Data Collection and Organisation
Every day, we come across numbers and information — the marks you scored in a test, the number of students in each class, the temperature of your city over a week. All this information is called data.
But raw data on its own is hard to understand. If someone tells you the marks of 40 students one by one, it is confusing. We need to collect this data properly and organise it so that it makes sense and we can draw conclusions from it.
In Class 6 Mathematics (NCERT), this topic is studied in the chapter Data Handling. You will learn what data means, how to collect it, how to arrange it using tally marks and frequency tables, and how to read information from organised data.
What is Data Collection and Organisation?
Definition: Data is a collection of numbers, facts, or information gathered for a purpose.
Key terms:
- Data: Numbers or facts collected for study. Example: marks of students, heights of children, favourite colours of classmates.
- Raw data: Data that has just been collected and is not yet arranged or sorted. It is messy and hard to read.
- Observation: Each piece of data or each entry. If 30 students tell their marks, there are 30 observations.
- Frequency: The number of times a particular value appears in the data. If 8 students scored 75, the frequency of 75 is 8.
- Tally marks: A quick way to count. We draw lines (||||) and cross the fifth one to make groups of 5 (||||).
- Frequency table: A table that shows each value and how many times it appears (its frequency).
- Primary data: Data you collect yourself (by asking questions, measuring, experimenting).
- Secondary data: Data collected by someone else that you use (from books, newspapers, internet).
Data Collection and Organisation Formula
There is no single formula for data collection. However, here are the key methods and rules:
Methods of collecting data:
- Observation: Watching and recording (e.g., counting cars on a road for 1 hour).
- Survey / Questionnaire: Asking people questions (e.g., "What is your favourite sport?").
- Interview: Talking to people one-on-one and recording answers.
- Experiment: Doing a test and recording results (e.g., tossing a coin 50 times).
Rules for making tally marks:
| = 1, || = 2, ||| = 3, |||| = 4, |||| = 5
For every 5th count, draw a line across the previous four to make a group of 5. This makes counting easier.
Total frequency check:
Sum of all frequencies = Total number of observations
Always verify this after making a frequency table.
Derivation and Proof
Why do we organise data?
Problem with raw data:
- Suppose these are marks of 20 students: 45, 67, 82, 45, 91, 67, 55, 82, 45, 67, 91, 55, 45, 82, 67, 55, 91, 82, 67, 45.
- Can you quickly tell which mark appeared the most? It is hard to see from this jumble.
After organising into a frequency table:
- 45 appears 5 times
- 55 appears 3 times
- 67 appears 5 times
- 82 appears 4 times
- 91 appears 3 times
- Total: 5 + 3 + 5 + 4 + 3 = 20 ✓
Now you can easily see:
- 45 and 67 appeared the most (5 times each).
- 55 and 91 appeared the least (3 times each).
- The range of marks is from 45 to 91.
Steps to organise data:
- Collect the raw data.
- Sort it — arrange from smallest to largest (or by category).
- Count using tally marks — go through each value and make a tally.
- Make a frequency table — list each value and its count.
- Verify — check that the total of all frequencies equals the total observations.
Types and Properties
Types of data organisation:
1. Ungrouped frequency table:
- Each individual value gets its own row.
- Best when there are few different values.
- Example: Favourite colour of 30 students — Red (8), Blue (12), Green (5), Yellow (5).
2. Grouped frequency table:
- Values are grouped into class intervals (ranges).
- Best when there are many different values spread across a wide range.
- Example: Marks grouped as 0-10, 10-20, 20-30, etc.
- You will study this in detail in higher classes.
3. Tally chart:
- Uses tally marks to count each value as you go through the data.
- Quick and easy method for counting.
4. Pictograph:
- Uses pictures or symbols to represent data.
- Each picture represents a fixed number.
5. Bar graph:
- Uses bars of different heights to show data.
- Easy to compare different categories.
Solved Examples
Example 1: Example 1: Making a frequency table from raw data
Problem: The blood groups of 20 students are: A, B, O, A, AB, O, A, B, O, A, B, AB, O, A, B, O, AB, A, B, O.
Organise this data in a frequency table.
Solution:
Step 1: List all different blood groups: A, B, O, AB.
Step 2: Count using tally marks:
- A: |||| | → Frequency = 6
- B: |||| → Frequency = 5
- O: |||| | → Frequency = 6
- AB: ||| → Frequency = 3
Step 3: Verify: 6 + 5 + 6 + 3 = 20 ✓
Answer: Blood group A and O are the most common (6 students each). AB is the least common (3 students).
Example 2: Example 2: Collecting data through a survey
Problem: You want to find out the favourite sport of students in your class. How would you collect and organise this data?
Solution:
Step 1: Collect data
- Ask each student: "What is your favourite sport?"
- Write down each answer. This gives you raw data.
Step 2: Sort the data
- List all the different sports mentioned: Cricket, Football, Badminton, etc.
Step 3: Make a tally chart
- Go through each answer and put a tally mark next to the matching sport.
Step 4: Make a frequency table
- Count the tally marks for each sport.
- Write the sport name and its frequency in a table.
Step 5: Verify
- Total of all frequencies should equal the number of students you asked.
Example 3: Example 3: Reading a frequency table
Problem: The following table shows marks obtained by students in a test:
- Marks 5: Frequency 3
- Marks 6: Frequency 7
- Marks 7: Frequency 10
- Marks 8: Frequency 6
- Marks 9: Frequency 4
Answer: (a) How many students took the test? (b) Which mark was scored by the most students? (c) How many students scored 8 or above?
Solution:
(a) Total students = 3 + 7 + 10 + 6 + 4 = 30
(b) The highest frequency is 10, for marks = 7. So 7 was scored by the most students.
(c) Students scoring 8 or above = 6 (scored 8) + 4 (scored 9) = 10 students.
Example 4: Example 4: Tally marks to frequency
Problem: Convert these tally marks to numbers:
- (a) |||| |||| ||
- (b) |||| |||
- (c) |||| |||| |||| |
- (d) ||||
Solution:
- (a) |||| |||| || = 5 + 5 + 2 = 12
- (b) |||| ||| = 5 + 3 = 8
- (c) |||| |||| |||| | = 5 + 5 + 5 + 1 = 16
- (d) |||| = 5
Example 5: Example 5: Organising marks data
Problem: Marks of 25 students: 7, 8, 5, 9, 6, 8, 7, 5, 8, 9, 7, 6, 8, 5, 7, 9, 8, 6, 7, 5, 8, 7, 9, 6, 5.
Make a frequency table.
Solution:
Count each value:
- 5: |||| → Frequency = 5
- 6: |||| → Frequency = 4
- 7: |||| | → Frequency = 6
- 8: |||| | → Frequency = 6
- 9: |||| → Frequency = 4
Verify: 5 + 4 + 6 + 6 + 4 = 25 ✓
Answer: Marks 7 and 8 were scored by the most students (6 each).
Example 6: Example 6: Primary vs secondary data
Problem: Classify each as primary or secondary data:
- (a) You count the number of trees in your school garden.
- (b) You read the population of India from a textbook.
- (c) You measure the heights of your classmates.
- (d) You find rainfall data from a weather website.
Solution:
- (a) Primary data — you collected it yourself by counting.
- (b) Secondary data — someone else collected it; you read it from a book.
- (c) Primary data — you measured it yourself.
- (d) Secondary data — someone else recorded it; you found it online.
Example 7: Example 7: Finding the mode from a frequency table
Problem: From the data: 2, 3, 4, 2, 5, 2, 3, 4, 2, 3, 5, 2. Which number appears the most?
Solution:
Make a frequency table:
- 2: appears 5 times
- 3: appears 3 times
- 4: appears 2 times
- 5: appears 2 times
Total: 5 + 3 + 2 + 2 = 12 ✓
Answer: The number 2 appears the most (5 times). This most frequent value is called the mode.
Example 8: Example 8: Collecting data by experiment
Problem: Throw a dice 20 times and record the results. The results are: 3, 5, 1, 6, 2, 3, 4, 1, 5, 6, 3, 2, 4, 1, 6, 5, 3, 2, 4, 1. Organise this data.
Solution:
Frequency table:
- 1: |||| → 4 times
- 2: ||| → 3 times
- 3: |||| → 4 times
- 4: ||| → 3 times
- 5: ||| → 3 times
- 6: ||| → 3 times
Verify: 4 + 3 + 4 + 3 + 3 + 3 = 20 ✓
Answer: 1 and 3 appeared most often (4 times each). Each face of the dice came up roughly the same number of times.
Example 9: Example 9: Organising data about favourite fruits
Problem: 30 students were asked their favourite fruit. Results: Mango-12, Apple-8, Banana-5, Grapes-3, Orange-2. Verify the data and find which fruit is least liked.
Solution:
Verify:
- 12 + 8 + 5 + 3 + 2 = 30 ✓ (matches total students)
Most liked: Mango (12 students)
Least liked: Orange (2 students)
Answer: Orange is the least liked fruit (chosen by only 2 students).
Example 10: Example 10: Spotting errors in data
Problem: A class has 35 students. The frequency table shows: Cat-10, Dog-8, Fish-7, Bird-6, Rabbit-5. Is the data correct?
Solution:
Check the total:
- 10 + 8 + 7 + 6 + 5 = 36
But the class has 35 students.
- 36 ≠ 35. The total does not match!
Answer: The data has an error. The sum of frequencies (36) does not equal the number of students (35). One of the counts must be wrong and needs to be rechecked.
Real-World Applications
Where is data collection and organisation used?
- School: Teachers collect marks of students and organise them to find averages, highest and lowest scores, and pass percentages.
- Weather: The meteorological department collects temperature, rainfall, and humidity data daily. This is organised to predict weather patterns.
- Census: The government collects data about population, occupations, and education levels to plan policies.
- Sports: Coaches collect data about player performance — runs scored, goals made, time taken. This helps improve training.
- Hospitals: Doctors collect patient data — blood pressure, temperature, weight — to track health over time.
- Business: Shops record daily sales. This helps them know which products sell the most and plan stock accordingly.
- Elections: Vote counts are organised constituency-wise to announce results.
Key Points to Remember
- Data is a collection of facts, numbers, or information gathered for a purpose.
- Raw data is unorganised data. It is hard to read and draw conclusions from.
- Organising data means arranging it in a meaningful way using tables, tally marks, or charts.
- Frequency = how many times a value appears in the data.
- Tally marks help count quickly: every 5th mark crosses the previous four (||||).
- A frequency table shows each value and its frequency in a neat table.
- Always verify: sum of all frequencies = total observations.
- Primary data is collected by you. Secondary data is collected by someone else.
- Data can be collected through observation, surveys, interviews, or experiments.
- Organised data helps us see patterns, find the most and least common values, and make decisions.
Practice Problems
- The shoe sizes of 15 students are: 5, 6, 7, 5, 6, 8, 7, 5, 6, 7, 8, 5, 6, 7, 6. Make a frequency table.
- Give 2 examples of primary data and 2 examples of secondary data.
- Roll a coin 30 times and record Heads or Tails. Make a frequency table of your results.
- The favourite subjects of 25 students are: Maths-9, Science-7, English-5, Hindi-4. Verify the total and find the most popular subject.
- Convert to tally marks: (a) 13, (b) 7, (c) 22, (d) 11.
- A school records the number of students absent each day for a week: Mon-5, Tue-3, Wed-8, Thu-2, Fri-7. What was the total number of absences? Which day had the most absences?
- Collect the birth months of 20 people you know. Organise into a frequency table. Which month has the most birthdays?
- Why is it important to verify that the sum of frequencies equals the total number of observations?
Frequently Asked Questions
Q1. What is data in maths?
Data is a collection of facts, numbers, or information gathered for a specific purpose. Examples include marks of students in a test, heights of children in a class, or daily temperatures of a city.
Q2. What is the difference between raw data and organised data?
Raw data is just a list of numbers or facts with no order — it is messy and hard to understand. Organised data is arranged in a meaningful way (like a frequency table) so that patterns and conclusions can easily be seen.
Q3. What are tally marks?
Tally marks are a way of counting by drawing short lines. For each count, draw a vertical line (|). Every 5th count, draw a line across the previous four to make a group. This makes counting in groups of 5 easy.
Q4. What is frequency?
Frequency is the number of times a particular value appears in a set of data. If 7 students scored 80 marks, the frequency of 80 is 7.
Q5. What is the difference between primary and secondary data?
Primary data is data you collect yourself through surveys, experiments, or observation. Secondary data is data someone else collected, which you use from books, websites, or reports.
Q6. Why do we organise data?
We organise data to make it easier to understand, compare, and draw conclusions. Raw data is like a jumble of numbers — organising it into tables and charts shows patterns, the most and least common values, and helps in decision-making.
Q7. What is a frequency table?
A frequency table is a table that lists each different value in the data along with how many times it appears (its frequency). It usually has three columns: the value, tally marks, and the frequency count.
Q8. How do you check if your frequency table is correct?
Add up all the frequencies in the table. The total should equal the number of observations in your original data. If it does not match, recount the tally marks.
