Class 6 Maths · Chapter 4
Short answer: Class 6 Maths Ganita Prakash ka Chapter 4 "Data Handling and Presentation" sikhata hai ki roz-marra ka data (jaise favourite subjects, rainfall, vehicle count) kaise collect karke tally marks se organize karte hain, aur phir usko pictograph aur bar graph me visually present karte hain.
Class 6 Maths ke Ganita Prakash textbook ka Chapter 4, "Data Handling and Presentation", bachchon ko sikhata hai ki roz-marra ki zindagi me collect hone wale data — jaise class ke students ke favourite fruits, ek hafte ka temperature, ya kisi road pe guzarne wali gaadiyon ki ginti — ko kaise organize aur present kiya jaaye taaki wo samajhne me aasan ho jaaye.
Ye chapter statistics ki neev hai. Yahan seekhe gaye concepts — raw data, tally marks, frequency distribution table, pictograph aur bar graph — aage Class 7-8 ke "Data Handling" advanced topics (mean, median, mode, pie charts) ki base banate hain. Jaise Class 10 Chemistry me Chapter 1 poori kitab ki neev hota hai, waise hi ye chapter data-based reasoning ki shuruaat hai jo boards tak chalti hai.
Naye rationalised syllabus (2026-27 session) me is chapter ka scope purani 14-chapter "Mathematics" textbook ke comparison me expand kiya gaya hai — pictograph aur bar graph dono ko zyada depth se cover kiya gaya hai, aur real-world data collection activities add ki gayi hain. Poore Ganita Prakash Class 6 syllabus me total 10 rationalised chapters hain: Patterns in Mathematics, Lines and Angles, Number Play, Data Handling and Presentation, Prime Time, Perimeter and Area, Fractions, Playing with Constructions, Symmetry, aur The Other Side of Zero — is chapter-wise list ko do independent sources se verify kiya gaya hai taaki NCERT Class 6 Maths new syllabus vs old syllabus ka comparison clear rahe.
Chapter 4 Summary — 5 Minute Revision
"Data Handling and Presentation" chapter 4 major skills sikhata hai:
- Data collection — survey ya observation se raw (unorganized) data ikattha karna, jaise "Class ke 30 students me se kaun sa fruit sabse zyada pasand hai" jaisa sawaal poochh kar.
- Organizing data — tally marks (|, ||, |||, ||||, ठ) ka use karke frequency distribution table banana, jisse raw data readable form me aa jaata hai.
- Pictograph — data ko pictures/symbols ke through represent karna, jahan har symbol ek fixed value (scale, jaise "1 symbol = 5 students") represent karta hai.
- Bar graph — data ko equal-width rectangular bars ke through represent karna, jahan bar ki height/length uss category ki frequency ke proportional hoti hai.
- Data ko interpret karna — graph ya table dekh kar sawaalon ke jawaab nikalna, jaise "sabse zyada/kam frequency kis category ki hai" ya "do categories ka difference kitna hai".
In sab concepts ka real-life application hai — school surveys, weather records, sports scores, aur market research — isliye ye chapter sirf exam ke liye nahi, practical life-skill ke liye bhi important hai.
In-Text Questions — Solutions
Ek class me 20 students se poocha gaya ki unka favourite season kaunsa hai. Jawaab yeh mile: Summer, Winter, Summer, Rainy, Winter, Summer, Winter, Rainy, Summer, Winter, Summer, Winter, Rainy, Summer, Winter, Summer, Rainy, Winter, Summer, Winter. Tally marks bana kar frequency table banao.
Solution:
| Season | Tally Marks | Frequency |
|---|---|---|
| Summer | ठ ||| | 8 |
| Winter | ठ ||| | 8 |
| Rainy | |||| | 4 |
↔ Table ko side me swipe karein
Total students = 8 + 8 + 4 = 20
Frequency table banane ke baad hamesha total ko original data points ki ginti se match karo — yahan total 20 diye gaye data points ke barabar hai, isliye tally sahi hai.
Ek pictograph me agar 1 symbol (🍎) = 10 apples represent karta ho, aur 'Monday' row me 3.5 symbols dikhaye gaye hon, to Monday ko kitne apples beche gaye?
Solution:
1 symbol = 10 apples
3.5 symbols = 3.5 × 10 = 35 apples
Isliye Monday ko 35 apples beche gaye. Half symbol ka matlab hota hai scale value ka aadha (yahan 10 ka half = 5).
Bar graph me x-axis pe 'Fruits' (Apple, Banana, Mango, Grapes) diye hain aur y-axis pe 'Number of students who like it' diya hai, scale 1 unit = 2 students. Agar Mango ka bar 9 units tak jaata hai, to kitne students ko Mango pasand hai?
Solution:
1 unit = 2 students
9 units = 9 × 2 = 18 students
Isliye 18 students ko Mango pasand hai. Bar graph padhte waqt hamesha pehle scale check karo, phir bar ki height ko scale se multiply karo — seedha number of units mat likh do.
Neeche di gayi frequency table se bar graph banane ke liye scale kaise choose karoge agar values 5, 40, 25, 15 hain?
Solution: Jab data me values ka range chhota se bada (5 se 40) ho, to hume aisa scale choose karna chahiye jisse graph na zyada bada ho na zyada chhota.
Agar hum 1 unit = 5 le, to bars honge: 1, 8, 5, 3 units — ye readable aur compact hoga.
Agar hum 1 unit = 1 le, to Apple ka bar 40 units tak jaayega, jo bahut lamba ho jaayega aur page pe fit nahi hoga.
Isliye scale hamesha data ke maximum value aur available graph space dono ko dekh kar choose kiya jaata hai.
Exercise Questions — Solutions (Q1–Q5)
Ek shopkeeper ne pichle 6 dinon me becha hua ice-cream cones ka data record kiya: Mon-12, Tue-18, Wed-9, Thu-15, Fri-20, Sat-24. Is data ko bar graph me represent karne ke liye ek suitable scale suggest karo aur table banao.
Solution:
| Day | Cones Sold |
|---|---|
| Monday | 12 |
| Tuesday | 18 |
| Wednesday | 9 |
| Thursday | 15 |
| Friday | 20 |
| Saturday | 24 |
↔ Table ko side me swipe karein
Maximum value 24 hai, isliye suitable scale 1 unit = 3 cones lena theek hoga (24 ÷ 3 = 8 units, jo manageable hai).
Monday: 12 ÷ 3 = 4 units, Tuesday: 18 ÷ 3 = 6 units, Wednesday: 9 ÷ 3 = 3 units, Thursday: 15 ÷ 3 = 5 units, Friday: 20 ÷ 3 = 6.67 units (approx 6.7), Saturday: 24 ÷ 3 = 8 units
X-axis pe Days, Y-axis pe Number of Cones (scale 1 unit = 3) rakh kar bars draw karo.
Ek class ke 25 students ka favourite subject survey kiya gaya: Maths-8, Science-6, Hindi-4, English-5, Social Science-2. (a) Frequency table banao. (b) Kaunsa subject sabse zyada pasand kiya gaya? (c) Maths aur Hindi pasand karne walon ka difference nikaalo.
(a) Solution:
| Subject | Number of Students |
|---|---|
| Maths | 8 |
| Science | 6 |
| Hindi | 4 |
| English | 5 |
| Social Science | 2 |
↔ Table ko side me swipe karein
Total = 8 + 6 + 4 + 5 + 2 = 25 ✓ (matches given total)
(b) Sabse zyada pasand kiya gaya subject Maths hai (8 students).
(c) Difference = 8 − 4 = 4 students
Ek pictograph me 'Number of cars sold by a showroom' diya gaya hai, jahan 1 🚗 symbol = 4 cars. January me 5 symbols, February me 3.5 symbols, March me 6 symbols dikhaye gaye hain. Har mahine ke actual cars nikaalo aur total sales calculate karo.
Solution:
1 symbol = 4 cars
January = 5 × 4 = 20 cars
February = 3.5 × 4 = 14 cars
March = 6 × 4 = 24 cars
Total sales = 20 + 14 + 24 = 58 cars
Neeche diye gaye raw data ko tally marks se organize karo: Blood groups of 15 students — A, B, O, A, AB, O, A, B, O, O, A, AB, O, A, B
Solution:
| Blood Group | Tally Marks | Frequency |
|---|---|---|
| A | ठ | 5 |
| B | ||| | 3 |
| O | ठ | 5 |
| AB | || | 2 |
↔ Table ko side me swipe karein
Total = 5 + 3 + 5 + 2 = 15
Frequency table banane ke baad total ko original 15 data points se match karke verify kiya gaya — sabhi entries sahi tally hui hain.
Ek bar graph me y-axis pe scale '1 unit = 50 books' diya hai. Agar 'Story Books' ka bar 4.5 units tak jaata hai aur 'Comics' ka bar 6 units tak jaata hai, to dono categories ke beech books ka difference nikaalo.
Solution:
Story Books = 4.5 × 50 = 225 books
Comics = 6 × 50 = 300 books
Difference = 300 − 225 = 75 books
Important Equations — Ek Nazar Me
| Term | Definition / Formula |
|---|---|
| Raw Data | Bina organize kiya hua original data jo survey/observation se collect hota hai |
| Tally Marks | Har item ke liye ek vertical line (|); 5th item ke liye 4 lines ko cross karke (ठ) group banate hain |
| Frequency | Kisi particular value/category ke repeat hone ki total ginti |
| Pictograph Value | Actual Value = Number of Symbols × Scale (1 symbol jitna represent karta hai) |
| Bar Graph Value | Actual Value = Bar ki Height (in units) × Scale (1 unit jitna represent karta hai) |
| Range of Data | Range = Maximum value − Minimum value |
| Scale Selection Rule | Scale = aisa number choose karo jisse maximum value ka bar readable size ka bane (na zyada chhota, na zyada bada) |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Tally marks banate waqt 5th mark ko pehle 4 marks ko cross karke nahi banate — students seedhi 5 vertical lines bana dete hain, jisse counting mushkil ho jaati hai
- Pictograph padhte waqt scale (1 symbol = kitni value) ignore kar dete hain aur directly symbols ki ginti likh dete hain jawaab me
- Half ya quarter symbol ka matlab samajhne me galti karte hain — half symbol hamesha scale value ka half hota hai, poora symbol nahi
- Bar graph banate waqt bars ki width alag-alag rakh dete hain, jabki har bar ki width equal honi chahiye — sirf height/length data represent karti hai
- Frequency table banane ke baad total sum check nahi karte, jisse koi tally mark miss ho jaaye to bhi pata nahi chalta
- Bar graph ka scale choose karte waqt maximum value ko consider nahi karte, jisse graph ya to bahut chhota ban jaata hai ya page se bahar chala jaata hai
Board-Style Important Questions
- Class 6 school-level assessments me tally marks se frequency table banane wale questions frequently poochhe jaate hain
- Pictograph se related 'find the actual value using scale' type questions common hain periodic tests me
- Bar graph draw karne aur usse data interpret karne wale combined questions unit tests me aate hain
- Real-life survey-based data (favourite subject, fruit, sport) collect karke organize karne wale project-style questions bhi poochhe jaate hain
- Do bar graphs/pictographs compare karke difference nikaalne wale application-based questions bhi dekhe gaye hain
Aksar Poochhe Jaane Wale Sawaal
Class 6 Maths Chapter 4 Data Handling and Presentation me kya-kya topics cover hote hain?
Is chapter me raw data collect karna, tally marks se frequency table banana, pictograph banana/padhna, aur bar graph banana/padhna cover hota hai — sabhi real-life examples ke saath.
Tally marks kaise banate hain?
Har occurrence ke liye ek vertical line (|) banate hain. Jab 5th occurrence aaye, to pehle ki 4 lines ko ek diagonal/horizontal line se cross kar dete hain (ठ), jisse ek group of 5 ban jaata hai — isse counting fast ho jaati hai.
Pictograph aur bar graph me kya difference hai?
Pictograph me data ko symbols/pictures se represent karte hain (har symbol ek fixed value ke barabar hota hai), jabki bar graph me data ko rectangular bars se represent karte hain jinki height/length value ke proportional hoti hai. Bar graph generally zyada precise hota hai, especially decimal values ke liye.
Is chapter ka naam poore rationalised Ganita Prakash syllabus me kaunse number pe aata hai?
Ganita Prakash Class 6 Maths (2026-27 session) me total 10 chapters hain, aur 'Data Handling and Presentation' inme se ek hai. Poori list: Patterns in Mathematics, Lines and Angles, Number Play, Data Handling and Presentation, Prime Time, Perimeter and Area, Fractions, Playing with Constructions, Symmetry, The Other Side of Zero.
Is chapter ke solutions/notes PDF me kahan milenge?
NCERT ki official website (ncert.nic.in) se Ganita Prakash Class 6 Maths ka current session (2026-27) ka PDF free download kiya ja sakta hai. Har chapter ka separate PDF available hota hai.
Ye chapter Class 7-8 ke liye kaise important hai?
Class 6 me seekhe gaye data organization aur graph-reading skills, Class 7-8 me advanced Data Handling topics jaise mean, median, mode, pie charts, aur probability ki neev banate hain — isliye is chapter ki solid understanding aage ke concepts ko easy bana deti hai.
Class 6 Maths — Saare Chapters
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