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JAC • Class 6 • Mathematics • Ch 18

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Data Handling

In JAC Board Class 6 Mathematics, "Data Handling" explores the collection, organization, and visual representation of quantitative data. Students master tally mark frequency tables, construct and interpret pictographs with scaling keys, and create bar graphs with uniform bar widths and proportional heights.

View All Chapters JCERT Hindi Textbook

Overview Core Concepts Formulas & Identities Solved Examples Common Traps Summary Self Check Take MCQ Test

📊 Have You Ever Wondered?

How do election news channels and cricket broadcasts summarize millions of votes and scores in a split second?

Data is the new gold! Learn how tally marks, pictographs, and bar charts transform raw chaos into clear visual intelligence.

Why This Chapter Matters

Before You Begin (Prerequisites)

Counting and basic arithmetic
Using a ruler

What You Will Learn (Core Objectives)

Record and organize raw data using Tally Mark tables.
Interpret and draw Pictographs with appropriate scaling symbols.
Interpret and draw Bar Graphs with uniform spacing, width, and scale.

Chapter Roadmap & Progression

1 Syllabus and book alignment

2 1. Data, Tally Marks & Frequency

3 2. Pictographs

4 3. Bar Graphs

Complete Concept Guide (100% Curriculum Coverage)

Syllabus and book alignment

JCERT 2026–27: Regular schools (Non-SOE) — Chapter 18 · Data Handling. Syllabus pages 277–294. These notes follow this topic. Official syllabus. Official JCERT Hindi textbook. Some source PDFs are damaged. The supplementary reference uses different chapter numbering.

1. Data, Tally Marks & Frequency

Data is a collection of numbers gathered to give information. Tally marks group counts into bundles of 5 (four vertical strokes crossed by a fifth diagonal stroke: ~~||||~~) for rapid counting.

2. Pictographs

A Pictograph represents data through pictures or symbols of objects. A scale/key must be clearly stated (e.g., 1 icon = 100 books, or 1 icon = 10 cars). Half symbols represent half quantities.

3. Bar Graphs

A Bar Graph represents data using bars of uniform width drawn with equal spacing between them. The length or height of each bar represents the given frequency along a chosen scale (e.g., 1 unit length = 10 students).

Key Formulas, Identities & Theorems

Bar Height Formula

$$\text{Height of Bar} = \frac{\text{Data Value}}{\text{Scale Unit Value}}$$

Calculates bar units on y-axis.

Conceptual Solved Examples & Case Studies

Example 1

If a pictograph uses 1 tree symbol to represent 20 trees, how many symbols represent 90 trees?

Step-by-Step Solution:

Number of symbols $= \frac{90}{20} = 4.5$, which is drawn as 4 complete tree symbols and 1 half-tree symbol.

Common Misconceptions & Examiner Traps

Common Misconception

Drawing bars of unequal widths or unequal spaces between them in a bar graph.

Scientific Reality & Correction

All bars must have identical width, and the horizontal spacing between consecutive bars must remain uniform.

Visual Learning & Conceptual Map

Data Representation Modalities

Tally Tables -> Pictographs -> Bar Graphs

Tally Marks

Bundles of 5 for counting raw data.

Pictograph

Picture symbols with a defined key.

Bar Graph

Uniform bars; height proportional to value.

Chapter Summary & 10 Key Takeaways

Takeaway 1

Data is organized using tally marks in frequency tables.

Takeaway 2

Pictographs use symbols and keys to depict quantities.

Takeaway 3

Bar graphs use bars of uniform width and equal spacing to visualize comparative data.

Check Your Understanding (Diagnostic Practice Questions)

Diagnostic questions testing core conceptual clarity. Answers are hidden initially — solve each problem first, then click to reveal the step-by-step verified solution.

Why is choosing an appropriate scale critical when drawing a bar graph?

Reveal Answer & Explanation

Answer: If the scale is too small, the bars will be too tall to fit on the paper. If the scale is too large, differences between categories will be microscopic and unreadable.
Balance page size with readability.

Chapter practice

CBT tests for this chapter are not published yet. Solve the self-check questions above and compare your answers.

All Class 6 Mathematics Chapters

Ch 1: Knowing Our Numbers Ch 2: Whole Numbers Ch 3: Integers Ch 4: Playing with Numbers Ch 5: Fractions Ch 6: Decimals Ch 7: Ratio and Proportion Ch 8: Algebra Ch 9: Line, Line Segment and Ray Ch 10: Pairs of Lines Ch 11: Angles Ch 12: Polygons Ch 13: Circle Ch 14: Three-Dimensional Shapes Ch 15: Symmetry Ch 16: Practical Geometry Ch 17: Perimeter and Area Ch 18: Data Handling

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