What is the formula of mode?

For ungrouped data the mode is the value that occurs most frequently in a dataset. For grouped data the formula is Mode = L + [(f1 − f0) / (2f1 − f0 − f2)] × h.

What is the mode formula for grouped data?

Mode = L + [(f1 − f0) / (2f1 − f0 − f2)] × h where L is the lower boundary of the modal class, f1 is the frequency of the modal class, f0 is the preceding class frequency, f2 is the succeeding class frequency, and h is the class width.

What is a modal class?

The modal class is the class interval that has the highest frequency in a grouped frequency distribution.

Why is the mode important in statistics?

The mode helps identify the most common or frequently occurring value in a dataset and is useful for understanding data distribution.

Mode formula in statistics (with example)

Q: Can a dataset have more than one mode?

Yes. A dataset may have one mode (unimodal), two modes (bimodal), or multiple modes (multimodal) depending on how frequently values appear.

What Is the Mode Formula?

The mode formula in statistics identifies the most frequently occurring value in a dataset.

Mode Formula for Ungrouped Data

For raw, ungrouped datasets, the mode is the value that occurs most frequently.

Formula: Mode = Value with highest frequency

Where:

Symbol	Meaning
Mode	Most frequently occurring value
x	Individual observation
n	Total number of observations

Steps to Calculate Mode (Ungrouped):

List all values in your dataset
Count the frequency of each value
Identify the maximum frequency
The value(s) with the highest frequency is the mode

Example Ungrouped Data (Unimodal):

Dataset: 2, 3, 3, 5, 6 Mode = 3

Example Bimodal Dataset:

Dataset: 1, 2, 2, 3, 3, 4, 5 Modes = 2 and 3

Example Multimodal Dataset:

Dataset: 1, 1, 2, 2, 3, 3, 4 Modes = 1, 2, 3

Mode Formula for Grouped Data (Frequency Distribution)

For datasets organized into class intervals, the mode is estimated using the modal class:

Formula (Grouped Mode):

Mode = L + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h

Where:

Symbol	Meaning
L	Lower boundary of the modal class
f₁	Frequency of the modal class
f₀	Frequency of the class preceding modal class
f₂	Frequency of the class succeeding modal class
f₂	Frequency of the class succeeding modal class

Steps to Calculate Mode (Grouped):

Construct a frequency distribution table
Identify the modal class (class with the highest frequency, f₁)
Note f₀ and f₂ (neighboring class frequencies)
Apply the formula above
Compute the estimated mode

Example Grouped Data:

Example Grouped Data

Special Cases in Mode Calculation

Multiple Modes: Two or more classes have the same highest frequency
Irregular Frequencies: The mode can still be estimated even when frequencies vary
No Mode: All classes have the same frequency

Symbols & Entities Used in Mode Formulas

Entities included for semantic depth:

Symbol	Meaning
Mode	Most frequent value
f₀	Frequency of previous class
f₁	Frequency of modal class
f₂	Frequency of next class
L	Lower boundary of modal class
h	Class width
n	Total observations
x	Individual observation

Frequently Asked Questions about Mode

What is the formula for mode?

Ungrouped: Mode = Value with highest frequency
Grouped: Mode = L + [(f₁ − f₀) / (2f₁ − f₀ − f₂)] × h

How do I identify the modal class?

The modal class is the class interval with the highest frequency in a grouped dataset.

Can a dataset have more than one mode?

Yes. Bimodal datasets have two modes; multimodal datasets have more than two.

Do outliers affect the mode?

No. Mode is frequency-based and independent of magnitude.