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Frequency Distribution – Construction & Types 📊📏

Raw data is scattered, messy, and hard to understand.
A Frequency Distribution converts this raw data into organized, meaningful groups (class intervals), showing how many observations fall within each class.

It is the foundation for:

  • Histograms
  • Ogives
  • Mean/Median calculations
  • Standard deviation
  • Correlation

What Is a Frequency Distribution?

Definition:

A frequency distribution is a tabular arrangement of data showing class intervals and the number of observations (frequency) in each interval.

Example (Raw data → Organized):

Raw Data:
18, 22, 25, 29, 31, 33, 35, 38, 41…

Organized Table:

Age GroupFrequency
10–201
20–304
30–403
40–501

Why Use Frequency Distribution?

✔ Shows patterns and trends
✔ Converts large data into small, meaningful tables
✔ Essential for graphs and statistical calculations
✔ Helps identify concentration of values

Steps in Constructing a Frequency Distribution 🧩

1. Arrange Raw Data (Asc/Desc Order)

Example:
8, 12, 10, 14 → 8, 10, 12, 14

2. Decide the Number of Classes

Typically 5–15 classes depending on:

  • Size of data
  • Range
  • Required detail

3. Find the Range

Range = Highest value – Lowest value

Example:
Highest = 98
Lowest = 52
Range = 98 − 52 = 46

4. Determine Class Width (Interval Size)

Class width = Range ÷ No. of classes

Example:
Range = 46
Classes = 5
Class width ≈ 10

5. Fix Class Intervals

Examples:

  • 50–60
  • 60–70
  • 70–80

Classes must be:

  • Continuous
  • Mutually exclusive
  • Equal width (generally)

6. Tally the Data

A tally system is used to count frequencies.

Example:

ClassTallyFrequency
50–60
60–70
70–80

7. Prepare the Final Frequency Table

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Types of Frequency Distributions 📚

1. Exclusive Class Interval Method

Upper limit is excluded.

Example:
10–20, 20–30, 30–40

20 belongs to second class.

2. Inclusive Class Interval Method

Upper limit is included.

Example:
1–10, 11–20, 21–30

Used for discrete data like marks.

3. Cumulative Frequency Distribution

Used to find:

  • Median
  • Ogive
  • Percentiles
  • Quartiles

Two types:

(a) Less Than Cumulative Frequency

Example:
Less than 10 = 2
Less than 20 = 7
Less than 30 = 13

(b) More Than Cumulative Frequency

Example:
More than 10 = 18
More than 20 = 11
More than 30 = 6

4. Relative Frequency Distribution

Frequency as a percentage of total.

Example:
If 10 out of 100 students score 80+ marks → 10%

5. Bivariate Frequency Distribution

Used for two variables.

Example:
Income vs Education.

ASCII Diagram — Types of Frequency Distributions

Exclusive
↓
Inclusive
↓
Cumulative (Less/More)
↓
Relative
↓
Bivariate

Summary ✨

  • Frequency distribution organizes data into equal class intervals.
  • Steps: Arrange → Range → Class width → Intervals → Tally → Table.
  • Types include exclusive, inclusive, cumulative, relative, and bivariate.

Quiz Time! 🎯

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