Introduction

In statistics and Machine Learning, we often work with large datasets. A dataset may contain hundreds, thousands, or even millions of values. To understand such data quickly, we need a single representative value that can describe the center or typical behavior of the data.

Mean, Median, and Mode are three important statistical measures used to describe the central tendency of a dataset. Central tendency means the central or typical value around which most data values are located.

Prerequisites

Before learning Mean, Median, and Mode, students should have basic understanding of the following topics:

What is Central Tendency?

Central tendency is a statistical concept that describes the center point or representative value of a dataset. It helps summarize an entire dataset using one meaningful value.

For example, if we have marks of 50 students, instead of looking at all 50 marks separately, we can calculate the mean, median, or mode to understand the general performance of the class.

Quick Overview

1. Mean

Mean is the arithmetic average of all values in a dataset. It is calculated by adding all values and dividing the sum by the total number of values.

Here:
\( \bar{x} \) = Mean
\( x_1, x_2, x_3, ... x_n \) = Data values
\( n \) = Total number of values

Example of Mean

Suppose the marks of five students are:

80, 70, 90, 60, 100

To find the mean:

So, the mean marks are 80.

Mean and Outlier Problem

Consider the following salary data:

30000, 32000, 35000, 38000, 1000000

Here, 1000000 is an extreme value. If we calculate the mean, it becomes very high and may not represent the typical salary correctly.

2. Median

Median is the middle value of a dataset when the values are arranged in ascending or descending order. It divides the dataset into two equal halves.

Steps to Find Median

Example 1: Median for Odd Number of Values

Dataset:

30, 10, 50, 20, 40

First, arrange in ascending order:

10, 20, 30, 40, 50

There are 5 values, so the middle value is:

Example 2: Median for Even Number of Values

Dataset:

10, 20, 30, 40

There are 4 values, so there are two middle values: 20 and 30.

So, the median is 25.

3. Mode

Mode is the value that appears most frequently in a dataset. It is useful when we want to identify the most common value or most popular category.

Example of Mode

Dataset:

2, 3, 3, 5, 6, 3, 8

Here, 3 appears three times, more than any other value.

Types of Mode

A dataset can have one mode, more than one mode, or no mode depending on frequency.

Mean vs Median vs Mode

Mean, median, and mode all describe the center of data, but they work differently. Choosing the correct measure depends on the type and shape of the data.

When Should We Use Mean, Median, or Mode?

Mean, Median, Mode and Data Distribution

The relationship between mean, median, and mode can also help us understand the shape of data distribution.

Importance in Machine Learning

Mean, median, and mode are not only mathematical concepts. They are used practically in Machine Learning projects during data exploration, data cleaning, feature engineering, and preprocessing.

Real-World Examples

Python Example

The following example shows how to calculate mean, median, and mode using Python.

import pandas as pd

# Sample marks dataset
marks = [80, 70, 90, 60, 100, 70, 85]

# Convert list into pandas Series
data = pd.Series(marks)

# Calculate mean, median, and mode
mean_value = data.mean()
median_value = data.median()
mode_value = data.mode()[0]

print("Mean:", mean_value)
print("Median:", median_value)
print("Mode:", mode_value)

Output

Mean: 79.28571428571429
Median: 80.0
Mode: 70

In this example:
Mean gives the average marks.
Median gives the middle marks after sorting.
Mode gives the most repeated marks.

NumPy and SciPy Example

In Machine Learning, NumPy and SciPy are commonly used for numerical calculations.

import numpy as np
from scipy import stats

speed = [99, 86, 87, 88, 111, 86, 103, 87, 94, 78, 77, 85, 86]

mean_speed = np.mean(speed)
median_speed = np.median(speed)
mode_speed = stats.mode(speed, keepdims=True)

print("Mean Speed:", mean_speed)
print("Median Speed:", median_speed)
print("Mode Speed:", mode_speed.mode[0])

Complete Hand Calculation Example

Let us calculate mean, median, and mode for the following dataset:

10, 20, 20, 30, 40

Mean

Median

Data is already sorted:

10, 20, 20, 30, 40

Mode

The value 20 appears two times, more than any other value.

Advantages

Limitations

Common Mistakes Students Make

Quick Revision

Interview Questions

Conclusion

Mean, Median, and Mode are the three most important measures of central tendency. They help summarize data and identify the typical or central value of a dataset. Mean gives the average, median gives the middle value, and mode gives the most frequent value.

In Machine Learning, these concepts are useful for data understanding, missing value treatment, outlier analysis, feature engineering, and exploratory data analysis. A good data analyst or Machine Learning learner should know not only how to calculate them, but also when to use each one correctly.