Difference Between Mean And Median

# Difference Between Mean And Median

Anshuman Singh
Senior Executive - Content
Updated on Oct 3, 2023 12:07 IST

Mean and Median are two most popular terms used in mathematics. However, many people are perplexed whether these words are related in any way. In this article, we will look at the difference between Mean and Median.

Mean and Median are important concepts in mathematics. One cannot consider any aspect of mathematics without considering these two terms, as each has its own significance and plays a distinct role in data collection and other tasks. Hence, it is necessary to understand the difference between Mean and Median and the concepts of Mean and Median.

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So what exactly id the difference between mean and median. Before, we answer that, let’s go through the topics that we will be covering in this article:

## Difference Between Mean and Median

To understand the difference between Mean and Median, in a better way, let’s go through the differences in a tabular format:

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## What is Mean?

Mean definition: The mean is the average of a set of values in mathematics and statistics.

Mean is a statistical concept with significant financial implications. The concept is used in various financial fields, including portfolio management and business valuation.

## How to Calculate Mean?

There are various ways to calculate Mean, but in this article, we will be looking at the most popular ones:

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The arithmetic mean is the sum of all the values in a set divided by the number of numbers in the set. To calculate the arithmetic mean, you can use this formula:

The geometric mean is the nth root of the product of all numbers in a collection. To calculate the geometric mean, you can use this formula:

Let’s go through an example to understand how to calculate the mean.

### Question: Find the mean of set A = {2, 4, 6, 8, 10, 12}

Answer: Here are the steps to find the mean of set A:

1 Step: 2+4+6+8+10+12 =42

2 Step: Count the total number of numbers in set A

3 Step: Divide the sum by the total number of numbers in set A, i.e., 42/6 = 7

Hence, the mean of set A = 7

## What is Median?

Median definition: Median is the middle value of the given list of data when arranged in an order.

This order can be either ascending order or descending order.

## How to Calculate Median?

The median formula differs for odd and even numbers of observations. Let’s go through the formula for an odd number:

For an odd number of observations:

Median = {(n+1)/2}thterm

Here, n is the number of observations.

For an even number of observations:

Median  = [(n/2)th term + {(n/2)+1}th]/2

Here, n is the number of observations.

Let’s go through an example to understand how to calculate median.

### Question: Find the median of set A = {1, 2, 2, 3, 4, 3}

Answer: Here are the steps to find median of set A.

1 Step: Arrange the set in ascending order; the new sequence will be: Set A = {1,2,2,3,3,4}

2 Step: Count the number of observations. Total observation = 6

3 Step: Use this formula, as the number of observations is even:

Median  = [(n/2)th term + {(n/2)+1}th]/2

4 Step: Placing the value of n, in the above formula. Here, n =6.

5 Step: ( (6/2)th observation+(6/2 +1)th observation ) / 2

6 Step: (3rd observation + 4th observation)/ 2

7 Step: Placing the value of 3rd and 4th observations in step 6.

8 Step: (2+3)/2 = 2.5

Hence, the median of set A = 2.5

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## Conclusion

The mean is the average value of a given data set, and the median is the middle value when the data set is arranged in ascending or descending order. Now that you understand the difference between Mean and Median, you can use these concepts more effectively.

## FAQs

What is the difference between mean and median?

The mean is the average value of a set of given data, and the median is the middle value when the data set is arranged in ascending or descending order.

Is the mean or the median better?

It depends on the situation, as the mean is best used when the dispersion of data values is balanced and there are no obvious outliers. When the dispersion of data values is distorted or there are obvious outliers, it is best to use the median.

Which is more reliable, mean or median?

The median is a more reliable and stable number than the mean because the mean's value will change (decrease), but the median's value will not change until a larger change occurs.