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