Classification & Tabulation of Data: Frequency Distribution

1. Organizing Raw Data

When questionnaires return from the field, they contain hundreds of unorganized sheets known as Raw Data. To make this mass of figures intelligible, statisticians perform two essential operations:

1. Classification: Grouping data according to similarities and characteristics.
2. Tabulation: Presenting classified data systematically in rows and columns.

2. Classification of Data: 4 Main Types

Data can be classified along 4 distinct dimensions:

3. Tabulation of Data & Parts of a Statistical Table

Tabulation is the systematic and logical presentation of numerical data in horizontal Rows and vertical Columns.

The 8 Essential Components of a Statistical Table:

4. Understanding Frequency Distributions

In Business Statistics, data is analyzed across three distinct types of series:

A. Individual Series (Raw Data Series)

Items are listed individually without grouping or frequencies.

• Example: Marks of 5 BBA students in Business Statistics: 45, 62, 78, 55, 84.

B. Discrete Frequency Distribution (Ungrouped Frequency Series)

Values of variable X are listed along with their corresponding frequency f (how many times that exact value occurs).

• Example: Number of defective bulbs per carton:

C. Continuous Frequency Distribution (Grouped Series)

When data covers a wide range of values (e.g., salaries from ₹15,000 to ₹1,50,000), values are grouped into Class Intervals.

5. Key Concepts of Continuous Class Intervals

1. Class Limits:
   • Lower Limit (L1): Minimum value of class (e.g., in 10 - 20, L1 = 10).
   • Upper Limit (L2): Maximum value of class (e.g., in 10 - 20, L2 = 20).
2. Class Magnitude / Width (i or c):
   • Formula: i = L2 - L1 (e.g., 20 - 10 = 10).
3. Mid-Value / Class Mark (m or x):
   • Formula: m = (L1 + L2) ÷ 2 (e.g., (10 + 20) ÷ 2 = 15).

Exclusive vs. Inclusive Methods:

• Exclusive Method (Standard Continuous):
  • Classes: 10 - 20, 20 - 30, 30 - 40.
  • The upper limit of one class is the lower limit of the next.
  • A student scoring exactly 20 is excluded from 10 - 20 and counted in 20 - 30.
• Inclusive Method:
  • Classes: 10 - 19, 20 - 29, 30 - 39.
  • Both limits are included in the same group.
  • Conversion Rule: Subtract 0.5 from lower limits and add 0.5 to upper limits → becomes 9.5 - 19.5, 19.5 - 29.5.

6. Cumulative Frequency Distribution: “Less Than” and “More Than”

To find how many students scored below or above a certain benchmark, we compute Cumulative Frequencies (cf):

Suppose marks are: 0-10: 5, 10-20: 8, 20-30: 12, 30-40: 15.