Difference Between Mean And Median

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:

Table of Contents (TOC)

• Difference Between Mean and Median
• What is Mean?
• How to calculate Mean?
• What is Median?
• How to calculate Median?

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:

Parameter	Mean	Median
What it is	Average taken for a set of numbers	The middle value in the data set
Application	Normal distributions	Skewed distributions
Sensitive to outliers data	Yes	No
Robust and reliable	Less in comparison to the Median	Yes
Can be found by	Adding all the values and dividing the total by the number of values	Listing all of the numbers in the set in ascending order and then locating the number in the center of the distribution
Considered as	Arithmetic average	Positional average
What it defines	The central value of the data set	The center of gravity of the midpoint of the data set
Every data of the set is taken into account	Yes	No

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: (3^rd observation + 4^th observation)/ 2 

7 Step: Placing the value of 3^rd and 4^th 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.

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