Mode – Determination & Uses 🎯📊

The Mode is the value that occurs most frequently in a dataset. It represents the most typical, most popular, or most common observation.

Mode is especially useful when dealing with:

• Repeated values
• Qualitative data (e.g., favourite brand)
• Skewed distributions

Definition

The Mode is the value that appears maximum number of times in a series.

It is a descriptive average and is easy to understand and compute.

Mode for Ungrouped Data

Simply identify the value that occurs most frequently.

Example 1

Data: 4, 6, 8, 8, 10, 12

Mode = 8 (appears twice)

Example 2

Data: 2, 3, 3, 4, 4, 5

Bimodal distribution → Modes = 3 and 4

Example 3

Data: 5, 7, 9, 11

No value repeats → No Mode

Mode for Discrete Frequency Distribution

Identify the value of X with the highest frequency.

Example

Mode = 30 (highest frequency = 8)

Mode for Grouped (Continuous) Data

In grouped data, the modal value lies in the class with the highest frequency.

This class is called the modal class.

Formula

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

Where:

• L = lower limit of modal class
• f1 = frequency of modal class
• f0 = frequency of class before modal class
• f2 = frequency of class after modal class
• h = class width

Steps to Calculate Mode (Grouped Data)

1. Identify the modal class (highest f).
2. Note f0, f1, f2.
3. Apply formula.

Worked Example – Grouped Data

Example Table

Here, highest frequency = 12 → Modal class = 20–30.

L = 20
f0 = 7
f1 = 12
f2 = 9
h = 10

Apply formula:

Mode = 20 + [(12 - 7) / (2×12 - 7 - 9)] × 10
     = 20 + [5 / (24 - 16)] × 10
     = 20 + (5/8) × 10
     = 20 + 6.25
Mode = 26.25

Empirical Relationship (When Mode Is Not Clear)

Used when distribution is moderately skewed:

Mode = 3Median - 2Mean

Properties of Mode ⭐

1. Represents most common value

2. Not affected by extreme values

3. Can be used for open-ended classes

4. Useful for qualitative data

5. Possible even when mean & median are not meaningful

Advantages ✔️

• Very easy to understand
• Best for retail, fashion, marketing, and consumer behavior
• Suitable for nominal/qualitative data (e.g., favourite brand)

Limitations ❌

• Not based on all observations
• May not be unique (bimodal or multimodal)
• Formula less reliable when frequencies fluctuate heavily

When to Use Mode?

Use Mode when:

• Data describes preferences or categories
• Distribution is skewed
• Most common value is more important than average

Examples:

• Most preferred mobile brand
• Most sold shoe size
• Most common customer complaint

Summary ✨

• Mode = most frequent value
• Grouped data → use modal class formula
• Works best for qualitative data and skewed distributions
• May be bimodal or multimodal
• Useful empirical relation → Mode = 3Median - 2Mean

Quiz Time 🎯