Class 8 Mathematics - Quick Revision Notes & Formula Sheet

Chapter: Data Handling (आंकड़ों का प्रबंधन)

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1. Basic Definitions & Concepts (मूलभूत परिभाषाएं)

• Data (आंकड़े): Information collected in the form of numerical figures or facts.
• Raw Data (यथाप्राप्त आंकड़े): Data collected originally in an unorganized form.
• Frequency (बारंबारता): The number of times a particular entry or observation occurs in the given data.
• Frequency Distribution Table (बारंबारता बंटन सारणी): A table showing data along with its frequencies, often organized using Tally Marks (मिलान चिन्ह).

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2. Grouped Data & Terms (समूहीकृत आंकड़े)

When data is large, it is grouped into class intervals.

• Class Interval (वर्ग अंतराल): Groups like 0–10, 10–20, 20–30, etc.
• Lower Class Limit (निम्न वर्ग सीमा): The lowest value of a class interval.
  • Example: In 10 - 20, Lower Limit = 10.
• Upper Class Limit (उच्च वर्ग सीमा): The highest value of a class interval.
  • Example: In 10 - 20, Upper Limit = 20.
• Class Size / Width (वर्ग माप): The difference between the upper class limit and lower class limit. $$\text{Class Size} = \text{Upper Limit} - \text{Lower Limit}$$
• Class Mark (वर्ग चिन्ह): The midpoint of a class interval. $$\text{Class Mark} = \frac{\text{Upper Limit} + \text{Lower Limit}}{2}$$

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3. Graphical Representation of Data (आंकड़ों का आलेखी निरूपण)

A. Bar Graph (दण्ड आलेख)

• Display of information using bars of uniform width with equal spacing between them.
• Height of each bar represents the frequency.

B. Double Bar Graph (द्वि-दण्ड आलेख)

• A bar graph showing two sets of data simultaneously.
• Used for comparing two sets of information (e.g., marks in Term 1 vs Term 2).

C. Histogram (आयताचित्र)

• Graphical representation of continuous class intervals.
• Bars are drawn with no gaps between them because class intervals are continuous.
• A jagged line or broken line (zig-zag / kink) on the horizontal axis indicates that the scale does not start from zero.

D. Circle Graph or Pie Chart (वृत्त आलेख)

• Shows the relationship between a whole and its parts.
• The total angle at the center of a circle is 360°.

Key Formula for Pie Chart:

$$\text{Central Angle of a Component} = \left( \frac{\text{Value of the Component}}{\text{Total Value}} \right) \times 360^\circ$$

• Finding Component Value from Angle: $$\text{Value of Component} = \left( \frac{\text{Central Angle}}{360^\circ} \right) \times \text{Total Value}$$

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4. Chance and Probability (प्रायिकता)

• Random Experiment (यादृच्छिक प्रयोग): An experiment whose outcome cannot be predicted with certainty before it is conducted.
  • Example: Tossing a coin, rolling a die.
• Outcomes (परिणाम): The possible results of a random experiment.
  • Example: Tossing a coin gives 2 outcomes: Head (H) or Tail (T).
• Equally Likely Outcomes (समसंभाव्य परिणाम): Outcomes that have equal chance of occurring.
• Event (घटना): One or more outcomes of an experiment.

Formula for Probability of an Event $P(E)$:

$$P(E) = \frac{\text{Number of outcomes favorable to the event}}{\text{Total number of possible outcomes}}$$

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5. Important Rules & Properties (मुख्य नियम)

1. Range of Probability: $$0 \le P(E) \le 1$$
2. Sure / Certain Event (निश्चित घटना): Probability = 1
3. Impossible Event (असंभव घटना): Probability = 0
4. Sum of Probabilities: Sum of probabilities of all elementary events in an experiment is always equal to 1.

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6. Quick Formula Summary (त्वरित सूत्र सूची)

Concept	Formula
Class Size	Upper Limit - Lower Limit
Class Mark	(Upper Limit + Lower Limit) / 2
Central Angle (Pie Chart)	(Value of Component / Total Value) × 360°
Probability P(E)	Favorable Outcomes / Total Outcomes

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💡 Quick Exam Tips for MP Board

• Always use a ruler and pencil to draw Bar Graphs, Histograms, and Pie Charts.
• Ensure all sections of a Pie Chart add up to 360°.
• In Histograms, remember to draw a kink (jagged line) on the X-axis if the scale does not start from 0.
• Probability must always be written in its simplest fraction form or standard decimal.