Class 6 Mathematics Notes Chapter 9 (Data Handling) – Mathematics Book

Detailed Notes with MCQs of Chapter 9: Data Handling. This is a fundamental chapter that introduces you to how we collect, organize, and interpret information, which is a crucial skill not just in mathematics but in many areas, including for your competitive exams.

Chapter 9: Data Handling - Detailed Notes

1. Introduction to Data

• What is Data? Data is a collection of numbers, figures, words, or facts gathered to get some information. Think of it as raw information.
  • Examples: Number of students in different classes, marks obtained by students in a test, favourite colours of children in a group, temperature recorded daily for a month.
• Why Handle Data? Raw data is often difficult to understand. We need methods to organize and represent it clearly so we can:
  • Extract meaningful information.
  • Make comparisons.
  • Draw conclusions.
  • Make decisions.

2. Recording Data

• This is the first step where we simply note down the information as we collect it.
• It can be messy if not done systematically. For example, listing the favourite fruit of 30 students might look like: Apple, Banana, Orange, Apple, Guava, Banana, Apple... etc. This is hard to read quickly.

3. Organizing Data

• To make sense of raw data, we need to organize it. A common and effective method taught in this chapter is using Tally Marks and creating a Frequency Distribution Table.
• Tally Marks:
  • A simple way to keep track of counting in groups.
  • We use vertical bars (|) for each occurrence.
  • Every fifth tally mark is drawn diagonally across the previous four ( |||| ), forming a bundle of 5. This makes counting easier.
  • Example: To represent 7, we use |||| ||. To represent 12, we use |||| |||| ||.
• Frequency:
  • Frequency means the number of times a particular observation or item occurs in the data set.
  • In the tally mark system, the frequency is the total count represented by the tally marks.
• Frequency Distribution Table:

  • A table that shows the different items (or observations) and their corresponding frequencies.

  • It typically has three columns:

    1. Item/Observation (e.g., Fruit Name, Colour, Mark)
    2. Tally Marks
    3. Frequency (Number of occurrences)

  • Example Table Structure:

    Favourite Colour	Tally Marks	Frequency (No. of Students)
    Red
    Blue
    Green
    Yellow
    Total		24

  • This table makes it very easy to see which colour is most popular (Yellow) and least popular (Green).

4. Pictographs

• What is a Pictograph? It is a way of representing data using pictures or symbols. Each picture represents a certain number of items.
• Key/Scale: This is the MOST important part of a pictograph. The key tells you what quantity each symbol stands for. Without the key, the pictograph is meaningless.
  • Example: If the symbol is 🧍 and the key says 🧍 = 10 students, then 🧍🧍🧍 represents 30 students.
• Interpretation: To find the frequency of an item, count the number of symbols associated with it and multiply by the value given in the key.
• Advantages: Visually appealing, easy to understand for simple comparisons.
• Disadvantages: Difficult to represent fractions (e.g., if 🧍 = 10, how to show 15 students accurately?), can be time-consuming to draw, choice of symbol matters.

5. Bar Graphs (or Bar Charts)

• What is a Bar Graph? A bar graph displays data using rectangular bars of uniform width. The length (or height) of the bars is proportional to the values they represent.
• Components:
  • Title: Tells what the graph is about.
  • Axes: Two perpendicular lines - the horizontal axis (X-axis) and the vertical axis (Y-axis).
  • Labels: Each axis is labelled to show what it represents (e.g., 'Subjects' on X-axis, 'Marks Obtained' on Y-axis).
  • Scale: A chosen scale on one axis (usually the Y-axis) determines the length of the bars. The scale should be chosen carefully to fit the data range on the graph paper. (e.g., 1 unit length = 5 marks).
  • Bars: Rectangular bars representing the data values. They should have equal width and equal spacing between them. Bars can be drawn vertically or horizontally.
• Interpretation: Bar graphs are excellent for comparing quantities easily. You can quickly see which item has the highest or lowest value, or compare the values of different items.
• Drawing a Bar Graph:
  1. Draw the X and Y axes.
  2. Label the axes.
  3. Choose an appropriate scale for the axis representing the numerical values. Mark the scale clearly.
  4. Mark the items (categories) on the other axis at equal intervals.
  5. Draw bars of uniform width corresponding to the given values, maintaining equal spacing between bars.
  6. Give the graph a suitable title.
• Advantages: Clear comparison of data, can represent larger numbers more easily than pictographs, shows trends.
• Disadvantages: Can be complex if the range of values is very large, requires careful choice of scale.

Key Takeaways for Exams:

• Understand the difference between raw data and organized data.
• Be proficient in using Tally Marks and creating Frequency Distribution Tables.
• Know how to read and interpret Pictographs, paying close attention to the Key.
• Know how to read and interpret Bar Graphs, paying close attention to the Scale and Labels.
• Be able to compare values represented in both types of graphs.
• Understand the basic components of a bar graph (Title, Axes, Labels, Scale, Bars).

Multiple Choice Questions (MCQs)

Here are 10 MCQs based on Chapter 9 - Data Handling for practice:

1. A collection of numbers gathered to give some information is called:
   (A) Frequency
   (B) Tally Mark
   (C) Data
   (D) Bar Graph

2. In a frequency distribution table, the number of times a particular observation occurs is called its:
   (A) Tally Mark
   (B) Range
   (C) Frequency
   (D) Scale

3. Which symbol represents the number 5 in the Tally Mark system?
   (A) |||||
   (B) |||| /
   (C) V
   (D) \\\

4. In a pictograph, the 'Key' indicates:
   (A) The title of the graph
   (B) The number of items represented by each symbol
   (C) The total number of items
   (D) The labels of the axes

5. A pictograph uses a symbol 🚗 to represent 8 cars. How many symbols are needed to represent 32 cars?
   (A) 8
   (B) 32
   (C) 4
   (D) 5

6. In a bar graph, the rectangular bars should have:
   (A) Uniform width
   (B) Uniform height
   (C) Different widths
   (D) No spacing between them

7. A bar graph shows the marks obtained by students in a test. The heights of the bars represent:
   (A) The names of the students
   (B) The subjects
   (C) The marks obtained
   (D) The scale chosen

8. Refer to the Frequency Distribution Table example given in the notes (Favourite Colour). What is the frequency of the colour 'Blue'?
   (A) 7
   (B) 5
   (C) 3
   (D) 9

9. If a bar graph has a scale on the Y-axis where 1 unit length represents 10 books, how long would a bar representing 45 books be?
   (A) 4 units
   (B) 5 units
   (C) 4.5 units
   (D) 10 units

10. Which of the following is best suited for comparing the performance of a student across different subjects in an examination?
    (A) Tally Marks
    (B) Raw Data List
    (C) Pictograph
    (D) Bar Graph

Answer Key for MCQs:

1. (C) Data
2. (C) Frequency
3. (B) |||| / (Note: The diagonal slash completes the group of 5)
4. (B) The number of items represented by each symbol
5. (C) 4 (Because 32 cars / 8 cars per symbol = 4 symbols)
6. (A) Uniform width
7. (C) The marks obtained
8. (B) 5
9. (C) 4.5 units (Because 45 books / 10 books per unit = 4.5 units)
10. (D) Bar Graph (Best for direct visual comparison of quantities across categories)

Study these notes carefully, practice interpreting and drawing these representations, and you'll be well-prepared for questions from this chapter. Good luck!