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Calculation of Mean, Median, and Mode

Learn the calculation of mean, median, and mode, the core statistical tools to analyze data effectively. Understand their formulas, examples, and applications in real-world scenarios.
authorImageMuskan Verma9 Oct, 2025
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Calculation of Mean, Median, and Mode

In statistics, mean, median and mode are fundamental tools used to analyze data and understand its distribution. Known collectively as the measures of central tendency , these three statistical methods summarize a dataset, offering insights into its central values. Each measure has unique attributes and applications, and understanding how to calculate and interpret them is essential for solving statistical problems.

In this blog, we’ll learn the definitions, formulas, and step-by-step calculations of mean , median , and mode , along with examples and their relevance in real-world scenarios.

What Are Mean, Median, and Mode?

Mean : The arithmetic average of a dataset, calculated by dividing the total sum of all values by the number of values. It is widely used but can be affected by extreme values (outliers). Median : The middle value in an ordered dataset. For an odd number of observations, it is the central value; for an even number, it is the average of the two middle values. The median is particularly useful for skewed datasets. Mode : The value that appears most frequently in a dataset. Mode is ideal for categorical data or when identifying the most common value. These measures help summarize data meaningfully, making it easier to interpret and draw conclusions.

Mean Calculation

The mean is the simplest and most commonly used measure of central tendency. It is calculated using the formula: Where:
  • Σx: Sum of all data values
  • N: Total number of observations

Example :

Dataset: 12,15,18,20,25 For weighted mean , weights ( w ) are assigned to each value ( x ) to reflect their importance:

Median Calculation

The median represents the middle value of a dataset arranged in ascending or descending order.
  • For odd numbers of observations, it is the middle value.
  • For even numbers, it is the average of the two middle values.

Formula :

To find the median position: For grouped or continuous data, the formula becomes: Where:
  • l : Lower boundary of the median class
  • c : Cumulative frequency before the median class
  • f : Frequency of the median class
  • h : Class width

Example :

Dataset: 10,12,14,16,18 The median is the 3rd value: 14 . For a dataset with even observations, such as 10,12,14,16,18,20 : The middle two values are 14 and 16

Mode Calculation

The mode is the value that appears most frequently in a dataset. It is particularly useful in datasets with repeated values. For grouped or continuous data, the mode is calculated using the formula: Where:
  • l : Lower boundary of the modal class
  • fm : Frequency of the modal class
  • f1 : Frequency of the class before the modal class
  • f2 : Frequency of the class after the modal class
  • h : Class width

Example :

Class intervals: 0−10,10−20,20−30,30−40 , frequencies: 5,12,18,7 . Modal class: 20−30 (highest frequency: fm=18 ). f1=12 , f2=7 , l=20 , h=10

Choosing Between Mean, Median, and Mode

Each measure has unique applications depending on the data's characteristics:
  • Mean : Best for symmetric distributions without outliers.
  • Median : Suitable for skewed distributions or when outliers are present.
  • Mode : Ideal for categorical data or when the most frequent value is required.

Applications in Real Life

  1. Education : Mean is used to calculate average test scores, while median helps identify the middle-performing student in a class.
  2. Healthcare : Median income or age is often used for demographic analysis.
  3. Business : Mode identifies the most popular product or service in a market survey.
  4. Finance : Mean calculates average returns, while median can highlight central tendencies in income distributions.
The calculation of mean, median, and mode is fundamental to understanding and interpreting data. While these measures summarize data efficiently, selecting the right measure is crucial depending on the dataset and the purpose of analysis. A solid grasp of these concepts equips students and professionals to analyze data effectively and make informed decisions. With consistent practice and understanding, anyone can master these statistical tools and apply them confidently across various domains.
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Calculation of Mean, Median, and Mode FAQs

What is the main difference between mean, median, and mode?

Mean is the arithmetic average of all values in a dataset. Median is the middle value when the data is arranged in ascending or descending order. Mode is the value that occurs most frequently in the dataset.

When should I use the median instead of the mean?

The median is preferred over the mean when the dataset has extreme values (outliers) that can skew the average. For example, in income data where a few very high incomes distort the average, the median gives a better representation of the central value.

What is the significance of mode in real-life applications?

Mode is especially useful in identifying the most common item in a dataset. For instance: In marketing, it helps identify the most popular product. In education, it determines the most frequently scored marks in an exam.

How are mean, median, and mode affected by skewed data?

Mean is highly sensitive to extreme values and can be skewed in either direction. Median remains unaffected by outliers and better represents the central value in a skewed dataset. Mode is not influenced by outliers and only reflects the most frequent value, making it less indicative of central tendency in skewed data.
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