NCERT Solutions for Class 6 Maths Chapter 9 — Data Handling
Key Concepts
| Concept | Definition | Example | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Data | A collection of facts, numbers, or information gathered for a specific purpose | Marks scored by students in a test | |||||||
| Raw Data | Data in its original form, unorganised and not arranged in any order | 45, 32, 67, 45, 89, 32, 45 | |||||||
| Array | Data arranged in ascending or descending order | 32, 32, 45, 45, 45, 67, 89 | |||||||
| Tally Marks | A quick way of counting and recording frequency using vertical lines; every fifth mark crosses the previous four | \ | \ | \ | \ | = 5, \ | \ | \ | = 3 |
| Pictograph | A graph that uses pictures or symbols to represent data | One book icon = 10 books sold | |||||||
| Bar Graph | A graph using rectangular bars of equal width with heights proportional to the values they represent | A bar of height 5 cm for 50 students | |||||||
| Scale | The value that each symbol or unit represents in a graph | In a pictograph, 1 symbol = 5 items | |||||||
| Reading Data | Extracting information from graphs, tables, or pictographs | Finding which category has the most/least | |||||||
| Organising Data | Arranging raw data into a systematic format like tables or graphs for easier understanding | Creating a frequency table from raw data |
Exercise 9.1 — Recording and Organising Data
Q1. In a Maths test, the marks obtained by 15 students are: 45, 32, 67, 45, 89, 32, 45, 56, 67, 45, 78, 32, 56, 89, 56. Organise this data in ascending order.
Step 2: Create a frequency table:
| Marks | Tally | Frequency | ||||
|---|---|---|---|---|---|---|
| 32 | \ | \ | \ | 3 | ||
| 45 | \ | \ | \ | \ | 4 | |
| 56 | \ | \ | \ | 3 | ||
| 67 | \ | \ | 2 | |||
| 78 | \ | 1 | ||||
| 89 | \ | \ | 2 | |||
| Total | 15 |
Most common mark = 45 (frequency 4)
Q2. The number of students absent in a class during a week is as follows:
| Day | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
|---|---|---|---|---|---|---|
| Absent | 5 | 3 | 4 | 7 | 2 | 1 |
How many students were absent on Wednesday? On which day were the maximum number of students absent?
- Students absent on Wednesday = 4
- Maximum absentees: Looking at the data, Thursday has the highest number (7).
- Maximum students absent on Thursday = 7
Q3. The following data shows the favourite fruits of 30 students in a class: Mango, Apple, Mango, Banana, Apple, Mango, Banana, Apple, Mango, Mango, Apple, Banana, Mango, Apple, Banana, Mango, Apple, Mango, Banana, Apple, Mango, Banana, Mango, Apple, Mango, Banana, Apple, Mango, Apple, Banana. Organise the data using tally marks.
| Fruit | Tally | Frequency | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Mango | \ | \ | \ | \ | \ | \ | \ | \ | \ | \ | 12 | |
| Apple | \ | \ | \ | \ | \ | \ | \ | 9 | ||||
| Banana | \ | \ | \ | \ | \ | \ | \ | 9 | ||||
| Total | 30 |
Mango is the most favourite fruit (12 students).
Q4. The weights (in kg) of 10 students are: 35, 42, 38, 35, 40, 42, 38, 35, 42, 38. Make a frequency table.
| Weight (kg) | Tally | Frequency | ||||
|---|---|---|---|---|---|---|
| 35 | \ | \ | \ | 3 | ||
| 38 | \ | \ | \ | \ | 4 | |
| 40 | \ | 1 | ||||
| 42 | \ | \ | \ | 3 | ||
| Total | 10 |
Most common weight = 38 kg (frequency 4)
Q5. A teacher asked 20 students about their favourite colour. The responses were: Red, Blue, Red, Green, Blue, Red, Blue, Green, Red, Blue, Red, Green, Blue, Red, Green, Blue, Red, Blue, Green, Red. Represent the data in a frequency table.
| Colour | Tally | Frequency | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Red | \ | \ | \ | \ | \ | \ | \ | \ | 8 | |
| Blue | \ | \ | \ | \ | \ | \ | \ | 7 | ||
| Green | \ | \ | \ | \ | \ | 5 | ||||
| Total | 20 |
Red is the most favourite colour (8 students).
Exercise 9.2 — Pictographs
Q1. A pictograph shows the number of books sold by a shop on different days. One book symbol represents 5 books.
| Day | Books Sold (symbols) |
|---|---|
| Monday | 📚📚📚📚 |
| Tuesday | 📚📚📚 |
| Wednesday | 📚📚📚📚📚📚 |
| Thursday | 📚📚 |
| Friday | 📚📚📚📚📚 |
How many books were sold on Monday? On which day were the most books sold?
- Monday: 4 × 5 = 20 books
- Tuesday: 3 × 5 = 15 books
- Wednesday: 6 × 5 = 30 books (maximum)
- Thursday: 2 × 5 = 10 books
- Friday: 5 × 5 = 25 books
Most books were sold on Wednesday (30 books).
Q2. The following pictograph shows the number of cars sold by a dealer in four months. One car symbol represents 10 cars.
| Month | Cars Sold |
|---|---|
| January | 🚗🚗🚗🚗🚗🚗 |
| February | 🚗🚗🚗🚗 |
| March | 🚗🚗🚗🚗🚗🚗🚗🚗 |
| April | 🚗🚗🚗🚗🚗 |
(a) How many cars were sold in March? (b) In which month were the least cars sold? (c) What is the total number of cars sold?
(a) March: 8 × 10 = 80 cars
(b) February has the fewest symbols (4), so: February: 4 × 10 = 40 cars (least)
(c) Total = (6 + 4 + 8 + 5) × 10 = 23 × 10 = 230 cars
Q3. A survey shows the number of TV sets in 100 houses. The data is shown using a pictograph where each TV symbol represents 5 houses.
| Number of TV Sets | Houses |
|---|---|
| 0 | 📺📺 |
| 1 | 📺📺📺📺📺📺📺📺📺📺 |
| 2 | 📺📺📺📺📺📺📺📺📺📺📺📺📺📺📺📺 |
| 3 | 📺📺📺📺📺📺 |
| More than 3 | 📺📺 |
How many houses have no TV? How many houses have exactly 2 TV sets?
- Houses with 0 TV: 2 × 5 = 10 houses
- Houses with 1 TV: 10 × 5 = 50 houses
- Houses with 2 TVs: 16 × 5 = 80 houses
- Houses with 3 TVs: 6 × 5 = 30 houses
- Houses with more than 3 TVs: 2 × 5 = 10 houses
Houses with no TV = 10. Houses with exactly 2 TV sets = 80.
Note: Total should equal 100. Here 10 + 50 + 80 + 30 + 10 = 180, which exceeds 100. This illustrates why checking data consistency is important.
Q4. The following pictograph shows the number of absentees in a class on different days. Each face symbol represents 2 absentees.
| Day | Absentees |
|---|---|
| Monday | 😊😊😊 |
| Tuesday | 😊😊 |
| Wednesday | 😊😊😊😊 |
| Thursday | 😊 |
| Friday | 😊😊😊 |
Find the total number of absentees during the week. On which day were the maximum absentees?
- Monday: 3 × 2 = 6
- Tuesday: 2 × 2 = 4
- Wednesday: 4 × 2 = 8 (maximum)
- Thursday: 1 × 2 = 2
- Friday: 3 × 2 = 6
Total absentees = 6 + 4 + 8 + 2 + 6 = 26
Maximum absentees on Wednesday (8).
Exercise 9.3 — Drawing and Reading Pictographs
Q1. The number of different ice-cream flavours sold by a shop is given below. Draw a pictograph using a suitable scale.
| Flavour | Number Sold |
|---|---|
| Vanilla | 20 |
| Chocolate | 35 |
| Strawberry | 15 |
| Mango | 25 |
| Butterscotch | 10 |
| Flavour | Number Sold | Pictograph (1 cone = 5) |
|---|---|---|
| Vanilla | 20 | 🍦🍦🍦🍦 |
| Chocolate | 35 | 🍦🍦🍦🍦🍦🍦🍦 |
| Strawberry | 15 | 🍦🍦🍦 |
| Mango | 25 | 🍦🍦🍦🍦🍦 |
| Butterscotch | 10 | 🍦🍦 |
Title: Ice-Cream Flavours Sold Scale: 1 cone symbol = 5 ice creams
Q2. The following table shows the number of students who opted for different sports. Draw a pictograph using a suitable symbol and scale.
| Sport | Number of Students |
|---|---|
| Cricket | 40 |
| Football | 25 |
| Basketball | 15 |
| Hockey | 30 |
| Volleyball | 20 |
| Sport | Number of Students | Pictograph (1 ball = 5 students) |
|---|---|---|
| Cricket | 40 | ⚾⚾⚾⚾⚾⚾⚾⚾ |
| Football | 25 | ⚾⚾⚾⚾⚾ |
| Basketball | 15 | ⚾⚾⚾ |
| Hockey | 30 | ⚾⚾⚾⚾⚾⚾ |
| Volleyball | 20 | ⚾⚾⚾⚾ |
Title: Students' Sports Preferences Scale: 1 ball symbol = 5 students
Q3. Read the pictograph below and answer the questions. The pictograph shows the number of trees planted by different schools. Each tree symbol represents 10 trees.
| School | Trees Planted |
|---|---|
| School A | 🌳🌳🌳 |
| School B | 🌳🌳🌳🌳🌳🌳 |
| School C | 🌳🌳🌳🌳🌳 |
| School D | 🌳🌳🌳🌳🌳🌳🌳 |
(a) How many trees did School B plant? (b) Which school planted the most trees? (c) Which school planted the least trees?
(a) School B: 6 × 10 = 60 trees
(b) School D has the most symbols (7), so School D planted the most trees: 7 × 10 = 70 trees
(c) School A has the fewest symbols (3), so School A planted the least trees: 3 × 10 = 30 trees
Q4. The number of vehicles passing through a crossing every hour from 8 AM to 12 noon is shown below:
| Time | 8-9 AM | 9-10 AM | 10-11 AM | 11-12 noon |
|---|---|---|---|---|
| Vehicles | 30 | 45 | 60 | 25 |
Draw a pictograph using a suitable scale. Which time period has the maximum traffic?
| Time | Vehicles | Pictograph |
|---|---|---|
| 8-9 AM | 30 | 🚗🚗 |
| 9-10 AM | 45 | 🚗🚗🚗 |
| 10-11 AM | 60 | 🚗🚗🚗🚗 |
| 11-12 noon | 25 | 🚗🚗 (approximately) |
Maximum traffic during 10-11 AM (60 vehicles).
Exercise 9.4 — Bar Graphs (Drawing and Interpreting)
Q1. The following bar graph shows the number of students in different classes of a school.
Bar Graph Description:
- Class 6: 40 students (bar height represents 40)
- Class 7: 50 students
- Class 8: 45 students
- Class 9: 55 students
- Class 10: 60 students
Scale: 1 unit on Y-axis = 10 students
Answer the following: (a) Which class has the maximum number of students? (b) Which class has the minimum number of students? (c) How many students are there in Class 8? (d) What is the total number of students?
(a) Class 10 has the tallest bar (60 students). Class 10 has the maximum number of students.
(b) Class 6 has the shortest bar (40 students). Class 6 has the minimum number of students.
(c) The bar for Class 8 reaches the 4.5 mark on the Y-axis (since scale is 10 students per unit). Class 8 has 45 students.
(d) Total = 40 + 50 + 45 + 55 + 60 = 250 students
Q2. The following table shows the favourite subjects of students in Class 6. Draw a bar graph.
| Subject | Number of Students |
|---|---|
| Maths | 12 |
| Science | 10 |
| English | 8 |
| Hindi | 6 |
| Art | 4 |
5. All bars should have equal width and equal gaps between them. 6. Give the graph a title: "Favourite Subjects of Class 6 Students"
- Maths: height = 6 units (12 students)
- Science: height = 5 units (10 students)
- English: height = 4 units (8 students)
- Hindi: height = 3 units (6 students)
- Art: height = 2 units (4 students)
Scale: 1 unit on Y-axis = 2 students
Q3. The bar graph below shows the rainfall (in cm) in a city from June to November.
Bar Graph Description:
- June: 15 cm
- July: 25 cm
- August: 30 cm
- September: 20 cm
- October: 10 cm
- November: 5 cm
Answer the following: (a) In which month was the rainfall maximum? (b) In which month was the rainfall minimum? (c) What was the total rainfall from June to November? (d) How much more did it rain in August than in September?
(a) August has the tallest bar. Maximum rainfall in August = 30 cm.
(b) November has the shortest bar. Minimum rainfall in November = 5 cm.
(c) Total rainfall = 15 + 25 + 30 + 20 + 10 + 5 = 105 cm
(d) August rainfall = 30 cm, September rainfall = 20 cm Difference = 30 − 20 = 10 cm more in August.
Q4. The number of books sold by a bookshop from Monday to Saturday is given below. Draw a bar graph.
| Day | Books Sold |
|---|---|
| Monday | 20 |
| Tuesday | 35 |
| Wednesday | 25 |
| Thursday | 40 |
| Friday | 15 |
| Saturday | 45 |
5. All bars of equal width with equal spacing. 6. Title: "Books Sold by a Bookshop (Monday to Saturday)"
- Monday: 4 units (20 books)
- Tuesday: 7 units (35 books)
- Wednesday: 5 units (25 books)
- Thursday: 8 units (40 books)
- Friday: 3 units (15 books)
- Saturday: 9 units (45 books)
Scale: 1 unit on Y-axis = 5 books
Q5. Read the following bar graph and answer the questions.
Bar Graph Description — Production of Cars by a Factory (2019-2023):
- 2019: 800 cars
- 2020: 600 cars
- 2021: 900 cars
- 2022: 1100 cars
- 2023: 1000 cars
Scale: 1 unit on Y-axis = 200 cars
(a) What information does the bar graph give? (b) In which year was the production maximum? (c) In which year was the production minimum? (d) What is the difference between the maximum and minimum production?
(a) The bar graph shows the production of cars by a factory from 2019 to 2023.
(b) 2022 has the tallest bar (1100 cars). Maximum production in 2022 = 1100 cars.
(c) 2020 has the shortest bar (600 cars). Minimum production in 2020 = 600 cars.
(d) Difference = 1100 − 600 = 500 cars
Common Mistakes
| 1. Wrong tally mark counting — Remember that every fifth tally mark is drawn as a diagonal cross through the previous four (\ | \ | \ | \ | ), not as a fifth separate vertical line. Practice: \ | \ | \ | = 3, \ | \ | \ | \ | = 4, \ | \ | \ | \ | = 5. |
|---|
2. Choosing an inappropriate scale — The scale should be chosen so that the largest value fits on the graph paper and the bars are easy to read. If the largest value is 100, a scale of 1 unit = 10 works well; using 1 unit = 1 would make the graph too tall.
3. Unequal bar widths or gaps — In a bar graph, all bars must have the same width and equal gaps between them. Different widths make the graph misleading.
4. Forgetting to label axes — Always label both axes. The X-axis shows categories (days, subjects, etc.) and the Y-axis shows values with a clear scale. Also include a title.
5. Incorrect multiplication with pictograph scale — If one symbol represents 5 items and there are 7 symbols, the answer is 7 × 5 = 35, not 7 + 5 = 12 or 7/5. Always multiply the number of symbols by the scale value.
6. Not reading the scale properly — Before reading any graph, always check the scale first. If the Y-axis has 1 unit = 20 students, then a bar reaching the 3rd unit represents 60 students, not 3 students.
Exam Checklist
- [ ] I can organise raw data into ascending/descending order
- [ ] I can create a frequency table using tally marks
- [ ] I can read and interpret data from a frequency table
- [ ] I can read a pictograph and answer questions based on it
- [ ] I can draw a pictograph using an appropriate symbol and scale
- [ ] I can choose a suitable scale for a pictograph or bar graph (the largest value should fit on the page)
- [ ] I can draw a bar graph with equal-width bars, equal gaps, labelled axes, and a title
- [ ] I can read and interpret a bar graph to find maximum, minimum, and total values
- [ ] I can find the difference between two values shown on a bar graph
- [ ] I remember to always state the scale used in my graph
- [ ] I can solve word problems by organising given data and extracting the required information