100 LearnersLast updated on June 4th, 2025
Median
The concept of median is a statistical term that means the measure of a central tendency that represents the middle value in a sorted list of numbers. When the list of numbers that are provided is odd, then the median is the middle number. If the list of numbers is even, then the median is the average of the two middle values. The median is a more reliable statistical indicator of a central value of the data.
What is median in math?
In mathematics, the concept of median is the measure of the central value of a given dataset. If the dataset contains an odd number of values, the median is the middle number. If the dataset has an even number of values, then the median is calculated by averaging the middle values of the dataset.
History of Median
The concept of median goes back to the 18th century. The concept was first used by Joseph Boscovich in 1760 when he was using it for analyzing data with minimal error. Later on, in the 19th century, the term median was introduced by Francis Galton.
The median has gained major importance in measuring the central tendency, particularly in fields like statistics and economics, as it represents the skewed dataset better than the mean. Over time, it has been used for various fields like social sciences, finance, and machine learning.
Types of Median
There are many types of median. The two most common types of median are given below:
- Simple Median
- Grouped Median
Let us now see what do the above two types of median
Simple Median
Simple median are used for a basic set of numbers which are arranged in an order. For odd datasets, it is the middle value and for even data sets, it is the average of the two middle values.
Grouped Median
We use a grouped median when the dataset is grouped into class intervals or classes which is grouped in a frequency table. We use the following formula to find the grouped median:
L + (N2 - F) x h/f.
Where;
L = Lower boundary of the median class
N = Total Frequency
F = Cumulative Frequency before the median class
f = frequency of the median class
h = class width.
Tips and Tricks to Master Median
Sometimes the students get confused with the concept of median and the best way to cope with that confusion is to follow some tips and tricks, here are some of the tips and tricks mentioned below:
Formulas:
If the student practices the formulas, it will help the student in understanding the concept of median. They should be able to differentiate between the odd and even datasets.
Handling Duplicates:
Sometimes students can get confused with the number of duplicate values and forget to take the value that has been repeated. The median is calculated the same way and the duplicates are included.
Large data sets:
For large datasets, students can take the help of a software or a calculator to find the median, as it is the most effective way to find a median.
Common Mistakes and How to Avoid them in Median
Students tend to make a lot of mistakes while solving median problems in statistics. Here are some of the problems that the students might face and the solutions to the said given problems are mentioned below:
Mistake 1
Forgetting to Order the Data
Students must always arrange the data either by ascending or descending order. Students must always double-check whether they have included all the numbers and have not skipped any number.
Real World Applications of Median
We use the concept of median in various fields and applications. Let us now see how median is used as a real world application.
Economics and Income:
We use the median to calculate the income distribution of a typical population. The median gives a more accurate representation of what most people earn. It also helps us understand about the poverty line.
Real Estate:
We use median in real estate to find out the housing prices of different datasets of houses.
Healthcare:
In healthcare, we use the concept of median to understand the patient data and help us study about the different types of illness and help the doctors navigate through the data.
Education:
We use the concept of median to calculate the average of the scores in a class of students by determining who scores more and who scores less.
Solved Examples of Median
Problem 1
Find the Median of {5, 2, 1, 9, 8}
The median of the following data set is 5
Explanation
First identify the numbers and arrange them:
{1, 2, 5, 8, 9}
As it is an odd set of data, the median would be the middle value, which is 5
Problem 2
Find the median of {4, 7, 2, 6, 9, 1}
The median is 5
Explanation
Step 1: Order the numbers in ascending order {1, 2, 4, 6, 7, 9}
The middle values of the set are 4 and 6
Hence, the median is (4+6)/2 = 5.
Problem 3
Find the median of {10, 5, 15, 20, 12}
The median of the data set is 12
Explanation
First order the following data set {5, 10, 12, 15, 20}
The middle value of the data set is 12
Hence, the median is 12
Problem 4
Find the median of {1, 1, 2, 2, 3, 3, 3, 4}
The median of the data set is 2.5
Explanation
First order the following data set {1, 1, 2, 2, 3, 3, 3, 4}
Middle values: 2 and 3
Hence, the median is (2 + 3)/2 = 2.5
Problem 5
Find the median of {-5, -2, 0, 3, 7}
The median of the data set is 0
Explanation
First order the following data set {-5, -2, 0, 3, 7}
The middle value of the data set is 0.
Hence, the median is 0
FAQs on Median
1.What is Median?
2.How do you find the median?
3.How to find the median of a large data set?
4.What if the data is negative?
5.Where do we use the median?
6.How can children in United States use numbers in everyday life to understand Median?
7.What are some fun ways kids in United States can practice Median with numbers?
8.What role do numbers and Median play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Median skills?
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Jaipreet Kour Wazir
About the Author
Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref
Fun Fact
: She compares datasets to puzzle games—the more you play with them, the clearer the picture becomes!
