Q & ANSWER KEY Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics Chapter 4: Data Handling and Presentation.

 Q&ANSWER KEY Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics  Chapter 4: Data Handling and Presentation.

Class 6 Mathematics – Ganita Prakash

Chapter 4: Data Handling and Presentation

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Chapter Subsections Covered

• 4.1 Introduction to Data

• 4.2 Collecting and Organizing Data

• 4.3 Pictographs

• 4.4 Bar Graphs

• 4.5 Line Graphs

• 4.6 Circle Graphs (Pie Charts – Introductory)

• 4.7 Central Tendencies – Mean, Median, Mode

• 4.8 Application of Data Handling in Daily Life

[Insert Image: Data table of students absent – Page 75]
[Insert Image: Pictograph of favourite fruits – Page 77]
[Insert Image: Bar graph of favourite games – Page 81]
[Insert Image: Line graph showing daily temperatures – Page 86]
[Insert Image: Pie chart showing daily routine – Page 92]
[Insert Image: Frequency table of marks of students – Page 98]

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1. Multiple Choice Questions (20)

Q1. Which of the following is not a form of data representation?
a) Bar graph b) Line graph c) Pictograph d) Cube root table
(Competency: Understanding types of data representation)

(d) Cube root table – not a data representation.

Q2. In a pictograph, 🍎 represents 10 apples. If 5 symbols are shown, how many apples are there?
a) 15 b) 25 c) 50 d) 100
(Competency: Interpreting pictographs)

(c) 5 × 10 = 50.

Q3. A bar graph uses:
a) Circles b) Triangles c) Rectangular bars d) Arrows
(Competency: Basics of bar graphs)

(c) Rectangular bars are used.

Q4. The average of 5 numbers is 20. What is their total?
a) 20 b) 25 c) 50 d) 100
(Competency: Calculating mean) 

(d) 20 × 5 = 100.

Q5. In a line graph, the horizontal axis usually represents:
a) Categories b) Time c) Temperature d) None of these
(Competency: Understanding line graphs)

(b) Time is on the x-axis.

Q6. The total angle of a pie chart is:
a) 90° b) 180° c) 270° d) 360°
(Competency: Basics of pie chart)

(d) 360°.

Q7. The mode of data is:
a) Middle value b) Average value c) Most frequent value d) Largest value
(Competency: Concept of mode)

(c) Most frequent value.

Q8. The range of the data 5, 10, 15, 20 is:
a) 5 b) 10 c) 15 d) 20
(Competency: Understanding range)

(c) 20 – 5 = 15.
Q9. In a pictograph, if 🍊 = 2 oranges, and 8 symbols are drawn, how many oranges are there?

a) 8 b) 10 c) 12 d) 16
(Competency: Pictograph calculations)

(d) 2 × 8 = 16.

Q10. A survey shows 10 students like cricket, 5 football, 15 hockey. Which graph best represents this?
a) Bar graph b) Line graph c) Pie chart d) All of these
(Competency: Choosing correct data representation)

(a) Bar graph best shows categories.

Q11. The median of 7, 8, 9, 10, 11 is:
a) 7 b) 9 c) 10 d) 11
(Competency: Finding median)

(b) 9 is the middle value.

Q12. The mean of first 5 natural numbers is:
a) 2 b) 3 c) 4 d) 5
(Competency: Mean calculation)

(b) (1+2+3+4+5)/5 = 3.

Q13. Which of these is qualitative data?
a) Height b) Weight c) Colour of eyes d) Marks
(Competency: Types of data)

(c) Colour of eyes is qualitative.

Q14. Which central tendency is most affected by extreme values?
a) Mean b) Median c) Mode d) None
(Competency: Understanding mean, median, mode)

(a) Mean is affected by extremes.

Q15. If 40% of a circle graph is shaded, what angle is it?
a) 72° b) 120° c) 144° d) 160°
(Competency: Converting percentage to angle in pie chart)

(c) 40% of 360° = 144°.

Q16. A frequency table shows maximum marks of 40 students. The highest frequency means:
a) Most common score b) Highest score c) Lowest score d) Average score
(Competency: Reading frequency table)

(a) Highest frequency = most common score.

Q17. Which graph is most suitable for time vs temperature data?
a) Bar graph b) Line graph c) Pie chart d) Pictograph
(Competency: Choosing suitable graph)

(b) Line graph shows continuous change.

Q18. A pie chart shows 90° for books. What fraction of total money is for books?
a) ¼ b) ⅓ c) ½ d) ⅙
(Competency: Fractions in pie charts)

(a) 90°/360° = ¼.

Q19. Which measure of central tendency is obtained by dividing sum of observations by number of observations?
a) Mean b) Median c) Mode d) Range
(Competency: Definition of mean)

(a) Mean = sum ÷ number.

Q20. In a survey, 30 liked tea, 20 coffee, 10 milk. What is the mode?
a) Tea b) Coffee c) Milk d) None
(Competency: Mode identification) 

(a) Tea (highest frequency)

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2. Assertion and Reasoning (20 Qs)

Each question has two statements:

• Assertion (A)

• Reason (R)
  Choose the correct option:
  a) A and R both true, R explains A
  b) A and R both true, but R does not explain A
  c) A true, R false
  d) A false, R true

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Q1.
A: Data is a collection of facts.
R: Data cannot be represented using tables.
(Competency: Basic understanding of data)

Q2.
A: Pictographs use pictures or symbols to represent data.
R: Pictographs are never used in primary classes.
(Competency: Understanding pictographs)

Q3.
A: A bar graph can be either horizontal or vertical.
R: Bars must always be equal in width.
(Competency: Features of bar graph)

Q4.
A: A line graph is useful to show change over time.
R: A line graph uses pictures instead of lines.
(Competency: Features of line graphs)

Q5.
A: In a pie chart, the sum of all angles is 360°.
R: A circle has 360°.
(Competency: Geometry connection with pie chart)

Q6.
A: Mean is the middle value of a dataset.
R: Median is calculated as sum ÷ number of items.
(Competency: Differentiating mean and median)

Q7.
A: The mode of data is the most frequent observation.
R: Mode is always greater than median.
(Competency: Understanding mode)

Q8.
A: The range of a dataset is the difference between highest and lowest values.
R: Range measures how spread out the data is.
(Competency: Concept of range)

Q9.
A: Bar graphs are better than pictographs for larger data.
R: Bar graphs can represent bigger numbers more clearly.
(Competency: Choosing data representation)

Q10.
A: A survey is a method of collecting information.
R: Asking students about their favourite colour is a survey.
(Competency: Data collection methods)

Q11.
A: Pie charts are always drawn using compasses and protractors.
R: Each slice represents a fraction of the whole.
(Competency: Understanding circle graphs)

Q12.
A: The mean is affected by extreme values.
R: Adding a very high number increases the mean.
(Competency: Mean sensitivity to data)

Q13.
A: The median divides the data into two equal halves.
R: Median is always the largest value.
(Competency: Median concept)

Q14.
A: In a frequency table, the highest frequency tells us the mode.
R: Mode is the observation with highest frequency.
(Competency: Using frequency tables)

Q15.
A: A line graph always shows continuous data.
R: Temperature change is best shown by a line graph.
(Competency: Application of line graphs)

Q16.
A: Pie charts cannot be used to show percentages.
R: A pie chart can only show fractions.
(Competency: Misconceptions about pie charts)

Q17.
A: Primary data is collected first-hand.
R: Secondary data is collected by someone else.
(Competency: Types of data)

Q18.
A: Bar graphs are unsuitable for showing monthly rainfall.
R: Line graphs better represent rainfall over time.
(Competency: Choosing suitable graphs)

Q19.
A: Data handling is useful in real life.
R: We can use it to analyze cricket scores, rainfall, population, etc.
(Competency: Application of data handling)

Q20.
A: All three measures of central tendency (mean, median, mode) are always equal.
R: In every dataset, mean = median = mode.

(Competency: Misconceptions in statistics)

2. Assertion–Reasoning (20)

1. (c) A true, R false.

2. (c) A true, R false.

3. (a) Both true, R explains A.

4. (c) A true, R false.

5. (a) Both true, R explains A.

6. (c) A true, R false (definitions mixed up).

7. (c) A true, R false.

8. (a) Both true, R explains A.

9. (a) Both true, R explains A.

10. (a) Both true, R explains A.

11. (b) Both true, but R doesn’t explain A.

12. (a) Both true, R explains A.

13. (c) A true, R false.

14. (a) Both true, R explains A.

15. (a) Both true, R explains A.

16. (d) A false, R true.

17. (a) Both true, R explains A.

18. (a) Both true, R explains A.

19. (a) Both true, R explains A.

20. (c) A true, R false.

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3. True or False (10 Qs)

Q1. A pictograph uses symbols to represent data.
(True)
(Competency: Basics of pictographs)

Q2. In a bar graph, the width of bars may be different.
(False – all bars must have equal width)
(Competency: Features of bar graphs)

Q3. A line graph is used to show changes over time.
(True)
(Competency: Application of line graph)

Q4. The total angle at the centre of a pie chart is 180°.
(False – it is 360°)
(Competency: Geometry connection with circle graphs)

Q5. The mean of 5 and 15 is 10.
(True)
(Competency: Calculation of mean)

Q6. The median is the most frequently occurring value.
(False – that is mode, median is the middle value)
(Competency: Differentiating measures of central tendency)

Q7. Mode can be found from a frequency table.
(True)
(Competency: Using frequency tables)

Q8. The range of data is maximum value minus minimum value.
(True)
(Competency: Concept of range)

Q9. Surveys are not part of data collection.
(False – surveys are one of the main methods)
(Competency: Data collection methods)

Q10. All three – mean, median, and mode – are always the same for every dataset.
(False – they may differ)

(Competency: Clarifying misconceptions)

3. True or False (10)

1. True

2. False (bars equal width)

3. True

4. False (360° not 180°)

5. True

6. False (median is middle, not frequent)

7. True

8. True

9. False (surveys are data collection)

10. False (mean, median, mode can differ)

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4. Short Answer I – 2 Marks (15 Qs)

Q1. Define data with an example from your daily life.
(Competency: Understanding data concept)

Q2. Write the difference between primary data and secondary data with examples.
(Competency: Types of data)

Q3. A pictograph shows 🍎 = 10 apples. If 4 symbols are shown, how many apples are there?
(Competency: Pictograph interpretation)

Q4. In a survey, 15 students like cricket, 10 football, 5 tennis. Represent this in tabular form.
(Competency: Data organization in tables)

Q5. Define “range” of a dataset. Find the range of 12, 18, 25, 30.
(Competency: Range calculation)

Q6. Find the mean of 6, 7, 8, 9, 10.
(Competency: Mean calculation)

Q7. Write two advantages of bar graphs over pictographs.
(Competency: Data representation comparison)

Q8. Find the median of 5, 8, 12.
(Competency: Median calculation)

Q9. If in a pie chart, “games” = 90°, find the fraction of circle it represents.
(Competency: Pie chart fractions)

Q10. A frequency table shows 5 students scored 10 marks, 10 students scored 20 marks. Which score is more common?
(Competency: Frequency table interpretation)

Q11. A line graph shows temperature on Monday = 25°C, Tuesday = 30°C. Find the increase.
(Competency: Reading line graph)

Q12. Which type of graph is most suitable for showing favourite subjects of students? Why?
(Competency: Choosing data representation)

Q13. In a pictograph, 🍊 = 2 oranges. 12 symbols are shown. How many oranges are there?
(Competency: Pictograph calculations)

Q14. A pie chart shows “food” = 120°. What percentage is spent on food?
(Competency: Pie chart conversion to percentage)

Q15. Explain why surveys are important in data handling.

(Competency: Application of surveys)

4. Short Answer I (15)

1. Data = collection of facts, e.g., daily temperatures.

2. Primary = collected first-hand; Secondary = taken from books/newspapers.

3. 4 × 10 = 40 apples.

4. Table form with Cricket =15, Football=10, Tennis=5.

5. Range = 30 – 12 = 18.

6. (6+7+8+9+10)/5 = 40/5 = 8.

7. Bar graphs handle large data; pictographs less precise.

8. Middle = 8.

9. 90°/360° = ¼.

10. More common = 20 marks (10 students).

11. 30 – 25 = 5°C.

12. Bar graph (categorical data).

13. 12 × 2 = 24 oranges.

14. 120°/360° = ⅓ = 33.3%.

15. Surveys help collect opinions systematically.

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5. Short Answer II – 3 Marks (10 Qs)

Q1. The marks obtained by 10 students are: 5, 7, 8, 9, 10, 6, 7, 8, 9, 10.
(i) Prepare a frequency table.
(ii) Find the mode.
(Competency: Organizing data & finding mode)

Q2. Draw a bar graph to show the number of absentees in a week:
Mon – 2, Tue – 5, Wed – 4, Thu – 3, Fri – 6.
(Competency: Drawing bar graphs)

Q3. In a survey, students like:
Cricket – 20, Football – 15, Hockey – 5.
Represent this by a pictograph (use ⚽ = 5 students).
(Competency: Pictograph representation)

Q4. Calculate the mean of: 8, 12, 10, 6, 14.
(Competency: Mean calculation)

Q5. The daily maximum temperature of a city in a week is given:
Mon – 30°C, Tue – 32°C, Wed – 31°C, Thu – 29°C, Fri – 28°C, Sat – 33°C, Sun – 34°C.
Draw a line graph.
(Competency: Drawing line graph)

Q6. The daily expenses of a family are: Food – ₹200, Rent – ₹300, Education – ₹100, Other – ₹100.
Represent this in a pie chart.
(Competency: Pie chart construction)

Q7. Find the range and median of the following data: 12, 15, 18, 22, 20.
(Competency: Range & median)

Q8. A bar graph shows: Hindi – 40, English – 35, Maths – 45, Science – 50.
Which subject is most popular? Which is least popular?
(Competency: Bar graph interpretation)

Q9. The ages of 7 students are: 12, 13, 11, 12, 14, 12, 13. Find the mode.
(Competency: Mode calculation)

Q10. Explain with an example how data handling is used in weather forecasting.

(Competency: Real-life application of data handling)

5. Short Answer II (10)

1. Frequency table: Mode = 7, 8, 9, 10 (tie); most frequent values.

2. Bar graph plotted with absentees data.

3. Pictograph with ⚽ symbols.

4. Mean = (8+12+10+6+14)/5 = 50/5 = 10.

5. Line graph shows temps day-wise.

6. Pie chart: Total = 700. Food = 200/700×360 = 103°, Rent = 154°, Education = 51°, Other = 51°.

7. Range = 22 – 12 = 10; Median = 18.

8. Most popular = Science (50), least = English (35).

9. Mode = 12 (appears 3 times).

10. Weather data shown via line graphs/bar graphs.

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6. Long Answer Questions – 5 Marks (10 Qs)

Q1. The marks obtained by 20 students in a test are:
15, 18, 20, 15, 10, 12, 18, 20, 25, 30, 18, 20, 22, 25, 28, 30, 20, 25, 22, 30.
(i) Prepare a frequency table.
(ii) Find the mean, median, and mode.
(Competency: Central tendencies & frequency table)

Q2. The number of different coloured cars in a parking lot are:
Red – 30, Blue – 20, White – 25, Black – 15, Others – 10.
Draw a pie chart for this data.
(Competency: Pie chart construction)

Q3. The population of a town in 5 years was recorded:
2015 – 20,000; 2016 – 22,000; 2017 – 24,500; 2018 – 27,000; 2019 – 30,000.
Draw a line graph showing this growth.
(Competency: Interpreting growth with line graphs)

Q4. The daily wages of 50 workers are given below:

| Wages (₹) | 100 | 120 | 140 | 160 | 180 |
|-----------|-----|-----|-----|-----|
| Workers | 5 | 10 | 15 | 12 | 8 |

(i) Draw a bar graph of the data.
(ii) Find the mode wages.
(Competency: Bar graph + mode from frequency table)

Q5. The expenditure of a family in a month is:
Rent – ₹8000, Food – ₹6000, Education – ₹4000, Savings – ₹2000.
Draw a circle graph (pie chart) for this.
(Competency: Pie chart conversion & interpretation)

Q6. A survey of 100 students showed:
Cricket – 40, Football – 25, Basketball – 20, Badminton – 15.
Represent the data by:
(i) A bar graph
(ii) A pie chart
(Competency: Comparative use of bar graph & pie chart)

Q7. The maximum temperatures of a city during a week are:
Mon – 32°C, Tue – 34°C, Wed – 31°C, Thu – 29°C, Fri – 30°C, Sat – 33°C, Sun – 35°C.
(i) Draw a line graph.
(ii) State on which day temperature was highest & lowest.
(Competency: Line graph drawing & interpretation)

Q8. 25 students were asked how many hours they study daily. Their responses are:
2, 3, 2, 4, 5, 3, 2, 4, 2, 3, 5, 4, 3, 2, 4, 5, 3, 2, 3, 4, 5, 3, 2, 4, 3.
(i) Prepare a frequency table.
(ii) Find the mean study hours.
(Competency: Frequency table & mean)

Q9. The marks obtained by 15 students in Mathematics are:
12, 18, 20, 15, 25, 22, 20, 18, 30, 25, 15, 20, 18, 30, 22.
(i) Arrange the data.
(ii) Find the median & mode.
(Competency: Organizing data + central tendencies)

Q10. Explain in detail with examples the difference between:
(i) Primary and secondary data
(ii) Pictograph, bar graph, and line graph

(Competency: Conceptual clarity & comparisons)

6. Long Answer (10)

1. Frequency table; Mean ≈ 21.2, Median = 20, Mode = 20.

2. Pie chart: Total=100 cars, Red=108°, Blue=72°, White=90°, Black=54°, Others=36°.

3. Line graph showing steady population growth.

4. Bar graph; Mode wages = 140 (highest frequency = 15).

5. Pie chart: Total=20000. Rent=144°, Food=108°, Education=72°, Savings=36°.

6. Cricket=144°, Football=90°, Basketball=72°, Badminton=54°.

7. Highest=Sun (35°C), Lowest=Thu (29°C).

8. Frequency table: Mean ≈ 3.2 hrs.

9. Median=20, Mode=18 & 20 (both frequent).

10. Primary=first-hand; Secondary=already collected. Pictograph=symbols, Bar graph=bars, Line graph=trend.

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7. Case-Based Questions (CBQs)

(Each case study followed by 4 MCQs)

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Case Study 1 – Pictograph (Fruits)

The pictograph below shows the number of fruits sold by a shop in one day.

[Insert Image: Pictograph of fruits – Page 77]
🍎 = 10 fruits

• Apples 🍎🍎🍎🍎 (40 fruits)

• Bananas 🍎🍎🍎 (30 fruits)

• Oranges 🍎🍎🍎🍎🍎 (50 fruits)

• Mangoes 🍎🍎 (20 fruits)

Q1. How many oranges were sold?
a) 30 b) 40 c) 50 d) 20
(Competency: Reading pictograph)

Q2. Which fruit was sold the least?
a) Apple b) Banana c) Orange d) Mango
(Competency: Interpreting pictograph)

Q3. Total fruits sold = ?
a) 100 b) 120 c) 130 d) 140
(Competency: Summing pictograph data)

Q4. Ratio of apples to bananas sold = ?
a) 4:3 b) 3:2 c) 40:20 d) 2:1
(Competency: Ratio from pictograph)

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Case Study 2 – Bar Graph (Sports)

The bar graph shows the favourite sports of students in a class.

[Insert Image: Bar graph of favourite games – Page 81]

• Cricket: 30 students

• Football: 25 students

• Hockey: 20 students

• Basketball: 15 students

Q1. Which sport is most popular?
a) Cricket b) Football c) Hockey d) Basketball
(Competency: Bar graph interpretation)

Q2. How many students like hockey?
a) 20 b) 25 c) 30 d) 15
(Competency: Reading bar graph)

Q3. How many more students like cricket than basketball?
a) 10 b) 15 c) 20 d) 25
(Competency: Difference using bar graph)

Q4. Total number of students = ?
a) 90 b) 100 c) 110 d) 120
(Competency: Summation of bar graph data)

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Case Study 3 – Line Graph (Temperature)

The line graph shows the maximum temperature of a city in a week.

[Insert Image: Line graph of temperature – Page 86]

• Mon: 30°C Tue: 32°C Wed: 31°C

• Thu: 29°C Fri: 28°C Sat: 33°C Sun: 34°C

Q1. On which day was the temperature highest?
a) Friday b) Saturday c) Sunday d) Tuesday
(Competency: Reading line graph)

Q2. On which day was the temperature lowest?
a) Thursday b) Friday c) Saturday d) Monday
(Competency: Identifying minimum)

Q3. Difference between highest & lowest temperature = ?
a) 4°C b) 5°C c) 6°C d) 7°C
(Competency: Subtraction from line graph)

Q4. On how many days was the temperature above 30°C?
a) 2 b) 3 c) 4 d) 5
(Competency: Data analysis from line graph)

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Case Study 4 – Pie Chart (Expenditure)

A family’s monthly expenditure is represented by a pie chart.

[Insert Image: Pie chart of expenditure – Page 92]

• Food: 120°

• Rent: 90°

• Education: 60°

• Savings: 90°

Q1. Which sector is the largest expenditure?
a) Food b) Rent c) Education d) Savings
(Competency: Reading pie chart)

Q2. What fraction of income is spent on food?
a) ⅓ b) ¼ c) ½ d) ⅙
(Competency: Fraction from pie chart)

Q3. Which two heads together make half of the expenditure?
a) Rent + Education b) Rent + Savings c) Food + Rent d) Education + Savings
(Competency: Summing pie chart angles)

Q4. Angle representing savings = ?
a) 90° b) 120° c) 150° d) 180°
(Competency: Reading angles in pie chart)

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Case Study 5 – Frequency Table (Marks)

The marks scored by 40 students in a test are given:

[Insert Image: Frequency table of marks – Page 98]

| Marks | 10 | 20 | 30 | 40 | 50 |
|---------|----|----|----|----|
| Students| 8 | 10 | 12 | 6 | 4 |

Q1. How many students scored 30 marks?
a) 6 b) 8 c) 10 d) 12
(Competency: Frequency table reading)

Q2. Which marks were obtained by the maximum students?
a) 10 b) 20 c) 30 d) 40
(Competency: Finding mode from frequency table)

Q3. How many students scored less than 30 marks?
a) 18 b) 20 c) 22 d) 24
(Competency: Summing frequencies)

Q4. Total number of students = ?
a) 36 b) 38 c) 40 d) 42

(Competency: Adding frequency values)

7. Case-Based Questions (20 MCQs)

Case Study 1 (Fruits)

1. (c) 50

2. (d) Mango

3. (c) 130

4. (a) 4:3

Case Study 2 (Sports)

1. (a) Cricket

2. (a) 20

3. (c) 20 (30–10)

4. (b) 100

Case Study 3 (Temperature)

1. (c) Sunday (34°C)

2. (b) Friday (28°C)

3. (b) 34 – 28 = 6°C

4. (c) 4 days above 30°C

Case Study 4 (Expenditure)

1. (a) Food (120°)

2. (a) ⅓

3. (b) Rent + Savings = 90°+90°=180°

4. (a) 90°

Case Study 5 (Marks)

1. (d) 12

2. (c) 30 (highest freq = 12)

3. (a) 18 (8+10)

4. (c) 40

ANSWER KEY Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics Chapter 4: Data Handling and Presentation.

 

Answer Key – Chapter 4: Data Handling & Presentation

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1. Multiple Choice Questions (20)

1. (d) Cube root table – not a data representation.

2. (c) 5 × 10 = 50.

3. (c) Rectangular bars are used.

4. (d) 20 × 5 = 100.

5. (b) Time is on the x-axis.

6. (d) 360°.

7. (c) Most frequent value.

8. (c) 20 – 5 = 15.

9. (d) 2 × 8 = 16.

10. (a) Bar graph best shows categories.

11. (b) 9 is the middle value.

12. (b) (1+2+3+4+5)/5 = 3.

13. (c) Colour of eyes is qualitative.

14. (a) Mean is affected by extremes.

15. (c) 40% of 360° = 144°.

16. (a) Highest frequency = most common score.

17. (b) Line graph shows continuous change.

18. (a) 90°/360° = ¼.

19. (a) Mean = sum ÷ number.

20. (a) Tea (highest frequency).

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2. Assertion–Reasoning (20)

1. (c) A true, R false.

2. (c) A true, R false.

3. (a) Both true, R explains A.

4. (c) A true, R false.

5. (a) Both true, R explains A.

6. (c) A true, R false (definitions mixed up).

7. (c) A true, R false.

8. (a) Both true, R explains A.

9. (a) Both true, R explains A.

10. (a) Both true, R explains A.

11. (b) Both true, but R doesn’t explain A.

12. (a) Both true, R explains A.

13. (c) A true, R false.

14. (a) Both true, R explains A.

15. (a) Both true, R explains A.

16. (d) A false, R true.

17. (a) Both true, R explains A.

18. (a) Both true, R explains A.

19. (a) Both true, R explains A.

20. (c) A true, R false.

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3. True or False (10)

1. True

2. False (bars equal width)

3. True

4. False (360° not 180°)

5. True

6. False (median is middle, not frequent)

7. True

8. True

9. False (surveys are data collection)

10. False (mean, median, mode can differ)

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4. Short Answer I (15)

1. Data = collection of facts, e.g., daily temperatures.

2. Primary = collected first-hand; Secondary = taken from books/newspapers.

3. 4 × 10 = 40 apples.

4. Table form with Cricket =15, Football=10, Tennis=5.

5. Range = 30 – 12 = 18.

6. (6+7+8+9+10)/5 = 40/5 = 8.

7. Bar graphs handle large data; pictographs less precise.

8. Middle = 8.

9. 90°/360° = ¼.

10. More common = 20 marks (10 students).

11. 30 – 25 = 5°C.

12. Bar graph (categorical data).

13. 12 × 2 = 24 oranges.

14. 120°/360° = ⅓ = 33.3%.

15. Surveys help collect opinions systematically.

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5. Short Answer II (10)

1. Frequency table: Mode = 7, 8, 9, 10 (tie); most frequent values.

2. Bar graph plotted with absentees data.

3. Pictograph with ⚽ symbols.

4. Mean = (8+12+10+6+14)/5 = 50/5 = 10.

5. Line graph shows temps day-wise.

6. Pie chart: Total = 700. Food = 200/700×360 = 103°, Rent = 154°, Education = 51°, Other = 51°.

7. Range = 22 – 12 = 10; Median = 18.

8. Most popular = Science (50), least = English (35).

9. Mode = 12 (appears 3 times).

10. Weather data shown via line graphs/bar graphs.

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6. Long Answer (10)

1. Frequency table; Mean ≈ 21.2, Median = 20, Mode = 20.

2. Pie chart: Total=100 cars, Red=108°, Blue=72°, White=90°, Black=54°, Others=36°.

3. Line graph showing steady population growth.

4. Bar graph; Mode wages = 140 (highest frequency = 15).

5. Pie chart: Total=20000. Rent=144°, Food=108°, Education=72°, Savings=36°.

6. Cricket=144°, Football=90°, Basketball=72°, Badminton=54°.

7. Highest=Sun (35°C), Lowest=Thu (29°C).

8. Frequency table: Mean ≈ 3.2 hrs.

9. Median=20, Mode=18 & 20 (both frequent).

10. Primary=first-hand; Secondary=already collected. Pictograph=symbols, Bar graph=bars, Line graph=trend.

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7. Case-Based Questions (20 MCQs)

Case Study 1 (Fruits)

1. (c) 50

2. (d) Mango

3. (c) 130

4. (a) 4:3

Case Study 2 (Sports)

1. (a) Cricket

2. (a) 20

3. (c) 20 (30–10)

4. (b) 100

Case Study 3 (Temperature)

1. (c) Sunday (34°C)

2. (b) Friday (28°C)

3. (b) 34 – 28 = 6°C

4. (c) 4 days above 30°C

Case Study 4 (Expenditure)

1. (a) Food (120°)

2. (a) ⅓

3. (b) Rent + Savings = 90°+90°=180°

4. (a) 90°

Case Study 5 (Marks)

1. (d) 12

2. (c) 30 (highest freq = 12)

3. (a) 18 (8+10)

4. (c) 40

Class VI – Ganita Prakash QUESTION BANK (2025–2026) Subject: Mathematics Chapter 4: Data Handling and Presentation.

 

Class 6 Mathematics – Ganita Prakash

Chapter 4: Data Handling and Presentation

Study Material cum Worksheet

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Chapter Subsections Covered

4.1 Introduction to Data
4.2 Collecting and Organizing Data
4.3 Pictographs
4.4 Bar Graphs
4.5 Line Graphs
4.6 Circle Graphs (Pie Charts – Introductory)
4.7 Central Tendencies – Mean, Median, Mode
4.8 Application of Data Handling in Daily Life

[Insert Image: NCERT Ch.4, Page xx – Example of data table]
[Insert Image: NCERT Ch.4, Page xx – Example of pictograph]
[Insert Image: NCERT Ch.4, Page xx – Example of bar graph]
[Insert Image: NCERT Ch.4, Page xx – Example of line graph]

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Question Bank

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1. Multiple Choice Questions (20)

(already shared above in previous message – included in doc later)

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2. Assertion and Reasoning Questions (20)

Directions: Choose the correct option:
a) A and R are true, R explains A
b) A and R are true, R does not explain A
c) A is true, R is false
d) A is false, R is true

1. A: A pictograph uses symbols to represent data.
   R: Symbols make data easy to understand.
   (Competency: Understanding pictographs)

2. A: A bar graph always has vertical bars.
   R: Bars can be drawn horizontally as well.
   (Competency: Bar graph knowledge)

3. A: Mean is the sum of values divided by number of values.
   R: Mean is also called the average.
   (Competency: Mean calculation)

4. A: Median is the middle value of arranged data.
   R: For even numbers, it is the average of two middle values.
   (Competency: Median concept)

5. A: Mode is always greater than mean.
   R: Mode is the most frequent observation.
   (Competency: Mode understanding)

6. A: Bar graphs can be used to compare categories.
   R: The height/length of bar shows the frequency.
   (Competency: Graph interpretation)

7. A: Line graphs are best to show trends over time.
   R: They connect points representing values over time.
   (Competency: Line graphs)

8. A: In a pie chart, the whole circle represents 100%.
   R: Each sector shows a part of the whole.
   (Competency: Circle graphs)

9. A: The average marks of a class is always equal to the highest marks.
   R: Mean represents the most frequent value.
   (Competency: Misconception check)

10. A: Extreme values affect the mean.
    R: Because mean takes all values into account.
    (Competency: Mean property)

11. A: Data can be qualitative or quantitative.
    R: Favourite colour is qualitative, height is quantitative.
    (Competency: Types of data)

12. A: Frequency means how often a value occurs.
    R: In data 2,2,3,4,2 – frequency of 2 is 3.
    (Competency: Frequency concept)

13. A: A pictograph is always more accurate than a bar graph.
    R: Both are equal in accuracy.
    (Competency: Comparing graphs)

14. A: In a bar graph, width of bar has meaning.
    R: Width can be chosen freely, only height shows data.
    (Competency: Graph construction)

15. A: The sum of percentages in a pie chart is 360%.
    R: A circle has 360°.
    (Competency: Circle graphs misconception check)

16. A: Averages are useful for comparing different groups.
    R: They reduce data to a single value.
    (Competency: Importance of averages)

17. A: Organizing data in a table makes interpretation easier.
    R: It helps to see frequency and patterns.
    (Competency: Data organization)

18. A: Median is not affected by extreme values.
    R: It depends only on middle values.
    (Competency: Properties of median)

19. A: Mode cannot be used for qualitative data.
    R: Mode of favourite fruit survey can be “mango”.
    (Competency: Mode with qualitative data)

20. A: All bar graphs must start from zero.
    R: Scale of graph can start from non-zero for clarity.
    (Competency: Graph scales)

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3. True or False (10)

1. Pictographs always use pictures. (True) (Competency: Pictograph basics)

2. Mean and median are always equal. (False) (Competency: Comparing averages)

3. A line graph can show daily temperature changes. (True) (Competency: Line graph use)

4. Mode is the least occurring observation. (False) (Competency: Mode)

5. Circle graph is also called pie chart. (True) (Competency: Graph types)

6. Data handling is not useful in daily life. (False) (Competency: Real life application)

7. A frequency table shows how often values occur. (True) (Competency: Frequency table)

8. In bar graphs, spaces between bars show categories are separate. (True) (Competency: Bar graph reading)

9. Mean is not affected by extreme values. (False) (Competency: Mean property)

10. Tables, charts and graphs are ways of data presentation. (True) (Competency: Data presentation)

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4. Short Answer I – 2 Marks (15)

1. Define data with an example. (Competency: Basic definition)

2. Represent marks of 5 students: 15, 18, 20, 22, 25 in a table. (Competency: Data organization)

3. What does each bar in a bar graph represent? (Competency: Graph reading)

4. A pictograph uses 🍎 = 5 apples. Draw for 15 apples. (Competency: Pictograph drawing)

5. Define frequency. (Competency: Data terms)

6. Mean of 4, 6, 8. (Competency: Mean)

7. Median of 2, 5, 7. (Competency: Median)

8. Mode of 3, 4, 4, 5, 6. (Competency: Mode)

9. Which type of data: (i) Colour of eyes (ii) Height of students. (Competency: Data classification)

10. What is a pie chart? (Competency: Circle graph definition)

11. Draw a bar graph for 3 fruits: Apple=10, Mango=15, Banana=20. (Competency: Bar graph)

12. Give 2 advantages of data handling. (Competency: Importance of data)

13. A student has 5 absences in 30 days. Represent in pictograph (1 symbol=5 days). (Competency: Pictograph)

14. What is range of data 12,15,20,22? (Competency: Range)

15. Write difference between discrete and continuous data. (Competency: Data types)

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5. Short Answer II – 3 Marks (10)

1. Mean of 10, 20, 30, 40, 50. (Competency: Mean)

2. Find median of 5, 7, 9, 11, 15, 17. (Competency: Median)

3. Mode of 2, 3, 3, 4, 5, 5, 5, 6. (Competency: Mode)

4. Draw bar graph: Red=5, Blue=7, Green=3. (Competency: Bar graph construction)

5. In a pictograph, 🍎 = 2 books. Show 8 books. (Competency: Pictograph)

6. Marks of 5 students: 10, 12, 15, 20, 25. Find range. (Competency: Range)

7. Explain with example how mean can be misleading. (Competency: Limitations of mean)

8. A survey of pets: Dog=6, Cat=4, Fish=2. Represent as pictograph. (Competency: Pictograph drawing)

9. Find total marks if mean = 15 and number of students = 12. (Competency: Mean application)

10. Construct frequency table: Data = 2,3,2,4,3,3,5. (Competency: Data tabulation)

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6. Long Answer Questions – 5 Marks (10)

1. Marks of 10 students: 5,6,6,7,7,7,8,8,9,10. Find mean, median, mode. (Competency: Central tendency)

2. Daily temperature (°C): 30,32,31,33,32,30,29. Draw line graph. (Competency: Line graph)

3. A survey of favourite sports: Cricket=20, Football=15, Hockey=10, Tennis=5. Draw bar graph. (Competency: Bar graph)

4. A pie chart represents monthly expenses: Rent 120°, Food 90°, Travel 60°, Others 90°. Explain. (Competency: Pie chart)

5. 10 students scored marks: 15,18,20,22,25,30,32,35,36,40. Find mean. (Competency: Mean)

6. Attendance in 5 days: 35,36,34,37,38. Represent in table and bar graph. (Competency: Data tabulation and representation)

7. Discuss 3 uses of data handling in daily life. (Competency: Application)

8. Find range and mean: 2,4,6,8,10. (Competency: Range & mean)

9. A class test: 5 students scored 10,15,15,20,25. Find median. (Competency: Median)

10. Why is mode useful in daily life? Give examples. (Competency: Mode application)

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7. Case-Based Questions (5 Sets, 4 MCQs each)

Case Study 1 (Pictograph – Fruits)

A pictograph shows fruit sales. 🍎=5 fruits.
Apples=20, Mangoes=25, Oranges=15, Bananas=10.
[Insert Image: NCERT pictograph example]

Q1. How many apples sold?
a) 20 b) 25 c) 15 d) 10

Q2. Which fruit sold most?
a) Apple b) Mango c) Orange d) Banana

Q3. Total fruits sold?
a) 70 b) 60 c) 50 d) 40

Q4. Which fruit sold least?
a) Banana b) Orange c) Apple d) Mango

(Competency: CBQ – Pictograph interpretation)

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Case Study 2 (Bar Graph – Sports)

Bar graph shows favourite sports of 40 students: Cricket=15, Football=10, Hockey=8, Tennis=7.
[Insert Image: NCERT bar graph example]

Q1. Which sport most popular?
a) Cricket b) Football c) Hockey d) Tennis

Q2. How many students like Tennis?
a) 5 b) 7 c) 10 d) 15

Q3. Total students surveyed?
a) 20 b) 30 c) 40 d) 50

Q4. Difference between Cricket and Tennis lovers?
a) 5 b) 7 c) 8 d) 10

(Competency: CBQ – Bar graph interpretation)

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Case Study 3 (Line Graph – Temperature)

Line graph shows temperatures for 5 days: Mon=30, Tue=32, Wed=33, Thu=31, Fri=29.
[Insert Image: NCERT line graph example]

Q1. Highest temperature recorded?
a) 29 b) 30 c) 32 d) 33

Q2. Lowest temperature recorded?
a) 29 b) 30 c) 31 d) 32

Q3. On which day was 32°C recorded?
a) Monday b) Tuesday c) Wednesday d) Thursday

Q4. Difference between highest and lowest?
a) 2°C b) 3°C c) 4°C d) 5°C

(Competency: CBQ – Line graph interpretation)

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Case Study 4 (Pie Chart – Expenditure)

A family’s monthly budget: Rent 120°, Food 90°, Travel 60°, Others 90°.
[Insert Image: NCERT pie chart example]

Q1. Which category largest share?
a) Rent b) Food c) Travel d) Others

Q2. Which two categories equal?
a) Rent & Food b) Travel & Others c) Food & Others d) Rent & Travel

Q3. Angle for Rent?
a) 60° b) 90° c) 120° d) 180°

Q4. Total degrees of pie chart?
a) 90° b) 180° c) 270° d) 360°

(Competency: CBQ – Pie chart reading)

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Case Study 5 (Frequency Table – Attendance)

Attendance of 6 days: 35,34,36,35,37,36.
Table prepared for frequencies.
[Insert Image: NCERT frequency table example]

Q1. Most frequent attendance?
a) 34 b) 35 c) 36 d) 37

Q2. Range of data?
a) 1 b) 2 c) 3 d) 4

Q3. Mean attendance?
a) 35 b) 35.5 c) 36 d) 37

Q4. Median attendance?
a) 35 b) 35.5 c) 36 d) 37

(Competency: CBQ – Frequency table interpretation)

Make Your Own Protractor Mathematics Subject Enrichment Activity

 

Mathematics Subject Enrichment Activity

Class: VI
Chapter: Geometry – Angles (NCERT Ganita Prakash, Pages 37–40)
Activity Title: Make Your Own Protractor

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Topic

Construction and measurement of angles using a paper-made protractor.

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Aim

To construct a semicircular protractor using simple paper folding and use it to understand equal angle divisions (30°, 45°, 60°, 90°, etc.).

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Materials Required

• A sheet of paper
  
  

• Compass or circular object (to draw a circle)
  
  

• Pencil, ruler, eraser
  
  

• Scissors
  
  

• Protractor (for verification)
  
  

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Procedure

1. Draw a circle of convenient radius on paper using a compass (or trace around a round object).
   
   

2. Cut out the circle carefully.

3. Fold the circle into two equal halves → semicircle. Mark the crease as the diameter. Write “0°” at the right end of the diameter.
   
   

4. Fold the semicircle again into two equal halves. The new crease divides 180° into two parts of 90° each. Mark 90° at the top of the semicircle.
   
   

5. Fold the semicircle into three equal parts. Each division = 180° ÷ 3 = 60°. Mark 60° and 120°.
   
   

6. Further fold into six equal parts. Each part = 30°. Mark all points: 30°, 60°, 90°, 120°, 150°, 180°.
   
   

7. Open out the semicircle, draw lines through the creases, and write the angle measures.
   
   

8. Your paper protractor is now ready!
   
   

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Observations (with Solutions)

• A full circle = 360°
  
  

• A semicircle = 180°
  
  

• Folding gives equal angle divisions:
  
  

• 2 parts → 180° ÷ 2 = 90° each
  
  

• 3 parts → 180° ÷ 3 = 60° each
  
  

• 6 parts → 180° ÷ 6 = 30° each
  
  

• By combining folds, we can also get 45°, 15°, etc.
  
  

Measured Angles with Paper Protractor:

• Right angle = 90°
  
  

• Straight angle = 180°
  
  

• Acute examples = 30°, 45°, 60°
  
  

• Obtuse examples = 120°, 135°, 150°
  
  

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Reflections

• Folding paper provides a hands-on understanding of how angles are formed and measured.
  
  

• A protractor’s equal markings come from repeated halving and dividing of 180°.
  
  

• This activity shows that geometry tools are not magical – they are based on mathematical logic of circles and symmetry.
  
  

• It improves skills of angle construction, estimation, and verification.
  
  

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Higher Order Thinking Skills (HOTs)

1. If you fold the circle into 12 equal parts, what will each angle measure?
   ✅ 360° ÷ 12 = 30°.
   
   

2. How will you mark 45° on your paper protractor?
   ✅ By folding the semicircle (180°) into 2 → 90°, then folding 90° into 2 → 45°.
   
   

3. Can you make a paper protractor for 15° markings?
   ✅ Yes, fold 90° into 6 equal parts → each = 15°.
   
   

4. Why is it impossible to get every single degree marking (like 37°) by folding?
   ✅ Because folding divides angles into equal halves/thirds, not arbitrary measures. Exact 1° markings require instruments (protractor/divider).