Quick Revision Notes: Class 7 Mathematics

Chapter: Data Handling

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1. Introduction to Data Handling

• Data (आँकड़े): A collection of numbers or information gathered to get some information.
• Raw Data (अवर्गीकृत आँकड़े): Data obtained in its original form, just as it is collected.

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2. Collection and Organisation of Data

• To make data useful and meaningful, we need to organise it.
• Frequency (आवृत्ति): The number of times a particular observation occurs in a data set.
• Frequency Distribution Table (बारंबारता बंटन सारणी): A table that shows the frequency of each data item using tally marks (|, ||, |||, ||||, CANCEL|).

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3. Representative Values (Central Tendency)

A representative value is a single value that represents the entire data. It lies somewhere between the highest and lowest values of the data. These are also called measures of Central Tendency (केंद्रीय प्रवृत्ति की माप).

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4. Arithmetic Mean (समांतर माध्य)

The mean is the most common representative value of a group of data. It is also simply called the average (औसत).

• Formula: $$\text{Mean} = \frac{\text{Sum of all observations}}{\text{Total number of observations}}$$

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5. Range (परिसर)

The range gives us an idea of the spread of the data. It is the difference between the highest and lowest observations.

• Formula: $$\text{Range} = \text{Highest Observation} - \text{Lowest Observation}$$

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6. Median (माध्यिका / माध्यक)

The median refers to the value which lies right in the middle of the data when arranged in an ascending or descending order.

• Steps to find the Median:
  1. Arrange the data in ascending or descending order.
  2. If the number of observations ($n$) is odd, the median is the middle term.
     • $\text{Median} = \left(\frac{n + 1}{2}\right)^{\text{th}} \text{ term}$

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7. Mode (बहुलक)

The mode of a set of observations is the observation that occurs most often (has the maximum frequency).

• Key Points:
  • A data set can have one mode, more than one mode (multimodal), or no mode if all values occur equally.
  • It is very useful for finding the most popular item (e.g., shoe size, favorite color).

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8. Use of Bar Graphs with a Difference

A bar graph is a representation of numbers using bars of uniform width.

• Double Bar Graph: A bar graph showing two sets of data simultaneously. It is very useful for comparing two collections of data at a glance (e.g., comparing students' marks in two successive terms).

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9. Chance and Probability (संभावना और प्रायिकता)

• Chance (संभावना): The likelihood of occurrence of an event.

• Probability (प्रायिकता): A quantitative measure of the chance of an event happening.

• Formula: $$\text{Probability of an Event} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$$

• Key Terms:

  • Event (घटना): A subset of outcomes of an experiment (e.g., getting a head when a coin is tossed).
  • Equally Likely Outcomes (समसंभाव्य परिणाम): Outcomes that have the same chance of occurring (e.g., getting Head or Tail on a fair coin).
  • Probability Value: Always lies between 0 and 1 (inclusive).
    • 0 means an impossible event.
    • 1 means a certain event.