This MCQ module is based on: Collecting and Organising Data
TOPIC 12 OF 41
Collecting and Organising Data
🎓 Class 6
Mathematics
CBSE
Theory
Ch 4 — Data Handling and Presentation
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Collecting and Organising Data
Targeting Class 6 level in Statistics, with Basic difficulty.
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Chapter 4 — Data Handling and Presentation
If you ask your classmates about their favourite colours, you will get a list of colours. This list is an example of data?. Similarly, if you measure the weight of each student in your class, you would get a collection of measurements — again, data. We live in an age of information. In this chapter, we learn how to collect, organise, present, and interpret data so we can make meaningful inferences.
Definition
Data is any collection of facts, numbers, measurements, observations or descriptions of things that convey information about those things.
4.1 Collecting and Organising Data
Navya and Naresh are discussing their favourite games. They want to find the most popular game in their class. Each classmate writes their name and favourite game on small chits. Naresh hands Navya a long unordered list.
Example list (p. 75)
Mehnoor–Kabaddi, Pushkal–Satoliya (Pittu), Ananya–Kabaddi, Jubinoor–Hockey, Denny–Badminton, Jivika–Satoliya (Pittu), Simran–Kabaddi, Jivika–Satoliya (Pittu), Rajesh–Football, Nand–Satoliya (Pittu), Leela–Hockey, Tisara–Football, Ankita–Kabaddi, Afshan–Hockey, Soumya–Cricket, Iman–Hockey, Reetat–Cricket, Navjot–Hockey, Yuvraj–Cricket, Gurpreet–Hockey, Hemal–Satoliya (Pittu), Rehana–Hockey, Arsh–Kabaddi, Debadyuta–Football, Aarna–Badminton, Bhavya–Cricket, Ananya–Hockey, Kunjal–Football, Sarah–Kabaddi, Hardik–Cricket, Tahira–Cricket.
"I have collected the data but can't see the most popular game now!" says Navya sadly. Organising the raw list makes it easier to answer questions.
Figure it Out (4.1)
Q1. What would you do to find the most popular game among Naresh's and Navya's classmates?
Count the number of students who preferred each game. Use a tally-mark table by listing unique games and making one mark per student. The game with the highest count is the most popular.
Q2. What is the most popular game in their class?
Counting the list — Hockey = 7, Kabaddi = 6, Cricket = 6, Satoliya(Pittu) = 5, Football = 4, Badminton = 2. Hockey is the most popular.
Q3. Try to find out the most popular game among your classmates.
Ask each classmate. Use a tally table. Each student adds one mark to their chosen game. Count totals. (Answers vary by classroom.)
Q4. Pair wants to respond to the questions given below. Put a tick (✓) for the questions where she needs to carry out data collection and a cross (✗) otherwise:
(a) What is the most popular TV show among her classmates?
(b) When did India get independence?
(c) How much water is getting wasted in her locality?
(d) What is the capital of India?
(a) ✓ Needs data (ask classmates).
(b) ✗ General-knowledge fact (1947).
(c) ✓ Needs observation/measurement in the locality.
(d) ✗ Fact (New Delhi).
(b) ✗ General-knowledge fact (1947).
(c) ✓ Needs observation/measurement in the locality.
(d) ✗ Fact (New Delhi).
Organising with tally marks — Shri Nilesh's sweet shop
Shri Nilesh is a teacher who brings sweets to class to celebrate the new year. The sweets shop nearby has jalebi, gulab jamun, gujiya, barfi, and rasgulla. He wants to know the choices of the children. He writes their names on the board and asks each child to tell their preference. He makes tally marks:
| Sweets | Tally Marks | No. of Students |
|---|---|---|
| Jalebi | |||| | | 6 |
| Gulab jamun | |||| |||| | 9 |
| Gujiya | |||| ||| | 8 |
| Barfi | ||| | 3 |
| Rasgulla | |||| || | 7 |
Tally marks group by fives — vertical strokes for 1 to 4, then a diagonal slash to complete 5.
Figure it Out (p. 76)
Complete the table to help Shri Nilesh to purchase the correct numbers of sweets:
(a) How many students chose jalebi?
(b) Barfi was chosen by ___ students?
(c) How many students chose gujiya?
(d) Rasgulla was chosen by ___ students?
(e) How many students chose gulab jamun?
(a) 6, (b) 3, (c) 8, (d) 7, (e) 9. Total = 6 + 9 + 8 + 3 + 7 = 33 students.
Q2. Is the above table sufficient to distribute each type of sweet to the correct student? Explain. If it is not sufficient, what is the alternative?
No. The table shows only the total count per sweet, not which student chose which sweet. Alternative: maintain a student-by-student record (each student's name next to their choice) for distribution.
Frequencies & Organising numbers — Sushri Sandhya's shoe-size data
Sushri Sandhya asked her students about the sizes of the shoes they wear:
4, 5, 3, 4, 3, 4, 5, 3, 5, 4
5, 5, 4, 4, 4, 4, 4, 3, 5, 6
4, 6, 4, 5, 7, 5, 4, 6, 6, 7.
To organise the data: list unique sizes and count how many times each appears — their frequency?.
| Shoe size | Tally | Frequency |
|---|---|---|
| 3 | |||| | 4 |
| 4 | |||| |||| || | 12 |
| 5 | |||| ||| | 8 |
| 6 | |||| | 4 |
| 7 | || | 2 |
Ascending order: 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7 — total 30 students.
Figure it Out (p. 77)
Help Sandhya answer:
(a) The largest shoe size in the class is ___.
(b) The smallest shoe size in the class is ___.
(c) There are ___ students who wear shoe size 5.
(d) There are ___ students who wear shoe sizes larger than 4.
(a) 7, (b) 3, (c) 8, (d) Larger than 4 = size 5 (8) + 6 (4) + 7 (2) = 14 students.
Q2. How did arranging the data in ascending order help to answer these questions?
Ordered data makes it easy to spot largest/smallest values at the ends. Frequencies of any value can be read directly. Arranged data is also quicker to search and summarise.
Q3. Are there other ways to arrange the data?
Yes — descending order, or grouped (frequency table), or tabulated with a bar chart, or as a pictograph.
Q4. Record the data of trees near your home-to-school walking route, in the format: Tree | No. of Trees. Then answer (a)(b)(c) about most common, least common, and same-number pairs.
Sample data — Peepal: 6, Neem: 4, Banyan: 2, Gulmohar: 5, Mango: 4. (a) Most common: Peepal. (b) Least common: Banyan. (c) Neem and Mango appear equally (both = 4). Answers vary with location.
Q5. Count the letters of c, e, i, r, x in a news article. Arrange in ascending frequency order. Why are most texts likely to show the order n, c, e, i, r, x?
English letter-frequency (typical): n > e > i > r > c > x. Vowels and common consonants appear more; 'x' is rare. So ascending: x, c, r, i, e, n — not exactly n, c, e, i, r, x but close, with 'x' consistently the least common.
Activity: Predict → Observe → Explain — Favourite Fruit Survey
Predict: Which fruit will be the most common choice in your class?
- List 5 fruits on the board (e.g. mango, apple, banana, orange, grapes).
- Each student raises hand for their favourite.
- Record tally marks and frequency.
- Arrange frequencies in descending order.
Observe: Rankings often change by region/season — in Indian schools, mango frequently tops summer surveys. Explain: Cultural availability, family habits and seasonal access influence data. Small-class surveys can be biased; larger samples give more reliable rankings.
Competency-Based Questions
Scenario: A class teacher collects favourite subject data from 40 students. The tally-mark frequencies are — Maths: 12, English: 8, Science: 10, Hindi: 6, Art: 4.
Q1. What is the most popular subject? What fraction of students chose it?
L3 ApplyMaths (12 students). Fraction = 12/40 = 3/10 or 30%.
Q2. Analyse: Why is a frequency table more useful than the raw list of 40 student responses?
L4 AnalyseA frequency table: (i) collapses 40 entries into 5 rows; (ii) shows counts instantly; (iii) makes comparisons easy; (iv) is the first step to making charts. Raw data preserves every individual's response but is hard to scan.
Q3. Evaluate: The teacher wants to give each student a subject-related gift (e.g. a science kit to Science-lovers). Is the frequency table alone sufficient? Justify.
L5 EvaluateNot sufficient. The table gives only counts, not names. She needs the list of who chose what (original raw data) to distribute gifts correctly.
Q4. Create a data-collection plan to find the most-used mode of transport among 100 students in a school. Describe at least 4 steps and a sample tally table.
L6 CreatePlan: (1) List transport modes (bus, car, bicycle, walk, auto, scooter). (2) Prepare a two-column tally sheet. (3) Visit each classroom; ask each student; add one tally per response. (4) Total each row; identify the mode with the highest frequency.
Sample:
Bus |||| |||| |||| ||| (18) Car |||| ||| (8) Bicycle |||| |||| |||| |||| ||| (23) Walk |||| |||| |||| || (17) Auto |||| |||| |||| |||| |||| | (26) Scooter |||| ||| (8). Total = 100.
Sample:
Bus |||| |||| |||| ||| (18) Car |||| ||| (8) Bicycle |||| |||| |||| |||| ||| (23) Walk |||| |||| |||| || (17) Auto |||| |||| |||| |||| |||| | (26) Scooter |||| ||| (8). Total = 100.
Assertion–Reason Questions
A: Tally marks are usually grouped in fives.
R: Groups of five are easier to count quickly than groups of any other size.
R: Groups of five are easier to count quickly than groups of any other size.
Answer: (a) — Fives match our fingers and decimal system.
A: A frequency table can replace all purposes of the original raw data.
R: Frequency tables preserve counts only, not individual identities.
R: Frequency tables preserve counts only, not individual identities.
Answer: (d) — A is false (table loses identities); R is true and explains why A is false.
A: Arranging numerical data in ascending order makes it easier to find the smallest and largest values.
R: In ascending order, the smallest value is at the start and the largest at the end.
R: In ascending order, the smallest value is at the start and the largest at the end.
Answer: (a) — Both true and R is the direct reason.
Frequently Asked Questions
What is data in Class 6 Maths?
Data is a collection of facts, numbers, or observations gathered to answer a question. In NCERT Class 6 Ganita Prakash Chapter 4, students collect real-world data such as favourite colours, ages, or pets, and learn to organise it meaningfully.
How do you organise data using tally marks?
Record each data point as a single vertical line (tally mark). Every fifth mark crosses the previous four to form a bundle of 5. Counting bundles of 5 plus leftovers gives the total count quickly. NCERT Class 6 Ganita Prakash Chapter 4 uses this method.
What is a frequency table?
A frequency table lists each category or value alongside how many times it occurs in the data set. It helps summarise and compare information at a glance. NCERT Class 6 Ganita Prakash Chapter 4 introduces frequency tables as a basic tool for data handling.
Why do we organise data?
Organising data makes it easy to see patterns, find the most common or rare values, and compare groups. Raw unsorted data is hard to interpret, but a neat table or chart communicates findings clearly. Class 6 NCERT Chapter 4 emphasises this skill.
What is the difference between data collection and data organisation?
Data collection means gathering raw facts (surveys, observations, measurements). Data organisation means arranging those facts into tables, tally sheets, or groups so they can be analysed. Both are foundational steps in NCERT Class 6 Ganita Prakash Chapter 4.
How do you choose what data to collect?
Start with a clear question such as 'What is the most common pet among classmates?' Collect only data relevant to that question. Keep categories well-defined to avoid confusion. NCERT Class 6 Ganita Prakash Chapter 4 guides students through this planning process.
Frequently Asked Questions — Data Handling and Presentation
What is Collecting and Organising Data in NCERT Class 6 Mathematics?
Collecting and Organising Data is a key concept covered in NCERT Class 6 Mathematics, Chapter 4: Data Handling and Presentation. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Collecting and Organising Data step by step?
To solve problems on Collecting and Organising Data, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 6 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 4: Data Handling and Presentation?
The essential formulas of Chapter 4 (Data Handling and Presentation) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Collecting and Organising Data important for the Class 6 board exam?
Collecting and Organising Data is part of the NCERT Class 6 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Collecting and Organising Data?
Common mistakes in Collecting and Organising Data include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Collecting and Organising Data?
End-of-chapter NCERT exercises for Collecting and Organising Data cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 4, and solve at least one previous-year board paper to consolidate your understanding.
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