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Data Handling and Presentation – Class 6 Maths Chapter 4 Notes & NCERT PDF

Class 6MathematicsChapter 4NCERT book: Ganita Prakash - Mathematics Class 6

Notes and a simple summary of Chapter 4 of the NCERT Class 6 Mathematics book, with the official chapter PDF, flashcards, an MCQ quiz and an AI tutor for your doubts.

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Chapter 4: Data Handling and Presentation

Introduction

Any collection of facts, numbers, measures, observations or other descriptions of things that convey information about those things is called data.

Favourite colours of classmates, weights of students, tickets sold at a station — all are data. This chapter shows how to collect, organise, present and interpret data using tally marks, frequency tables, pictographs and bar graphs, and warns how fancy pictures can mislead.

Key Ideas

4.1 Collecting and Organising Data

  • Navya and Naresh list each classmate's favourite game (31 children). The list alone does not show the winner; counting each game does. Hockey is most popular with 8 votes (Kabaddi 6, Cricket 6, Satoliya/Pittu 5, Football 4, Badminton 2).
  • Some questions need data collection (most popular TV show, water wasted in a locality); others don't (when India got independence, the capital of India).
  • Tally marks: Shri Nilesh records sweet choices with one mark per student, crossing every group of four with a fifth. Jalebi 6, Gulab jamun 9, Gujiya 13, Barfi 3, Rasgulla 7. These counts are frequencies. The table tells him how many of each sweet to buy but not which child chose which.
  • Ordering helps: Sushri Sandhya arranges shoe sizes in ascending order (3, 3, 3, 4, …, 7) and can instantly see the smallest size (3), largest (7), 10 students with size 5, and 15 students with sizes larger than 4.

    • 4.2 Pictographs

    A pictograph shows data with pictures. A key (scale) tells what one symbol stands for — 1 student, 5 students or 10 children. In Nand Kishor's sleep survey (1 symbol = 10 children): 5 symbols = 50 children always slept 9 hours, 2½ symbols = 25 sometimes, 4 symbols = 40 never. Half symbols show half the key. Pictographs get hard when data is large or counts (like 33 or 27) are not multiples of the key.

    4.3 Bar Graphs

    Bar graphs use bars of equal width with equal gaps; the length or height shows the frequency. A scale is chosen so the graph fits (e.g. 1 unit = 100 vehicles, 1 unit = 10 crore people). At a busy Delhi crossing, traffic peaked at 1200 vehicles (7–8 a.m.), then 1000 (8–9 a.m.), and was lowest (about 150) from 6–7 a.m. From 8 to 10 a.m. about 1000 + 800 = 1800 vehicles passed.

    4.4 Drawing a Bar Graph

  • Draw a horizontal and a vertical line.
  • Mark categories equally spaced on one line.
  • Choose a scale so the graph fits your paper; markings must start from zero.
  • Draw bars of equal width with equal gaps.

    • Imran's family budget with 1 unit = ₹200: rent ₹3000 → 15 units, food ₹3400 → 17 units, education ₹800 → 4, electricity ₹400 → 2, transport ₹600 → 3, miscellaneous ₹1200 → 6. Food is the biggest expense, then rent; electricity is half of education; education is less than one-fourth of food.

    4.5 Artistic and Aesthetic Considerations

  • Heights (like mountains) look natural as vertical bars (column graphs); lengths along the ground (like rivers or distances) suit horizontal bars.
  • Infographics add pictures and colour to data. But beware: in the mountain infographic, taller triangles are also wider, and Everest (8848 m) looks twice as tall as Elbrus (5642 m) — yet 5642 × 2 = 11,284, far more than 8848. Pretty pictures can mislead.

    • Worked Examples

  • Pictograph with key 1 symbol = 10 children: 2 full symbols + 1 half symbol = 20 + 5 = 25 children.
  • Finding the scale: Vidisha's bar (24 tickets) is 6 units; Jabalpur's (20 tickets) is 5 units → 24 ÷ 6 = 4 tickets per unit.
  • Mudhol hounds (18, 36, 12, 48, 18, 24): all are multiples of 6, so a good key is 1 symbol = 6 dogs. Village B needs 36 ÷ 6 = 6 symbols. B + D = 84, more than the other four villages together (72) — Kamini is right.
  • Bar heights: ₹3400 with 1 unit = ₹200 → 3400 ÷ 200 = 17 units.
  • Tigers in India: about 1400 (2006) to 3700 (2022), an increase of about 2300.

    • Figure it Out — Hints

  • Always read the key/scale first before counting symbols or bars.
  • For a frequency table, list categories, make tally marks, then count.
  • To find a total from a frequency table (like Bumrah's wickets), multiply each value by its frequency and add — don't just add 0 + 1 + 2 + … + 7.
  • Check any graph for errors: equal widths, equal gaps, scale starting at 0.

    • Maths Words

  • Data (आँकड़े), Frequency (बारंबारता)
  • Tally marks (मिलान चिह्न), Frequency table (बारंबारता सारणी)
  • Pictograph (चित्रालेख), Key / Scale (कुंजी / पैमाना)
  • Bar graph (दंड आलेख), Column graph (स्तंभ आलेख)
  • Ascending order (आरोही क्रम)
  • Infographic (इन्फोग्राफ़िक)
  • Survey (सर्वेक्षण)

    • Common Mistakes

  • Ignoring the key and counting each symbol as 1.
  • Bars of different widths or uneven gaps.
  • Starting the scale at a number other than 0, which exaggerates differences.
  • Adding only the category values instead of value × frequency for totals.
  • Trusting an infographic's picture instead of its numbers.

    • Maths in Daily Life

    Newspapers, election results, weather reports, school attendance and household budgets all use tables and graphs. Reading them carefully helps us make good decisions and avoid being misled.

    💡 Key Learning Points

    • ✓Understand data and organise it with tally marks and frequency tables
    • ✓Read and draw pictographs using a key, including half symbols
    • ✓Read and draw bar graphs with equal-width bars, equal gaps and a scale starting from zero
    • ✓Choose a sensible scale and orientation (vertical for heights, horizontal for lengths)
    • ✓Interpret data to answer questions and recognise misleading infographics

    👨‍🏫 Teaching Tips

    • →Run the favourite-game survey in your own class with tally marks, then compare with Navya and Naresh's result
    • →Let groups make the same data into a pictograph (with a key) and a bar graph, then discuss which is easier to read
    • →Give a bar graph with deliberate mistakes (unequal widths, scale not from 0) for students to fix, like the tiger graph
    • →Use newspaper graphs and ask students to find the scale and one fact the graph shows
    • →Have students count letters c, e, i, r, x in a news item and compare orders across the class
    • →Show the mountain infographic and ask: 'Is Everest really twice as tall as Elbrus?'
    • →Collect weekly class attendance and draw a live bar graph on the wall

    📋 Assessment Questions

    1. Can the student build a frequency table from raw data using tally marks?
    2. Can the student read a pictograph correctly using its key, including half symbols?
    3. Can the student choose a suitable scale and draw a neat bar graph?
    4. Can the student answer comparison questions (most, least, how many more) from a graph?
    5. Can the student explain why an infographic might be misleading?

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    Keep learning

    All chapters in Ganita Prakash - Mathematics Class 6

    1. 1. Patterns in Mathematics
    2. 2. Lines and Angles
    3. 3. Number Play
    4. 4. Data Handling and Presentation
    5. 5. Prime Time
    6. 6. Perimeter and Area
    7. 7. Fractions
    8. 8. Playing with Constructions
    9. 9. Symmetry
    10. 10. The Other Side of Zero