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Practice Paper 11 for Class 6 Mathematics Ganita Prakash Chapter 4, Data Handling and Presentation, is a 40-mark paper with 20 questions in five sections (A to E), and each question is followed by a worked solution. Its focus is on the first step of collecting raw data, finding minimum, maximum and totals, half symbols in pictographs of trees, cars and balloons, tallying test marks, and drawing a bar graph of school club membership with a scale of 15 students per unit.
Section A: Multiple Choice Questions (1 Mark Each)
(a) Make a frequency table
(b) Collect the raw data
(c) Draw a bar graph
(d) Assume the most popular subject
Show Answer & Explanation
Answer: (b) Collect the raw data
Explanation:
1. Before anything can be organised or drawn, we need the answers of the students.
2. So the first step is to collect the raw data by asking every student.
3. A frequency table and a bar graph come later; assuming an answer is not data at all.
Teacher's Note:
1. Order of work: collect, organise (table), then present (graph).
2. Data must come from real observation, not guessing.
(a)
(b)
(c)
(d)
Show Answer & Explanation
Answer: (a)
Explanation:
1. 75 ÷ 10 = 7.5, so we need 7 full symbols and half of one more.
2. 7 symbols show 70 trees and the half symbol shows 5 trees: 70 + 5 = 75.
3. So the answer is 7 symbols and a half symbol.
Teacher's Note:
1. Half a symbol stands for half of the key.
2. 8 symbols would mean 80 trees.
(a) 18 kg
(b) 250 kg
(c) 450 kg
(d) 200 kg
Show Answer & Explanation
Answer: (c) 450 kg
Explanation:
1. First bar: 8 × 25 = 200 kg. Second bar: 10 × 25 = 250 kg.
2. Total = 200 + 250 = 450 kg.
3. Or: (8 + 10) × 25 = 18 × 25 = 450 kg.
Teacher's Note:
1. 200 kg and 250 kg are the separate bars, not the total.
2. Add the units, then multiply by the scale.
(a) 17 units
(b) 15 units
(c) 85 units
(d) 5 units
Show Answer & Explanation
Answer: (a) 17 units
Explanation:
1. Each unit stands for 5 runs.
2. Height = 85 ÷ 5 = 17 units.
3. So the bar is 17 units tall.
Teacher's Note:
1. To find a height, divide the value by the scale.
2. Check: 17 × 5 = 85.
(a) 14
(b) 7
(c) 20
(d) 28
Show Answer & Explanation
Answer: (b) 7
Explanation:
1. Each symbol stands for 20 cars.
2. Number of symbols = 140 ÷ 20 = 7.
3. So 7 symbols are needed.
Teacher's Note:
1. Divide the total by the key.
2. 14 would be correct only if one symbol meant 10 cars.
(a) Add the values of the items.
(b) Add the frequencies.
(c) Multiply the values by their frequencies.
(d) Count the number of rows in the table.
Show Answer & Explanation
Answer: (b) Add the frequencies.
Explanation:
1. The frequency of each row tells how many items fall in that row.
2. Adding all the frequencies gives the total number of items.
3. So we should add the frequencies.
Teacher's Note:
1. Example: 5 students like Maths and 10 like Science, so 5 + 10 = 15 students in all.
2. The number of rows only tells how many categories there are.
(a) 35
(b) 60
(c) 70
(d) 65
Show Answer & Explanation
Answer: (c) 70
Explanation:
1. 3 complete symbols = 3 × 20 = 60 cars.
2. Half a symbol = 20 ÷ 2 = 10 cars.
3. Total = 60 + 10 = 70 cars.
Teacher's Note:
1. Half the key, not half of 1, is added for a half symbol.
2. 60 forgets the half symbol.
(a) 40 units
(b) 20 units
(c) 10 units
(d) 80 units
Show Answer & Explanation
Answer: (b) 20 units
Explanation:
1. Each unit stands for 2 students.
2. Height = 40 ÷ 2 = 20 units.
3. So the bar is 20 units tall.
Teacher's Note:
1. Divide, do not multiply, to get a height.
2. 80 comes from 40 × 2, which is wrong.
Assertion (A): In a bar graph, if the frequencies are large, a scale of 1 unit length = 1 frequency is often not suitable.
Reason (R): Using a 1:1 scale for large frequencies would make the bars too long to fit on the paper.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (a) Both A and R are true, and R is the correct explanation of A.
Explanation:
1. For a value like 500, a 1:1 scale needs a bar 500 units long, so another scale is chosen. A is true.
2. Such bars would be too long for the page, so R is true.
3. R is exactly why A holds, so the answer is (a).
Teacher's Note:
1. Large data needs a larger scale such as 1 unit = 50.
2. The scale must be written on the graph.
Assertion (A): The length or height of a bar in a bar graph represents the given number or frequency.
Reason (R): Bar graphs are used to represent data through pictures of objects.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation
Answer: (c) A is true, but R is false.
Explanation:
1. The longer the bar, the larger the number it shows. So A is true.
2. Pictures of objects are used in a pictograph, not in a bar graph. So R is false.
3. The answer is (c).
Teacher's Note:
1. Bar graph: bars. Pictograph: pictures.
2. Read each statement separately before linking them.
Section B: Short Answer Questions (2 Marks Each)
Question 11. A teacher collected data on the number of students who forgot their lunch box over a period of 5 days: 3, 5, 2, 0, 4. What is the minimum and maximum number of students who forgot their lunch box? How many students forgot their lunch box in total over the 5 days?
Answer:
In order: 0, 2, 3, 4, 5.
Minimum = 0 students; maximum = 5 students.
Total = 3 + 5 + 2 + 0 + 4 = 14 students.
In simple words: The smallest number is 0, the largest is 5, and together they make 14.
Teacher's Note:
1. 0 is a real value here: one day nobody forgot.
2. Sorting first makes the minimum and maximum easy to see.
Question 12. A pictograph uses a symbol to represent 10 trees. If a village planted 120 trees, 145 trees, and 90 trees in three consecutive years, how would you represent 145 trees using the given symbol?
Answer:
Number of symbols = 145 ÷ 10 = 14.5.
14 full symbols show 140 trees and the remaining 5 trees are half of 10.
So 145 trees are shown by 14 complete symbols and a half symbol:
In simple words: Draw 14 whole trees and half a tree, because 145 = 14 × 10 + 5.
Teacher's Note:
1. 5 is half of the key 10, so half a symbol is exact.
2. 120 and 90 are not needed for this question.
Question 13. The population of a city in different years is given as:
2001: 50,000, 2011: 75,000, 2021: 1,00,000.
If a bar graph is drawn with a scale of 1 unit length = 5,000 people, what would be the height of the bars for the years 2001 and 2021?
Answer:
Height = population ÷ 5,000.
2001: 50,000 ÷ 5,000 = 10 units.
2021: 1,00,000 ÷ 5,000 = 20 units.
In simple words: Divide each population by 5,000 to get 10 units and 20 units.
Teacher's Note:
1. 1,00,000 is one lakh in the Indian system.
2. Cancel the same zeros first: 100 ÷ 5 = 20.
Question 14. The following data shows the number of cars passing a toll plaza in 6 different hours:
150, 200, 150, 250, 100, 200.
How many times did 150 cars pass in an hour, and what is the total number of cars that passed in the given 6 hours?
Answer:
150 appears in the 1st and 3rd hours, so 2 times.
Total = 150 + 200 + 150 + 250 + 100 + 200 = 1050 cars.
In simple words: 150 comes up twice, and all six hours together make 1050 cars.
Teacher's Note:
1. Pair numbers to add quickly: 150 + 250 = 400, 200 + 200 = 400.
2. Then 400 + 400 + 150 + 100 = 1050.
Section C: Short Answer Questions (3 Marks Each)
House rent: ₹2500
Food: ₹4000
Education: ₹2000
Transport: ₹1500
Choose a suitable scale and calculate the height of the bars for each item if you were to represent this data using a bar graph.
Answer:
All amounts are multiples of 500, so take 1 unit length = ₹500.
| Item | Expenditure | Height of bar |
|---|---|---|
| House rent | ₹2500 | 2500 ÷ 500 = 5 units |
| Food | ₹4000 | 4000 ÷ 500 = 8 units |
| Education | ₹2000 | 2000 ÷ 500 = 4 units |
| Transport | ₹1500 | 1500 ÷ 500 = 3 units |
In simple words: With 1 unit = ₹500 the bars are 5, 8, 4 and 3 units tall.
Teacher's Note:
1. A scale that divides every value gives whole-number heights.
2. ₹1000 per unit would give 2.5 and 1.5 units, which is harder to draw.
15, 18, 12, 15, 18, 15, 12, 10, 18, 15, 18, 12, 15, 15, 15.
(a) Organize the data using a frequency table with tally marks.
(b) What is the most common mark obtained by the students?
Answer:
(a)
| Marks | Tally Marks | Frequency |
|---|---|---|
| 10 | 1 | |
| 12 | 3 | |
| 15 | 7 | |
| 18 | 4 | |
| Total | 15 |
Check: 1 + 3 + 7 + 4 = 15 students.
(b) The most common mark is 15, obtained by 7 students.
In simple words: 15 appears 7 times, more than any other mark.
Teacher's Note:
1. Strike off each mark as you tally it.
2. The total of frequencies must equal 15.
Question 17. A pictograph represents the number of cars manufactured by a company over a few years, with the key = 500 cars.
(a) If the company manufactured 3250 cars in a year, how many symbols would be needed?
(b) What is the total number of cars represented by 5 complete symbols and a half symbol?
Answer:
(a) 3250 ÷ 500 = 6.5, so 6 complete symbols and a half symbol (6 × 500 = 3000, and 250 is half of 500).
(b) 5 complete symbols = 5 × 500 = 2500 cars; half a symbol = 250 cars.
Total = 2500 + 250 = 2750 cars.
In simple words: 3250 is six and a half lots of 500, and 5½ symbols mean 2750 cars.
Teacher's Note:
1. Half a symbol here means 250 cars.
2. Check (a): 6.5 × 500 = 3250.
Section D: Long Answer Question (5 Marks)
Science Club: 60, Math Club: 45, Art Club: 75, Music Club: 30, Drama Club: 60.
(a) Prepare a frequency distribution table for the given data.
(b) Draw a bar graph to illustrate this data, choosing a suitable scale.
(c) Which club has the maximum number of students, and how many more students does it have compared to the Music Club?
Answer:
(a)
| Club | Number of students |
|---|---|
| Science Club | 60 |
| Math Club | 45 |
| Art Club | 75 |
| Music Club | 30 |
| Drama Club | 60 |
| Total | 270 |
(b) Every number is a multiple of 15, so take 1 unit length = 15 students.
Bar heights: Science 60 ÷ 15 = 4 units, Math 45 ÷ 15 = 3 units, Art 75 ÷ 15 = 5 units, Music 30 ÷ 15 = 2 units, Drama 60 ÷ 15 = 4 units.
(c) The Art Club has the most students (75).
It has 75 − 30 = 45 more students than the Music Club.
In simple words: Use 1 unit = 15 students; Art Club is tallest and beats Music Club by 45.
Teacher's Note:
1. A scale of 1 unit = 5 or 15 both divide all the values; 15 keeps the graph short.
2. Equal values (Science and Drama) give equal bars.
3. Name the axes and write the scale.
Section E: Case Study Based Questions (4 Marks Each)
Question 19. Case Study 1: The Class Birthday Chart
In Mrs. Sharma's classroom, a sense of excitement fills the air as the students work on a vibrant birthday chart. Each month is getting its own special column. To make the chart visually appealing and easy to read, they've decided to use a pictograph. The simple, cheerful symbol of a balloon will be their key, with each balloon representing two students' birthdays. The data they have for the number of birthdays each month is:
January: 6
February: 8
March: 10
April: 4
(a) How many birthday symbols would be needed to represent the birthdays in March?
(b) How many more birthdays were in February than in April?
(c) If the class has a total of 30 students, how many birthdays occurred in the months not listed?
(d) To make the pictograph for April, how would you use the symbol ?
Answer:
(a) March: 10 ÷ 2 = 5 balloons.
(b) February − April = 8 − 4 = 4 more birthdays.
(c) Birthdays in the listed months = 6 + 8 + 10 + 4 = 28. Each student has one birthday, so the other months have 30 − 28 = 2 birthdays.
(d) April has 4 birthdays and 4 ÷ 2 = 2, so draw 2 balloons in the April row.
The complete pictograph:
In simple words: Divide each month's count by 2 to get balloons; 2 birthdays fall in other months.
Teacher's Note:
1. Each balloon stands for 2 birthdays, so an odd number would need half a balloon.
2. In (b) compare birthdays, not balloons (that would be 2).
Question 20. Case Study 2: The Supermarket Survey
A local supermarket is on a mission to stock its shelves with the fruits its customers love most. To get a clear picture of consumer preferences, they conducted a detailed survey. They recorded the first 50 responses from shoppers, asking them to name their favourite fruit. The results are:
Apple: 15
Banana: 10
Mango: 12
Grapes: 8
Orange: 5
(a) What is the total number of responses recorded in this survey?
(b) Which fruit has the lowest frequency?
(c) If a bar graph is created with a scale of 1 unit length = 2 customers, what would be the height of the bar for Mangoes?
(d) How many more customers prefer Apples than Grapes?
Answer:
(a) Total = 15 + 10 + 12 + 8 + 5 = 50 responses (matching the first 50 shoppers).
(b) Orange has the lowest frequency (5).
(c) Mango bar = 12 ÷ 2 = 6 units.
(d) Apples − Grapes = 15 − 8 = 7 more customers.
In simple words: Add to get 50, Orange is lowest, the Mango bar is 6 units and Apple beats Grapes by 7.
Teacher's Note:
1. The total of the frequencies should match the number of people asked.
2. Lowest frequency means the smallest count.
Free study material for Mathematics
CBSE Class 6 Mathematics Assignments for Chapter 04 Data Handling and Presentation
Download Assignment: Chapter 04 Data Handling and Presentation (Class 6 Mathematics)
Access structured practice assignments for Chapter 04 Data Handling and Presentation designed in alignment with the latest CBSE curriculum for Class 6 Mathematics. These printable sets cover objective and descriptive problem types to support thorough revision.
Why Practice Class 6 Mathematics Assignments?
- Syllabus Compliance: Sets reflect current CBSE evaluation criteria and official marking frameworks.
- Multi-Format Practice: Includes varied problem types designed to deepen comprehension across all sub-topics.
- Time Management: Routine practice optimizes pacing to finish school examinations comfortably within schedule.
How to Approach Mathematics Chapter 04 Data Handling and Presentation Assignments
- Initial Reading: Begin by reading the NCERT book for Class 6 Mathematics to build a baseline understanding.
- Independent Testing: Attempt assignment questions unassisted, then verify work using provided answer keys.
- Supplementary Aids: Leverage revision notes and worksheets whenever you encounter difficult topics.
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