Economics: Class 11 (Part 2) — Chapter 3: Organisation of Data

Classification is the process of arranging or organizing things into groups or classes based on some criteria. It helps to:

• Bring order to raw data.
• Facilitate easy comparison and statistical analysis.
• Locate information quickly without searching through the entire dataset.

In Chronological Classification, data are grouped with reference to time, such as years, quarters, months, or weeks. The values are arranged in ascending or descending order of time.

In Spatial Classification, data are classified with reference to geographical locations, such as countries, states, cities, or districts.

When data are classified on the basis of attributes or non-measurable characteristics (qualities), it is called Qualitative Classification. Examples include nationality, literacy, religion, gender, and marital status.

Qualitative classification can be simple (presence or absence of one attribute) or manifold (sub-classified into multiple nested attributes, e.g., Population divided into Male/Female, and further into Married/Unmarried).

When data are grouped into classes based on characteristics that can be measured quantitatively (such as height, weight, age, income, or marks), it is called Quantitative Classification.

A continuous variable can take any numerical value (including fractional and decimal values) within a given range. Its values can be broken down into infinite gradations.

• Examples: Height, weight, time, distance, and temperature.

A discrete variable can take only certain specific values and changes by finite "jumps". It cannot take fractional values between two adjacent integral values.

• Examples: Number of students in a class, size of a household, or number of cars on the road.

• Class Limits: The two ends of a class. The lowest value is the Lower Class Limit, and the highest value is the Upper Class Limit.
• Class Interval (or Class Width): The difference between the upper class limit and the lower class limit. $$\text{Class Interval} = \text{Upper Class Limit} - \text{Lower Class Limit}$$
• Class Mid-Point (or Class Mark): The middle value of a class, calculated as: $$\text{Class Mid-Point} = \frac{\text{Upper Class Limit} + \text{Lower Class Limit}}{2}$$
• Class Frequency: The number of observations falling within a particular class.

There are two methods of forming class intervals:

1. Exclusive Method: Under this method, the upper class limit of one class is excluded from that class and included as the lower limit of the next class (e.g., in class 10–20, the value 20 is excluded and placed in 20–30).
2. Inclusive Method: Under this method, values equal to both the lower and upper limits are included in the same class (e.g., 800–899, where both 800 and 899 are included).

To maintain continuity when using the inclusive method for continuous variables, class limits must be adjusted:

1. Find the difference ($D$) between the lower limit of the second class and the upper limit of the first class.
2. Divide the difference by 2 ($D/2$, usually $0.5$).
3. Subtract this value from all lower class limits ($\text{Lower Limit} - 0.5$).
4. Add this value to all upper class limits ($\text{Upper Limit} + 0.5$).

The adjusted class mark is calculated as:

The counting of class frequency is done using tally marks. A vertical bar ($/$) is put against a class for each observation. The fifth tally is placed diagonally across the first four ($////$ with a slash) to form groups of five, making counting easier.

An inherent shortcoming of grouping data into a frequency distribution is the loss of information. Once raw data are grouped into classes, individual observations lose their unique identity. For further statistical calculations, all values in a class are assumed to be equal to the class mark.

For a discrete variable, the classification of data is known as a Frequency Array. Since discrete variables do not take fractional values, frequencies correspond directly to individual integral values rather than class intervals.

A Bivariate Frequency Distribution is the frequency distribution of two variables simultaneously (e.g., a table showing the relation between Sales and Advertisement Expenditure of various firms).