Class 6 Maths Data Handling and Presentation Notes

Class 6 Maths Data Handling and Presentation Notes

1. Introduction

  • Data handling is the process of collecting, organizing, and interpreting information.
  • Presentation of data helps us understand patterns and make decisions easily.
  • Data can be numerical (numbers) or categorical (names, types, groups).

2. Steps in Data Handling

  1. Collection of Data – Gather information from surveys, experiments, or observations.
  2. Organization of Data – Arrange data in tables, tally marks, or lists.
  3. Presentation of Data – Use charts, graphs, or pictograms to make data understandable.
  4. Interpretation – Draw conclusions from the presented data.

3. Organizing Data

  • Tally Marks: Quick way to count frequency.
    Example: Number of students liking fruits:
    Apple |||| (4)
    Banana |||| || (6)
    Mango ||| (3)
  • Frequency Table: Shows the number of times each category occurs. FruitNumber of StudentsApple4Banana6Mango3

4. Presentation of Data

  1. Pictogram (Picture Graph) – Represent each item with a picture or symbol.
    Example: 🍎 = 2 students → Apple = 2 🍎
  2. Bar Graph – Uses rectangular bars to show frequency.
    • Vertical or horizontal bars
    • Label x-axis (categories) and y-axis (frequency)
  3. Pie Chart / Circle Graph – Shows data as parts of a whole.
    • Useful to compare percentages

5. Reading Data

  • Find Maximum/Minimum: Which category has highest or lowest frequency?
  • Compare: Use charts to compare groups quickly.
  • Average: Can find mean for numerical data.

6. Examples

Example 1 – Tally Marks and Frequency Table
The number of students who like different sports:

SportTallyFrequency
Football
Cricket
Tennis

Example 2 – Bar Graph
Draw a bar graph from the table above.

  • X-axis: Sports
  • Y-axis: Number of students

Part A – Multiple Choice Questions (MCQs) – 15 Questions

  1. Which is the first step in data handling?
    a) Presentation
    b) Interpretation
    c) Collection
    d) Organization
  2. Tally marks are counted in groups of:
    a) 3
    b) 4
    c) 5
    d) 6
  3. A bar graph represents:
    a) Only numbers
    b) Frequency of data
    c) Only words
    d) None of these
  4. Pie charts are used to:
    a) Show parts of a whole
    b) Represent tally marks
    c) Represent only numbers
    d) None of these
  5. In a pictogram, 1 symbol can represent:
    a) 1 item
    b) 2 items
    c) Any number of items
    d) All of the above
  6. Which axis of a bar graph shows the categories?
    a) X-axis
    b) Y-axis
    c) Both
    d) None
  7. The circle in a pie chart represents:
    a) Part of the data
    b) Whole data
    c) Frequency
    d) None
  8. The tally |||| represents:
    a) 3
    b) 4
    c) 5
    d) 6
  9. Data collected by observing a survey is called:
    a) Primary data
    b) Secondary data
    c) Tertiary data
    d) None
  10. Data that cannot be counted is called:
    a) Numerical data
    b) Categorical data
    c) Frequency data
    d) None
  11. Bar graphs can be:
    a) Vertical
    b) Horizontal
    c) Both
    d) None
  12. Which type of graph uses pictures to represent data?
    a) Pie chart
    b) Bar graph
    c) Pictogram
    d) Line graph
  13. If 1 symbol represents 2 students and 3 symbols are shown for apples, the number of students is:
    a) 3
    b) 6
    c) 2
    d) 9
  14. A frequency table is used to:
    a) Organize data
    b) Count tally marks
    c) Represent data pictorially
    d) None of these
  15. Maximum frequency in data shows:
    a) The least common value
    b) The most common value
    c) Average
    d) Total items

Part B – Fill in the Blanks – 10 Questions

  1. Data that can be counted is called __________.
  2. A __________ chart uses pictures to show data.
  3. In a bar graph, the vertical axis shows __________.
  4. Pie charts are used to show __________.
  5. Tally marks are grouped in __________ for easy counting.
  6. Data collected by asking questions is called __________ data.
  7. A frequency table helps us to __________ data.
  8. The whole circle in a pie chart represents __________ percent.
  9. The sum of all frequencies in a frequency table is called __________.
  10. A bar graph can be drawn __________ or __________.

Part C – True/False – 5 Questions

  1. Tally marks are a quick way to count data. (True)
  2. Bar graphs cannot be horizontal. (False)
  3. Pictograms use symbols or pictures. (True)
  4. Pie charts always represent exact numbers. (False)
  5. Data interpretation is the last step in data handling. (True)

Part D – Match the Following – 5 Questions

Column AColumn B
31. Tally charta) Pictures or symbols
32. Pictogramb) Groups of 5 marks
33. Bar graphc) Rectangular bars
34. Pie chartd) Circle divided into sectors
35. Frequencye) Number of times an item occurs

Part E – Short Answer / Problem Solving – 15 Questions

  1. Collect data on your classmates’ favourite fruit (Apple, Banana, Mango, Orange) and make a tally table.
  2. Draw a bar graph for the data in Q36.
  3. Draw a pictogram for the same data (1 symbol = 2 students).
  4. Find which fruit is liked by the maximum students.
  5. Find which fruit is liked by the minimum students.
  6. The favourite subject of students in a class is:
    | Subject | Students |
    |——— | ———|
    | Maths | 12 |
    | Science | 10 |
    | English | 8 |
    | Hindi | 5 |
    Draw a bar graph for the above data.
  7. Draw a pie chart for the above data.
  8. Convert this tally chart into a frequency table:
    | Colour | Tally |
    |——–|——|
    | Red | |||| |
    | Blue | |||| || |
    | Green | ||| |
  9. A survey shows favourite pets of 20 students: Dog 8, Cat 6, Fish 4, Bird 2. Draw a pictogram (1 symbol = 2 students).
  10. In a bar graph, which axis represents frequency?
  11. What is the total number of students in Q44?
  12. What percent of students like dogs in Q44?
  13. Explain the difference between pictogram and bar graph.
  14. Draw a pie chart for students’ favourite ice cream flavours: Vanilla 10, Chocolate 5, Strawberry 5.
  15. How does data handling help in daily life? Give 2 examples.

Answers – Class 6 Maths: Data Handling and Presentation

Part A – MCQs (Answers)

  1. c) Collection
  2. c) 5
  3. b) Frequency of data
  4. a) Show parts of a whole
  5. d) All of the above
  6. a) X-axis
  7. b) Whole data
  8. b) 4
  9. a) Primary data
  10. b) Categorical data
  11. c) Both
  12. c) Pictogram
  13. b) 6
  14. a) Organize data
  15. b) The most common value

Part B – Fill in the Blanks (Answers)

  1. Numerical data
  2. Pictogram
  3. Frequency / Number of items
  4. Parts of a whole
  5. 5
  6. Primary
  7. Organize / Summarize
  8. 100%
  9. Total frequency
  10. Vertical or Horizontal

Part C – True/False (Answers)

  1. True
  2. False
  3. True
  4. False
  5. True

Part D – Match the Following (Answers)

Column AAnswer (Column B)
31. Tally chartb) Groups of 5 marks
32. Pictograma) Pictures or symbols
33. Bar graphc) Rectangular bars
34. Pie chartd) Circle divided into sectors
35. Frequencye) Number of times an item occurs

Part E – Short Answer / Problem Solving (Answers)

  1. Tally Table Example (students liking fruits):
FruitTallyFrequency
Apple
Banana
Mango
Orange
  1. Bar Graph:
  • X-axis: Fruits (Apple, Banana, Mango, Orange)
  • Y-axis: Number of students (Frequency)
  • Bars height: Apple=4, Banana=6, Mango=3, Orange=2
  1. Pictogram: (1 symbol = 2 students)
  • Apple: 2 symbols 🍎🍎
  • Banana: 3 symbols 🍌🍌🍌
  • Mango: 2 symbols 🥭
  • Orange: 1 symbol 🍊
  1. Maximum liked fruit → Banana (6 students)
  2. Minimum liked fruit → Orange (2 students)
  3. Bar Graph Example (Subjects):
  • Maths = 12
  • Science = 10
  • English = 8
  • Hindi = 5
  1. Pie Chart (Subjects):
  • Total = 12+10+8+5 = 35 students
  • Angle calculation:
    • Maths = (12/35)*360 ≈ 123°
    • Science = (10/35)*360 ≈ 103°
    • English = (8/35)*360 ≈ 82°
    • Hindi = (5/35)*360 ≈ 52°
  1. Frequency Table (from tally chart):
ColourFrequency
Red4
Blue6
Green3
  1. Pictogram (Favourite pets, 1 symbol = 2 students):
  • Dog = 4 symbols 🐶🐶🐶🐶
  • Cat = 3 symbols 🐱🐱🐱
  • Fish = 2 symbols 🐟🐟
  • Bird = 1 symbol 🐦
  1. In a bar graph, Y-axis represents frequency.
  2. Total students in Q44 = 10+6+4+2 = 22 → (Correction: tally from data: Dog=10, Cat=6, Fish=4, Bird=2 → Total = 22)
  3. Percent of students liking dogs: (10/22)*100 ≈ 45.45%
  4. Difference between pictogram and bar graph:
  • Pictogram: Uses pictures or symbols for representation.
  • Bar graph: Uses rectangular bars for numerical frequency.
  1. Pie chart (Ice cream flavours):
  • Total students = 10 + 5 + 5 = 20
  • Angles:
    • Vanilla: (10/20)*360 = 180°
    • Chocolate: (5/20)*360 = 90°
    • Strawberry: (5/20)*360 = 90°
  1. Usefulness of data handling in daily life:
  • Helps understand patterns (e.g., favourite food, study hours)
  • Helps in decision making (e.g., planning school activities, surveys)