Organisation of Data

Raw Data: A mass of unorganized, chaotic numerical observations collected directly from the field before any processing. It is difficult to comprehend and unsuited for mathematical analysis.

Classification: The process of arranging raw data into homogeneous groups, classes, or categories according to shared similarities and common characteristics.

The 4 Bases of Classification:

1. 1. Chronological (Temporal) Classification: Data classified according to periods of time (years, months, weeks). E.g., India's food grain production from 1950 to 2024.
2. 2. Spatial (Geographical) Classification: Data classified according to geographical locations or areas (countries, states, districts). E.g., Literacy rates across Indian states.
3. 3. Qualitative Classification: Data classified based on descriptive qualitative attributes that cannot be measured directly:
   • Simple Classification (Dichotomy): Divided into two mutually exclusive categories (e.g., Male vs Female; Employed vs Unemployed).
   • Manifold Classification: Divided into multiple hierarchical sub-classes (e.g., Population → Gender → Literacy → Employment status).
4. 4. Quantitative Classification: Data classified on the basis of measurable numerical characteristics (variables) such as income, height, weight, or marks. E.g., Number of families earning ₹20,000–₹30,000.

A Variable is an economic characteristic or quantity capable of taking different numerical values across individuals, households, or time periods:

A Frequency Distribution is a tabular summary of data showing the frequency (number of occurrences) of observations falling into each non-overlapping class interval:

Key Structural Definitions:

• Class Limits: The two extreme values defining a class:
  • Lower Class Limit ($L_1$): The minimum value that can belong to the class.
  • Upper Class Limit ($L_2$): The maximum value that can belong to the class.
• Class Interval (Width / Magnitude, $i$ or $h$): The difference between the upper class limit and the lower class limit: $$i = L_2 - L_1$$
• Class Mark (Mid-Value, $m$): The central value representing the class: $$m = \frac{L_1 + L_2}{2}$$
• Range: The difference between the largest ($L$) and smallest ($S$) values in the entire raw dataset: $$\text{Range} = L - S$$

A. Exclusive Method (Continuous Series):

The upper limit of one class is identical to the lower limit of the next class (e.g., 10–20, 20–30, 30–40). An observation exactly equal to the upper limit (e.g., 20) is excluded from that class and counted in the subsequent class. Essential for continuous mathematical modeling.

B. Inclusive Method (Discrete Class Intervals):

The upper limit of one class is included within that class itself (e.g., 10–19, 20–29, 30–39). Used for discrete integer data.

Conversion Rule: To calculate statistical measures (Median, Mode, Quartiles, Histograms), an inclusive series MUST be converted to an exclusive series by calculating the adjustment factor: $$\text{Correction Factor} = \frac{\text{Lower limit of 2nd class} - \text{Upper limit of 1st class}}{2} = \frac{20 - 19}{2} = 0.5$$ Deduct 0.5 from all lower limits ($L_1 - 0.5$) and add 0.5 to all upper limits ($L_2 + 0.5$). Series becomes: 9.5–19.5, 19.5–29.5, 29.5–39.5!

C. Cumulative Frequency Distributions:

• "Less Than" Cumulative Series: Frequencies are progressively added starting from the lowest class to the highest class, anchored at the upper class limits.
• "More Than" Cumulative Series: Frequencies are progressively deducted starting from the total frequency down to the lowest class, anchored at the lower class limits.