Quick Revision Notes: Economics (Class 11)

Chapter: Organisation of Data

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1. Introduction to Organisation of Data

• Organisation of Data (आंकड़ों का संगठन): It refers to the arrangement of raw data in some systematic form so that it becomes easy to understand, interpret, and analyze.
• Raw Data (अवर्गीकृत आंकड़े): Mass of data collected in its original, unorganized form.
• Classification (वर्गीकरण): The process of grouping raw data into different classes or groups according to their common characteristics.

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2. Variables (चर)

A characteristic or phenomenon which can be measured and whose value changes from one individual or observation to another.

• Continuous Variable (सतत चर): Can take any numerical value within a specific range (e.g., Height, Weight, Time: 10 - 20, 20 - 30).
• Discrete Variable (विविक्त चर): Can take only specific exact values and has breaks in between (e.g., Number of students in a class: 10, 11, 12).

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3. Types of Classification

Data can be classified according to four major characteristics:

1. Chronological Classification: Data classified on the basis of time (e.g., years, months).
2. Geographical Classification: Data classified on the basis of location or region (e.g., state, country, city).
3. Qualitative (Ordinal) Classification: Data classified on the basis of qualitative attributes or characteristics (e.g., gender, literacy, religion).
4. Quantitative Classification: Data classified on the basis of numerical characteristics or variables (e.g., marks, income, age).

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4. Important Technical Terms in Frequency Distribution

• Class Limits (वर्ग सीमाएं): The lowest and highest values of a class.
  • Lower Class Limit ($L_1$): The lowest value of the class.
  • Upper Class Limit ($L_2$): The highest value of the class.
• Class Interval ($i$ or $h$): The difference between the upper class limit and lower class limit.
  • Formula: Class Interval (i) = Upper Limit - Lower Limit (L_2 - L_1)
• Mid-Point / Mid-Value ($m$): The central value of a class interval.
  • Formula: Mid-Point (m) = (Upper Limit + Lower Limit) / 2 ((L_1 + L_2) / 2)
• Frequency ($f$): The number of times an observation occurs in a particular class interval.

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5. Types of Frequency Distributions

A. Exclusive Series (अपवर्जी श्रेणी)

• The upper limit of one class is the lower limit of the next class.
• Observations equal to the upper limit are included in the next higher class.
• Example: 0 - 10, 10 - 20, 20 - 30.

B. Inclusive Series (समावेशी श्रेणी)

• Both lower and upper limits are included in the class.
• The upper limit of a class does not match the lower limit of the next class.
• Example: 0 - 9, 10 - 19, 20 - 29.
• Conversion to Exclusive Series:
  • Find the difference ($d$) between the upper limit of a class and the lower limit of the next class.
  • Subtract $d/2$ from all lower limits and add $d/2$ to all upper limits.

C. Open-End Series (खुले सिरे की श्रेणी)

• A series where the lower limit of the first class or the upper limit of the last class is not specified (e.g., "Below 10" or "Above 50").

D. Cumulative Frequency Distribution (संचयी आवृत्ति वितरण)

• Less Than Cumulative Frequency: Obtained by successively adding the frequencies of all preceding classes from top to bottom.
• More Than Cumulative Frequency: Obtained by successively adding the frequencies from bottom to top.

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6. Univariate and Bivariate Frequency Distribution

• Univariate Distribution: Frequency distribution of a single variable (e.g., marks of students).
• Bivariate Distribution: Frequency distribution of two variables simultaneously (e.g., height and weight of students).