Class 8 Mathematics â€“ Data Handling | Interactive Visual Revision Notes

📝 Section 1 — Classroom Notes

🌎 Real-World Connection: The school cricket team scored 45, 62, 38, 55, 48, 62, and 70 in seven matches. The captain wants to know: What is the team’s average score (mean)? What was the middle score (median)? Which score appeared most often (mode)? News channels show bar charts of election results. Businesses use pie charts for their budgets. Data handling turns numbers into pictures and stories that everyone can understand!

📊 Topic 1: What Is Data?

Data means collected facts.
We gather data to learn things.
Data can be numbers or words.
Example: marks of students in a test.
Example: favourite fruits of your class.
Raw data is not sorted yet.

📊 Topic 2: Organising Data

Raw data is messy and hard to read.
We put it in a frequency table.
Frequency = how many times a value appears.
We use tally marks to count.
Every 5th tally is a cross line.
Tables make data easy to read.

📊 Topic 3: Grouped Data

When data has many values, we group it.
We make class intervals (ranges).
Example: 0–10, 10–20, 20–30.
Each group has a lower and upper limit.
The size of the class = upper − lower.
Grouped data is used for big data sets.

📊 Topic 4: Bar Graphs

A bar graph shows data using bars.
Bars can go up (vertical) or sideways (horizontal).
All bars have equal width.
The height of a bar = the value.
There is a gap between bars.
One axis shows items, the other shows numbers.

📊 Topic 5: Double Bar Graphs

A double bar graph compares two sets.
Two bars sit side by side for each item.
Each bar set has a different colour.
A legend tells which colour is which.
Example: boys vs girls in each sport.
It makes comparing very easy.

📊 Topic 6: Pie Charts

A pie chart is a circle chart.
The circle is cut into sectors (slices).
Each slice shows a part of the whole.
All slices add up to 100%.
All angles add up to 360 degrees.
Bigger slice = bigger share.

📊 Topic 7: Drawing Pie Charts

Find the angle for each item.
Use the formula below.
Draw a circle with a compass.
Use a protractor to mark angles.
Label each slice clearly.
Add a title to the chart.

Angle = (value ÷ total) × 360°

📊 Topic 8: Mean

Mean = average of all values.
Add up all the numbers.
Then divide by how many numbers there are.
Mean gives the central value.
Example: 2, 4, 6. Mean = 12 ÷ 3 = 4.
Mean is also called the arithmetic mean.

Mean = Sum of all values ÷ Number of values

📊 Topic 9: Median

Median = the middle value.
First, sort the numbers in order.
If count is odd, pick the middle one.
If count is even, average the two middles.
Example: 3, 5, 7. Median = 5.
Median is not changed by extreme values.

📊 Topic 10: Mode

Mode = the most frequent value.
It appears more often than others.
A data set can have no mode.
A data set can have two or more modes.
Example: 2, 3, 3, 5. Mode = 3.
Mode is useful for popular items.

🎨 Section 2 — Easy Illustrations

Picture 1: Frequency Table with Tally Marks

Tally marks help us count quickly. Every 5th mark goes across.

Picture 2: Bar Graph — Favourite Sports

Taller bars mean more students like that sport. Cricket is the favourite!

Picture 3: Double Bar Graph — Boys vs Girls

Two bars side by side make it easy to compare boys and girls.

Picture 4: Pie Chart — Monthly Expenses

Each slice is a part of the total. All slices add up to 360 degrees.

Picture 5: Mean, Median, Mode on a Number Line

Mean, median and mode are three ways to find the centre of data.

✏️ Section 3 — Worked Examples

Example 1: Draw a Pie Chart

Question: A family spends: Travel 30%, Food 25%, Rent 35%, Savings 10%. Draw a pie chart.

1 Find the angle for Travel: 30/100 × 360 = 108°.

2 Find the angle for Food: 25/100 × 360 = 90°.

3 Find the angle for Rent: 35/100 × 360 = 126°.

4 Find the angle for Savings: 10/100 × 360 = 36°.

5 Check: 108 + 90 + 126 + 36 = 360°. Correct!

6 Draw a circle. Mark each angle with a protractor.

7 Label each slice with the name and percentage.

Travel = 108°, Food = 90°, Rent = 126°, Savings = 36°

Formula: angle = (value ÷ total) × 360°

Example 2: Find Mean, Median and Mode

Question: Find mean, median and mode of: 4, 7, 3, 7, 9, 5, 7, 2, 8.

1 Mean: Add all numbers: 4+7+3+7+9+5+7+2+8 = 52.

2 Count the numbers: there are 9 values.

3 Mean = 52 ÷ 9 = 5.78 (rounded).

4 Median: Sort: 2, 3, 4, 5, 7, 7, 7, 8, 9.

5 9 values, so middle = 5th value = 7.

6 Mode: 7 appears 3 times (most often).

Mean ≈ 5.78, Median = 7, Mode = 7

Example 3: Reading a Double Bar Graph

Question: Cricket: Boys 15, Girls 12. Football: Boys 10, Girls 8. Tennis: Boys 7, Girls 11. Which sport has the most total players?

1 Cricket total = 15 + 12 = 27.

2 Football total = 10 + 8 = 18.

3 Tennis total = 7 + 11 = 18.

4 Compare: 27 > 18 = 18.

5 Cricket has the most total players.

Cricket has the most players (27 total)

Add both bars to find the total for each sport.

Term	What It Means	Key Fact
Data	Collected information	Numbers or facts
Frequency	How many times a value appears	Use tally marks
Class Interval	A group or range	0–10, 10–20
Bar Graph	Data shown using bars	Equal width bars
Double Bar Graph	Compares two data sets	Two bars side by side
Pie Chart	Circle divided into slices	Total = 360°
Angle Formula	Angle for a pie slice	(value/total) × 360
Mean	Sum ÷ count	The average
Median	Middle value when sorted	Sort first!
Mode	Most frequent value	Can have 0, 1, or more

📄 Section 5 — Take-Home Handout

📝 A. Fill in the Blanks

1. Data that is not organised is called _________ data.
2. A pie chart is a _________ divided into sectors.
3. The angle formula for a pie chart is (value ÷ total) × _________.
4. Mean is found by dividing the sum by the _________.
5. The value that appears most often is the _________.

✓ B. True or False

1. All bars in a bar graph must have equal width. _______
2. A pie chart can add up to 400 degrees. _______
3. The median needs data to be sorted first. _______
4. A data set can have more than one mode. _______
5. A double bar graph compares three data sets. _______

✏️ C. Solve These

1. Find the mean, median and mode of: 5, 3, 7, 3, 8, 3, 6.

Show your work here

2. A class has: Reading 40%, Sports 25%, Music 20%, Art 15%. Find the angle for each and draw a pie chart.

Show your work here

🔗 D. Match the Columns

Column A	Column B
1. Mean	a. Most frequent value
2. Mode	b. Circle chart
3. Pie chart	c. Middle value
4. Median	d. Sum ÷ count

🎨 E. Draw a Bar Graph

Draw a bar graph for: Maths = 12, Science = 9, English = 7, Hindi = 10. (Favourite subjects of 38 students.)

Draw your bar graph here

✅ Detailed Solutions — Section 5 Handout

A. Fill in the Blanks — Answers

1. Data that is not organised is called raw data.

2. A pie chart is a circle divided into sectors.

3. The angle formula for a pie chart is (value ÷ total) × 360°.

4. Mean is found by dividing the sum by the number of values.

5. The value that appears most often is the mode.

B. True or False — Answers

1. All bars in a bar graph must have equal width. — True. Bars should have equal width so they are fair to compare. ✓

2. A pie chart can add up to 400 degrees. — False. A full circle = 360°. Pie chart sectors always add to 360°.

3. The median needs data to be sorted first. — True. You must arrange values in order before finding the middle. ✓

4. A data set can have more than one mode. — True. If two values appear equally often, both are modes (bimodal data). ✓

5. A double bar graph compares three data sets. — False. A double bar graph compares two data sets side by side.

C1. Find mean, median and mode of: 5, 3, 7, 3, 8, 3, 6

1 Mean: Add all values: 5+3+7+3+8+3+6 = 35. Count = 7. Mean = 35 ÷ 7 = 5.

2 Median: Sort the data: 3, 3, 3, 5, 6, 7, 8. Middle value (4th of 7) = 5.

3 Mode: 3 appears 3 times (most frequent). Mode = 3.

Mean = 5, Median = 5, Mode = 3

C2. Pie chart angles: Reading 40%, Sports 25%, Music 20%, Art 15%

1 Formula: angle = (percentage ÷ 100) × 360°.

2 Reading: (40 ÷ 100) × 360 = 0.4 × 360 = 144°.

3 Sports: (25 ÷ 100) × 360 = 0.25 × 360 = 90°.

4 Music: (20 ÷ 100) × 360 = 0.20 × 360 = 72°.

5 Art: (15 ÷ 100) × 360 = 0.15 × 360 = 54°.

6 Check: 144 + 90 + 72 + 54 = 360°. ✓

Reading=144°, Sports=90°, Music=72°, Art=54°

D. Match the Columns — Answers

1. Mean → d. Sum ÷ count

2. Mode → a. Most frequent value

3. Pie chart → b. Circle chart

4. Median → c. Middle value

🃏 Section 6 — Revision Flashcards

👉

📊

What is data?

Data is collected information or facts. It can be numbers, words or observations.

🔢

What is a frequency table?

A table that shows each value and how many times it appears. Uses tally marks to count.

📈

How do you find the angle for a pie chart slice?

Angle = (value ÷ total) × 360°

All angles must add up to 360°.

🔎

What is the mean?

Mean = sum of all values divided by number of values. It is the average.

💡

What is the median?

Median is the middle value after sorting. If even count, average the two middle values.

🎯

What is the mode?

Mode is the value that appears most often. A set can have no mode, one mode, or many modes.

🔗

What is a double bar graph?

A bar graph with two bars side by side for each item. It compares two groups (like boys and girls).

🔧

Why do we group data?

When data has many different values, grouping into class intervals makes it easier to read and draw graphs.

Class 8 Mathematics — Data Handling

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Aligned with the Class 8 Mathematics syllabus. Independently created study material. Not affiliated with or endorsed by NCERT.

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📊 Class 8 Mathematics — Data Handling Interactive Visual Revision Notes Aligned with the Class 8 Mathematics syllabus. Independently created study material. Not affiliated with or endorsed by NCERT.

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