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

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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 Group	Frequency
10–20	1
20–30	4
30–40	3
40–50	1

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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

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Steps in Constructing a Frequency Distribution 🧩

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1. Arrange Raw Data (Asc/Desc Order)

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

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2. Decide the Number of Classes

Typically 5–15 classes depending on:

• Size of data
• Range
• Required detail

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3. Find the Range

Range = Highest value – Lowest value

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

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4. Determine Class Width (Interval Size)

Class width = Range ÷ No. of classes

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

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5. Fix Class Intervals

Examples:

• 50–60
• 60–70
• 70–80

Classes must be:

• Continuous
• Mutually exclusive
• Equal width (generally)

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6. Tally the Data

A tally system is used to count frequencies.

Example:

Class	Tally	Frequency
50–60
60–70
70–80

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7. Prepare the Final Frequency Table

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Types of Frequency Distributions 📚

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1. Exclusive Class Interval Method

Upper limit is excluded.

Example:
10–20, 20–30, 30–40

20 belongs to second class.

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2. Inclusive Class Interval Method

Upper limit is included.

Example:
1–10, 11–20, 21–30

Used for discrete data like marks.

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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

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4. Relative Frequency Distribution

Frequency as a percentage of total.

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

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5. Bivariate Frequency Distribution

Used for two variables.

Example:
Income vs Education.

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ASCII Diagram — Types of Frequency Distributions

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

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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.

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Quiz Time! 🎯