Introduction and Graphs Class 6 ICSE — Maths Chapter 25
Introduction and graphs class 6 ICSE maths shows how numbers become pictures you can read. Chapter 25 of the Class 6 Mathematics book opens with statistics, explains what data is, and then teaches three ways to draw it. You will learn the bar graph, the pie chart, and the line graph, and when each one fits best. Read the sections in order because each graph builds on the one before it.
Download Introduction and Graphs Class 6 ICSE Mathematics Chapter 25 PDF
Download the Introduction and Graphs Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 8 pages, 6 sections, 17 questions.
What is inside Chapter 25
8 pages · 6 sections · 10 worked examples · 17 exercise questions
| Section | Title |
|---|---|
| 25.1 | INTRODUCTION |
| 25.2 | DATA |
| 25.3 | REPRESENTATION OF DATA |
| 25.4 | BAR GRAPH (Column graph) |
| 25.5 | PIE GRAPH |
| 25.6 | LINE GRAPH |
- EXERCISE 25(A): 6 questions
- EXERCISE 25(B): 4 questions
- Revision Exercise (Chapter 25): 7 questions
25.1 INTRODUCTION
Statistics is the science that deals with the collection, classification, tabulation, representation and interpretation of data. Those five steps are the whole subject in one line. You gather numbers, sort them, put them in a table, draw them, and then say what they mean.
In statistics, numerical facts are collected as numbers, not as opinions. For instance, you measure the heights of Class 6 children from ten different schools in Delhi. That set of heights, written as figures, is the data statistics works with. The official CISCE syllabus at cisce.org frames what this Class 6 ICSE chapter expects you to do with such facts.
This chapter takes you from a raw list of numbers to a finished graph. Each of the next sections adds one skill: identifying data, choosing a picture, and drawing it correctly.
25.2 DATA
Each number collected to give required information is called data. One number alone is a single observation; the whole set is the data. Suppose you want to know how many members live in families in a locality. You visit, say, fifty families and record their answers.
The information can be summarised in a table. One column lists the number of members, the other lists how many families match that size. A short table shows the pattern at once, while a long list of fifty answers hides it. Data should always be put in a form that gives a fair idea of the information it carries.
Data is collected and used by government departments, educational institutions and companies. Figures on population, taxes, food, education, finances and agriculture all come from such records. Almost every field today uses statistical data in some form. You can find every chapter of this book, including the earlier work on solids, inside the Class 6 Mathematics book.
25.3 REPRESENTATION OF DATA
Statistical data can be presented in several ways: as a table, as pictures, as graphs, or as figures. Graphs and figures stay in the mind longer than written statements. A reader can see a rise or a fall at a glance, where a paragraph would need careful reading.
The common graph forms are pictographs, bar graphs, line graphs, pie charts and histograms. This chapter covers only three of them: the bar graph, the pie graph and the line graph. Histograms are named here so you know the full family of graphs, but they are not studied in this Class 6 ICSE chapter.
That scope matters for your practice. When you reach the exercises, you will draw bars, circles and line segments — nothing else. Focus your effort on those three forms. The habits you build here also carry across the rest of the Class 6 books.
25.4 BAR GRAPH (Column graph)
A bar graph is the simplest way to present data. It uses bars, usually vertical, all of the same width. The height of each bar matches the number it represents, so a taller bar always means a bigger value.
The drawing rules come straight from the book. Keep them in mind for every graph:
- Bars are rectangles; equal widths make comparison easy.
- The height of a bar represents a quantity; the width represents nothing.
- All bars must have the same width.
- The space between consecutive bars must be equal.
- Use graph paper or plain paper, as you prefer.
Here is a worked pattern with fresh numbers. Five students sold tickets: A sold 6, B sold 12, C sold 9, D sold 15 and E sold 8. Total sold is 6 + 12 + 9 + 15 + 8 = 50.
The average uses the formula:
\frac{\text{Total number of tickets sold}}{\text{Total number of students}}
= \frac{50}{5} = 10
So the average student sold 10 tickets. The most common errors here are unequal bar widths and unequal gaps between bars. Both make the graph misleading, because the eye reads size and spacing as meaning.
25.5 PIE GRAPH
When data is shown by the sectors of a circle, the result is called a pie graph or a pie chart. It is called a pie because the sectors look like slices cut from a pie.
The central idea is simple. A full circle has 360^\circ at its centre. To draw a pie chart, divide those 360^\circ in proportion to the given numbers.
The book gives three steps:
- Step 1: Build a table that lists each category, its value, and its central angle.
- Step 2: Draw a circle of any suitable radius.
- Step 3: For each central angle, draw a sector from the centre.
The angle for one category is \frac{\text{part}}{\text{total}} \times 360^\circ.
Worked pattern with original numbers. Suppose 40 children choose four activities: Reading 10, Sports 15, Music 5 and Art 10. The angles are:
\frac{10}{40} \times 360^\circ = 90^\circ,\quad \frac{15}{40} \times 360^\circ = 135^\circ
\frac{5}{40} \times 360^\circ = 45^\circ,\quad \frac{10}{40} \times 360^\circ = 90^\circ
The four angles add to 360^\circ, which is your check. If they do not, you have made an arithmetic slip.
25.6 LINE GRAPH
A line graph is made by marking each value as a thick point and then joining the points with straight line segments. It is best for showing how a quantity changes over time.
The book’s pattern uses temperatures. Days go along the horizontal axis, and temperatures go up the vertical axis. Each day gets one point at the right height, and the segments between points trace the rise and fall.
Here is the edge case the book stresses. If all temperatures lie between 30^\circ\mathrm{C} and 45^\circ\mathrm{C}, draw the vertical scale only for that range. Below 30^\circ\mathrm{C}, draw a zigzag line. That zigzag tells the reader the lower values are ignored, so the graph can use a larger, clearer scale.
Worked pattern. A week of readings: 31, 34, 33, 36, 38, 35, 32. All sit between 30 and 45, so the scale runs from 30 to 45 with a zigzag under 30. The points then spread over the full height of the paper instead of crowding at the bottom.
Here is how the three graphs compare:
| Graph | What it shows | Best used when |
|---|---|---|
| Bar graph | Separate categories compared by height | Comparing a few distinct items |
| Pie chart | Parts of a whole, as angles | Showing shares that add to 100% |
| Line graph | Change over time, point to point | Tracking a value across days or years |
Pick the graph that matches the story in your data.
What to practise from Introduction and Graphs Class 6 ICSE
The chapter carries three question blocks. Work through them in order.
- EXERCISE 25(A) — 6 questions on drawing and reading bar graphs.
- EXERCISE 25(B) — 4 questions on pie graphs and line graphs.
- Revision Exercise (Chapter 25) — 7 mixed questions covering all three graphs.
Attempt each question with the data tables in front of you, then check your angles add to 360^\circ and your bars keep equal widths.
Introduction and Graphs Class 6 ICSE frequently asked questions
What is the difference between a bar graph and a line graph in class 6 ICSE?
A bar graph uses separate bars of equal width, with height showing each value. A line graph marks values as points and joins them with segments. Use a bar graph for separate categories and a line graph for change over time.
How do I calculate the central angle for a pie chart?
Use \frac{\text{part}}{\text{total}} \times 360^\circ. For example, if 10 of 40 children chose reading, the angle is \frac{10}{40} \times 360^\circ = 90^\circ. Check that all angles add to 360^\circ.
What does the zigzag line mean in a line graph?
The zigzag line below the lowest value on the vertical scale shows that values under that point are ignored. It lets the graph start at a higher number, such as 30^\circ\mathrm{C}, so the plotted points spread across the page.
When should I use a bar graph instead of a pie chart?
Use a bar graph to compare a few separate items by size, such as tickets sold by different students. Use a pie chart when the data shows parts of a whole, where the shares should add to 100%.
Reference: ICSE Class 6 Mathematics textbook material, chapter 25: Introduction and Graphs — CISCE-aligned.