Median Calculator

Median Calculator allows you to find the median of a set of numbers. Also, it gives you the mean, mode, range, and many more.

Median:
Mean:
Mode:
Range:
Smallest:
Largest:
Count:
Sum:
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About Median Calculator

Median Calculator is a free online utility tool where you can find the median value from the even or odd data sets. In addition, it gives the mean, mode, range, sum, and count as a result. Therefore, it's one of the best tools for statistical analysis.

Median Calculator | Mean, Median, Mode, and Range Calculator

Now no need to remember the formula. Just input the values of the set and tap the "Calculate" button. That's it! Get correct and fast median results with minimal effort.

Also, it can accept any size of number set and that is best for statistical calculations. Moreover, it is programmed with the fastest algorithm to compute the median.

The outstanding feature about the median calculator is, you don't have to pre-specify any additional information. You just need to input the data set in the correct format. That's all. Also, no need to write your data set in ascending or descending order. Our calculator automatically sorts the values and gives you the proper results in less than a second.

It is useful for everyone whether you are a teacher, student, accountant, businessman, investor, or researcher. Even more, this article will give you the complete overview of our tool including the mathematics involved along with it. So, stay tuned till the end.

What is Median?

Till now we only talked about the calculator, now let's focus on the median and know more about it.

Median is a statistical concept that measures central tendency. In other words, it is a value that represents the center of the sorted observation.

Most importantly, the median is widely used in statistical data analysis. Most people consider average, mean, median, and mode as the same thing. But in actual they are used for different purposes. However, they also have something common in them.

Applications of Median

Median is used to determine the middlemost data in a data set. It gives the point from where 50% of data is more and 50% of data is less.

For example, if you want to know the performance of a cricketer then find the median of his match scores.

Another example can be when you want to find the average salary of an organization. It can be determined by taking the median of the salaries of all employees. This median of salaries can also be called the 50% income.

Median Formula

There are two possibilities for median calculation. So, we have explained two different formulas that can help you to solve the median.

1. If the data set is Odd:

Median Formula for Odd Data Set

Where,
Xm = Median
n = size of the data set

Quick Tip: For the odd data set, the median value will be exactly in the middle of the set.

2. If the data set is Even:

Median Formula for Even Data Set

Where,
Xm = Median
n = number of values

Quick Tip: If the data set is even then the median value will be the mean or average of the two numbers that are in the middle of the data set.

How to Calculate Median?

However, the best way to calculate the median is by using the median calculator. Using that, you can get results by eliminating the effort spent in the manual calculation.

But here we will take some examples and understand how the median is calculated manually using the formula.

Example 1

Find the median for the data set: {4, 6, 2, 7, 1}

Solution:

Firstly, we will arrange (sort) the numbers in ascending order that is from lowest to highest.
So, our set will become: {1, 2, 4, 6, 7}

The middle number in the data set is 4.

We selected middle because the size of the set is an odd number. Hence, for this data set, the median value is 4.

Mathematical Calculation:

As we can see, the total number of values in the data set is 5. That is odd. So, we will apply the formula for the odd data set to calculate the median.

Median = X(n+1/2)
= X(5+1/2) = X(6/2) = X3

When we check the 3rd value in the data set, it's 4.

So, the Median = 4.

Now, let's take an example of even data set. So, it will help you to clear both formulas and how you can differentiate them.

Example 2

Data Set = {3, 6, 1, 7, 8, 12, 4, 14}. Find the median.

Solution:

Firstly, we will sort all the numbers into ascending order.
So, we get: {1, 3, 4, 6, 7, 8, 12, 14}

Since the size of the set is even. Therefore, we have to find the mean or average of the two middle numbers.

Middle numbers are: {6, 7}
Mean of middle numbers = (6 + 7) / 2 = 6.5
So, Median = 6.5

Mathematical Calculation:

Here we will apply the even data set formula.

Median = ( X(n/2) + X(n/2 + 1) ) / 2
= ( X(8/2) + X(8/2 + 1) ) / 2
= ( X(4) + X(5) ) / 2

Now, let's find the 4th and 5th values from the data set.
That is: {6, 7}

= (6 + 7) / 2 = 13/2 = 6.5

So, the Median = 6.5.

Features of Median Calculator

  • The median calculator is very simple to use. You just have to input the values with comma or space separated and get the instant results. Also, it makes all the manual hassles like sorting and calculating are eliminated.
  • It's absolutely free of cost. No hidden charges or any kind of subscription fees.
  • No signup, registration, installation, or login is required. Just open the tool and use it as many times as you can.
  • It gives additional result fields like Mean, Mode, Range, Smallest, Largest, Count, and Sum.
  • Very fast and 100% accurate tool.

How to use the Median Calculator?

  1. Firstly, enter or paste the data set in the input box.
  2. Most importantly, the data set must be space or comma separated. For example: 1 5 7 8 10 4   or  1, 5, 7, 8, 10, 4. If you don't write in proper format then you will not get the results. So, make sure the data set is in a proper format.
  3. After entering the values, just click the "Calculate" button.
  4. As a result, you will get the median value just below. Also, our tool will give you some additional results. Such as mean, mode, range, smallest, largest, etc.
  5. For new calculations, use the "Reset" button.

FAQs

There is no limit on the data set size. So, you can calculate the median of any size of the input set.

Formula for Odd data set:
Median = X(n+1/2)

Formula for Even data set:
Median = (X(n/2) + X(n/2 + 1)) / 2

Yes, our tool supports negative, decimal, and fractional values. For example: 1/2, 0.75, -25.

Yes, our tool first sorts the data set in ascending or descending order and then calculates the median. It's an automatic process. So, you don't need to write the values in ascending or descending order.

Our tool is perfectly working on almost all the small to large devices. Such as mobile, iPad, laptop, and desktop.