Class 6 Mathematics Notes Chapter 9 (Chapter 9) – Exemplar Problem (English) Book

Alright class, let's get straight into Chapter 9: Data Handling from your NCERT Exemplar book. This chapter is crucial, not just for your school exams, but it also forms the foundation for interpreting information presented visually, a skill often tested in various government exams. Pay close attention!

Chapter 9: Data Handling - Detailed Notes

1. What is Data?

• Data is essentially a collection of information, usually in the form of numbers, figures, words, or observations, gathered to understand something or answer a question.
• Example: Marks obtained by students in a test, temperatures recorded daily in a city, types of vehicles passing a road, favourite sports of classmates.
• Raw Data: Data collected initially, without any organisation or arrangement, is called raw data. It's often difficult to understand or draw conclusions from raw data directly.

2. Why Organise Data?

• Raw data is confusing and doesn't give clear information easily.
• Organising data helps us to:
  • See patterns easily.
  • Compare different items quickly.
  • Find specific information (like the highest or lowest value) efficiently.
  • Draw meaningful conclusions.

3. Organising Data: Tally Marks and Frequency Distribution

• One common way to organise data is using tally marks.

• Tally Marks: These are vertical lines used to count occurrences.

  • We draw one vertical line (|) for each observation.
  • The fifth observation is marked by a diagonal line across the previous four (||||). This makes counting groups of 5 easy.

• Frequency: The number of times a particular observation or item occurs in the data is called its frequency.

• Frequency Distribution Table: A table that shows the different observations (or categories) along with their corresponding frequencies is called a frequency distribution table. It often includes a column for tally marks.

  Example: Suppose the favourite colours of 20 students are: Red, Blue, Green, Red, Yellow, Blue, Red, Green, Blue, Red, Yellow, Red, Blue, Green, Red, Blue, Yellow, Red, Blue, Green.

  Colour	Tally Marks	Frequency (No. of Students)
  Red
  Blue
  Green
  Yellow
  Total		20

4. Pictograph: Representing Data with Pictures

• A pictograph represents data using pictures or symbols.

• Key/Scale: This is the most important part of a pictograph. It tells you what each symbol represents (e.g., 1 picture = 10 items). Without the key, the pictograph is meaningless.

• How to Read: Count the symbols for each category and multiply by the value given in the key.

• Advantages: Visually appealing, easy to understand for simple data.

• Disadvantages: Difficult to show fractional values (e.g., if 1 symbol = 10 cars, how to show 15 cars?), can be time-consuming to draw, may not be accurate for large or precise numbers.

  Example: Production of apples in a farm (Key: 🍎 = 50 kg)

  • Monday: 🍎🍎🍎🍎 (4 x 50 = 200 kg)
  • Tuesday: 🍎🍎🍎🍎🍎 (5 x 50 = 250 kg)

5. Bar Graph (Bar Chart): Representing Data with Bars

• A bar graph uses rectangular bars of uniform width to represent data. The length (or height) of the bar corresponds to the value or frequency of the data item.

• Components:

  • Title: Tells what the graph is about.
  • Axes: Two perpendicular lines – Horizontal axis (X-axis) and Vertical axis (Y-axis).
  • Labels: Describe what each axis represents (e.g., 'Days' on X-axis, 'Temperature' on Y-axis).
  • Scale: A chosen ratio that determines the length of the bars (e.g., 1 unit length = 5 marks). The scale must be consistent along the axis.
  • Bars: Rectangular bars of equal width, with equal spacing between them. The height/length represents the data value. Bars can be drawn vertically or horizontally.

• How to Read: Locate the category on one axis and follow the top (or end) of the bar across to the other axis to read the corresponding value using the scale.

• Advantages: Good for comparing quantities across different categories, clearer representation of precise values compared to pictographs, can represent larger datasets effectively.

• Disadvantages: Not ideal for showing trends over time (line graphs are better for that, which you'll learn later).

  Example: A bar graph showing marks of a student in different subjects. You can easily compare in which subject the student scored highest or lowest, and find the exact marks using the scale on the Y-axis.

Key Takeaways for Government Exams:

• Focus on quick interpretation: Be able to quickly find the highest/lowest value, compare values between categories, and calculate totals or differences from tables, pictographs, and bar graphs.
• Always check the Title, Key (for pictographs), and Scale and Labels (for bar graphs) before interpreting. A misunderstanding here leads to wrong answers.
• Understand the purpose of each representation method (Tally table for organising, Pictograph for simple visual appeal, Bar graph for comparison).

Multiple Choice Questions (MCQs)

Here are 10 MCQs based on Chapter 9 concepts:

1. A collection of numbers gathered to give some information is called:
   (a) Tally Mark
   (b) Frequency
   (c) Data
   (d) Scale

2. In a frequency distribution table, the tally mark '|||| ||' represents which frequency?
   (a) 5
   (b) 6
   (c) 7
   (d) 8

3. A pictograph uses a symbol 🚗 to represent 10 cars. How many symbols are needed to represent 45 cars?
   (a) 4 symbols
   (b) 5 symbols
   (c) 4 and a half symbols
   (d) 45 symbols

4. In a bar graph, the rectangular bars have:
   (a) Uniform width and uniform spacing
   (b) Varying width but uniform spacing
   (c) Uniform width but varying spacing
   (d) Varying width and varying spacing

5. The primary purpose of drawing a bar graph is to:
   (a) Organise raw data
   (b) Show data using pictures
   (c) Compare quantities among different categories
   (d) Count occurrences using tally marks

6. Refer to the Frequency Distribution Table example in the notes (Favourite Colours). Which colour is the least favourite?
   (a) Red
   (b) Blue
   (c) Green
   (d) Yellow

7. In a bar graph showing the number of students in different classes of a school, the scale on the vertical axis is 1 unit = 20 students. If the bar for Class 6 has a height of 5 units, how many students are in Class 6?
   (a) 20
   (b) 25
   (c) 100
   (d) 5

8. What does the 'Key' or 'Scale' in a pictograph tell us?
   (a) The title of the pictograph
   (b) The number of categories
   (c) What each picture or symbol represents
   (d) The total frequency

9. Why is it necessary to organise raw data?
   (a) To make it look complicated
   (b) To make it easy to understand, compare, and interpret
   (c) To convert it into pictures
   (d) To increase the number of observations

10. A bar graph shows the runs scored by a cricket team in the first 5 overs: Over 1 - 6 runs, Over 2 - 4 runs, Over 3 - 10 runs, Over 4 - 2 runs, Over 5 - 8 runs. Which over had the highest runs scored?
    (a) Over 1
    (b) Over 3
    (c) Over 5
    (d) Over 4

Answer Key for MCQs:

1. (c)
2. (c)
3. (c) (4 full symbols for 40, and half a symbol for 5)
4. (a)
5. (c)
6. (d)
7. (c) (5 units * 20 students/unit = 100 students)
8. (c)
9. (b)
10. (b)

Study these notes carefully. Understanding how data is organised and represented is a very practical skill. Let me know if any part is unclear!