Chapter focus: Data is information collected about people, objects or events. Mathematics helps us organise data, represent it clearly and draw sensible conclusions from it.

🎯 Learning Goals

• Understand what data is and why it is collected.
• Organise information in tables using tally marks and frequencies.
• Read and construct pictographs.
• Read and construct simple bar graphs.
• Choose an appropriate scale while representing data.
• Answer questions by interpreting a data representation.
• Recognise that a graph must have a clear title, labels and scale.

📊 1. What Is Data?

Data is a collection of information gathered for a purpose.

For example, a teacher may record the number of books read by students in a month. The recorded numbers form data.

🗂️ 2. Organising Data

Raw data can be difficult to understand when it is written as a long list. A table helps us organise it.

✍️ 3. Tally Marks

Tally marks provide a quick way to count repeated observations. The fifth mark is drawn across the first four, forming a group of five.

Frequency tells us how many times an observation occurs.

🖼️ 4. Pictographs

A pictograph represents data using pictures or symbols. A key tells us what one picture represents.

Always check the key before counting pictures. One symbol does not necessarily mean one item.

📈 5. Bar Graphs

A bar graph uses rectangular bars to represent quantities. The height or length of a bar shows the value.

A simple bar graph should have:

• A clear title.
• Labels for the categories.
• A numerical scale.
• Equal intervals on the scale.
• Bars whose lengths match the data.

📏 6. Choosing a Scale

The scale tells us how values increase along the numerical axis. For small data, a scale such as 1 unit = 1 item may work. For larger data, one division might represent 2, 5, 10 or another suitable number.

The scale must be consistent. If one interval represents 5, the next equal interval should also represent 5.

🔍 7. Reading Data Carefully

Before answering a graph-based question, identify:

1. The title or topic.
2. What each category represents.
3. The scale or key.
4. The value represented by each bar or symbol.
5. Whether the question asks for a single value, comparison, total or difference.

📋 Worked Examples

Example 1 – Read a Table

Question: On which day were the most bottles sold?

Answer: Thursday, with 40 bottles.

Example 2 – Use a Pictograph Key

Suppose ★ represents 3 students. A category has 4 stars.

Calculation: 4 × 3 = 12.

Answer: 12 students.

Example 3 – Compare Data

If Class A collected 45 kg of paper and Class B collected 30 kg, then:

Difference = 45 − 30 = 15 kg.

Class A collected 15 kg more than Class B.

🧠 Data Reasoning

1. Why is a title important in a graph?
2. Why must the scale of a bar graph be consistent?
3. Why can a pictograph be misleading if its key is not given?
4. What is easier to compare: a long list of numbers or a suitable graph? Explain.
5. Can two different graphs represent the same data? Explain.

📝 Important Practice Questions

1. What is data? Give one example.
2. What is frequency?
3. What are tally marks used for?
4. What information does the key of a pictograph provide?
5. Name four features that should be checked before reading a bar graph.
6. Convert a small list of observations into a frequency table.
7. Create a pictograph using a suitable key for a set of classroom data.
8. Draw a simple bar graph from a table of four categories.
9. Find the greatest and least values in a given data set.
10. Find the difference between the greatest and least values.

🔥 Competency / HOTS Questions

1. A pictograph uses ★ = 4 students. One category has 7 symbols. How many students does it represent?
2. A graph has a scale of 5, 10, 15, 20, but one bar is drawn halfway between 10 and 15. What should you check before deciding its value?
3. Two students draw bar graphs for the same data but use different scales. Can both graphs be correct? Explain.
4. A student says the tallest-looking bar always represents the largest value. What other information must be checked?
5. Create a small data set about your class and decide whether a table, pictograph or bar graph would communicate it most clearly. Give a reason.

🧩 MCQ Practice

1. Data means —
   A. only numbers   B. collected information   C. only pictures   D. only measurements
2. Which is commonly used to count repeated observations quickly?
   A. Tally marks   B. Compass   C. Protractor   D. Ruler
3. In a pictograph, the key tells us —
   A. the title   B. what each symbol represents   C. the colour of the page   D. the order of questions
4. A bar graph should have a clear —
   A. scale   B. story   C. paragraph only   D. photograph
5. If ★ = 5 students, then ★★★ represents —
   A. 8   B. 10   C. 15   D. 20
6. Frequency tells us —
   A. how often an observation occurs   B. the colour of a bar   C. the title of a graph   D. the name of the student
7. Which is essential when reading a pictograph?
   A. Ignore the key   B. Check the key   C. Count only the first symbol   D. Ignore categories
8. The numerical intervals on a bar graph should be —
   A. random   B. inconsistent   C. clear and consistent   D. hidden

Answer Key: 1-B, 2-A, 3-B, 4-A, 5-C, 6-A, 7-B, 8-C

📄 Printable Worksheet

1. Define data in your own words.
2. Make a tally table for the following favourite fruits: Apple, Mango, Apple, Banana, Mango, Apple, Orange, Banana, Mango, Apple.
3. Convert the tally information into frequencies.
4. Create a pictograph where ★ = 2 students for four categories of your choice.
5. Write the key for your pictograph.
6. Use a given four-category data table to draw a bar graph.
7. Write a suitable title and label both axes.
8. Identify the greatest and least values from your graph.
9. Find the difference between the greatest and least values.
10. Write two conclusions that can be drawn from your graph.

🔁 Quick Revision Table

✅ Chapter Mastery Checklist

• ☐ I can explain what data means.
• ☐ I can organise data in a table.
• ☐ I can use tally marks and frequencies.
• ☐ I can read a pictograph and use its key.
• ☐ I can read a bar graph and interpret its scale.
• ☐ I can construct a simple bar graph.
• ☐ I can compare values and find differences.
• ☐ I can draw conclusions from data.

🔗 Continue Learning

← Back to Class 6 Mathematics Chapter Hub

Continue to Chapter 5 – Prime Time →

📖 Verify the current NCERT textbook →

Study note: TeachGyan provides original supplementary learning support. Students should follow the textbook prescribed by their school for the current academic session.