (Y)

    Each section = 90° = 1/4 of circle

Probability of getting Green:

Number of green sections = 1 Total number of sections = 4

Probability = 1 ÷ 4 = 1/4 = 0.25 = 25%

Meaning: If you spin 4 times, expect green to appear about 1 time.

Question 25: In a Class of 40 Students, 24 Like Mathematics. Find Probability That a Random Student Likes Mathematics

Answer: Given:

• Total students = 40

• Students who like Mathematics = 24

Calculation: Probability = 24 ÷ 40 = 3/5 = 0.6 = 60%

Verification: 24 ÷ 40 = 0.6

Meaning: 60% chance that a randomly chosen student likes Mathematics, or 3 out of 5 students like Mathematics.

Tips for Understanding Data Handling

Understand the Difference Between Measures

Mode = Most frequent value (most common) Median = Middle value (when arranged in order) Mean = Average value (sum ÷ count)

• Mode looks like "Most"

• Median has "mid" in it (middle)

• Mean sounds like "average"

• Use Mode when you want the most popular item

• Use Median when data has extreme values

• Use Mean for balanced understanding of data

Most Repeated Board Questions on Data Handling

Question 1: Creating Frequency Tables

Typical Question: "20 students were surveyed about their favorite subject. Organize the data in a frequency table: English, Hindi, English, Maths, Science, English, Maths, Science, English, Maths, Hindi, Science, English, Maths, Hindi, Science, English, Maths, Science, English"

Solution Approach:

1. Count each subject

2. Create table with subject and frequency

3. Verify total = 20

Tests organization skills and basic counting

Question 2: Reading Bar Graphs

The bar graph shows monthly sales. In which month were sales highest? What was the difference between highest and lowest sales.

Solution Approach:

1. Identify tallest bar (highest value)

2. Identify shortest bar (lowest value)

3. Calculate difference

Tests interpretation of visual data

Question 3: Pie Chart Calculations

A pie chart shows budget distribution. Education takes 40° in the pie chart. If total budget is Rs. 3600, find amount spent on education.

Solution Approach:

1. Use: Amount = (Degrees ÷ 360) × Total

2. Calculate: (40 ÷ 360) × 3600

3. Answer = Rs. 400

Tests pie chart understanding and percentage calculations

Question 4: Calculating Mean, Median, Mode

Find mean, median, and mode of: 5, 8, 5, 9, 5, 7

Solution Approach:

1. Mode: Count frequencies → 5 appears 3 times → Mode = 5

2. Median: Arrange in order: 5, 5, 5, 7, 8, 9 → Middle values are 5 and 7 → Median = 6

3. Mean: (5 + 8 + 5 + 9 + 5 + 7) ÷ 6 = 39 ÷ 6 = 6.5

Tests all three central tendencies together

Question 5: Probability Problems

Typical Question: "A box has 10 balls: 4 red, 3 blue, 3 green. What is the probability of drawing a red ball?"

Solution Approach:

1. Identify favorable outcomes = 4 (red balls)

2. Identify total outcomes = 10 (total balls)

3. Probability = 4 ÷ 10 = 2/5 = 0.4

Why it's repeated: Tests basic probability understanding

Question 6: Frequency and Percentage

In a class of 50 students, 20 like cricket. Express this as a percentage.

Solution:

1. Percentage = (Frequency ÷ Total) × 100

2. = (20 ÷ 50) × 100

3. = 0.4 × 100

4. = 40%

Converts data understanding to percentages

Question 7: Creating Bar Graphs from Data

Create a bar graph from the following frequency table.

Solution:

1. Draw two axes (horizontal and vertical)

2. Label axes with categories and frequencies

3. Choose appropriate scale

4. Draw bars of correct heights

5. Add title and labels

Tests visualization skills

1 - 2 Mark Questions (Very Frequently Asked):

1. Define frequency: How many times something appears in a dataset

2. What is mode? The value that appears most frequently

3. Define median: The middle value when data is arranged in order

4. What is mean? The average value of all data points

5. What is range? Difference between highest and lowest values

6. When do we use bar graphs? To compare amounts of different categories

7. When do we use pie charts? To show parts of a whole or percentages

8. What is probability? The chance that something will happen

9. Full circle = how many degrees? 360°

10. Probability of impossible event? 0 (or 0%)

3 - 4 Mark Questions (Frequently Asked):

1. Create frequency table from raw data: Given 20 data points, organize in frequency table

2. Calculate mean, median, mode: Find all three for given data set

3. Read and interpret bar graph: Answer questions based on given bar graph

4. Calculate percentage from frequency: Convert frequency to percentage

5. Draw simple bar graph: Create bar graph from frequency table

6. Calculate degrees for pie chart: Convert percentages to degrees

7. Draw pie chart: Create pie chart from given categories and percentages

8. Solve probability problem: Calculate probability from given information

9. Find range and mode: Identify both from dataset

10. Complete frequency table: Fill in missing frequencies

5 - 6 Mark Questions (Less Frequent but Important):

1. Complete data handling project: Collect, organize, analyze, and present data with graphs

2. Analyze multiple graphs: Compare data from different graphs and draw conclusions

3. Create both bar and pie charts: Show same data in two different ways

4. Detailed probability problems: Multi-step probability calculations

5. Comprehensive data interpretation: Analyze complex frequency tables and draw conclusions

6. Project-based assessment: Conduct survey, create all representations, write analysis

7. Compare statistical measures: Explain why mean/median/mode differ

8. Data prediction: Use probability to predict outcomes

9. Create and compare charts: Explain why one chart type is better than another

10. Statistical analysis: Calculate all measures and interpret what they mean