Median Formula

Median Formula (Table of Contents)

• Median Formula
• Median Formula Calculator
• Median Formula in Excel (With Excel Template)

Median Formula

A median is the middle value of a data set. In the given n number of grouped or ungrouped data set in statistics, the median is the number found right in the middle of the data set. It is used in many real-life situations.

Median is calculated using the following formula.

If you take the simple example, 1, 2, 3, 4, 5. The middle value is 3. We can find it manually since this is a small set of data. If you apply the same set of data in the above formula, n = 5, hence median = (5+1) / 2 = 3. So the third number is the median. For a large number of data, finding median manually is not possible. So it is essential to use the formula for a large number of data set.

Examples of Median Formula

Let’s take an example to understand the calculation of Median Formula in a better manner.

Example #1.1 – Finding the median for an odd amount of numbers

Consider the small data set A= 42, 21, 34, 65, 90, 45, 109. From the available data Calculate the Median.

Solution:

Arrange the data set in ascending order.

Median is calculated using the formula given below

Median = (n + 1) / 2

• Median = (7 + 1) / 2
• Median = 8 / 2
• Median = 4

Here 4th value is 45. So 45 is the median for this data set.

Example #1.2

Consider the large data set B = 1, 2, 3 …, 51.

Here the total numbers are 51. So n= 51.

Median is calculated using the formula given below

Median = (n + 1) / 2

• Median = (51 + 1) / 2
• Median = 52 / 2
• Median = 26

So the 26^th number is the median value. So 25 numbers should be below the median, 26^th number is the median and again 25 numbers are above.

Example #2.1 – Finding the median for an Even amount of numbers

Consider the small data set C= 2, 5, 89, 40, 66, 33, 14, 23, 90, 101. From the available data Calculate the Median.

Solution:

Arrange the data set in ascending order.

Median is calculated using the formula given below

Median = (n + 1) / 2

• Median = (10 + 1) / 2
• Median = 11 / 2
• Median = 5.5

5.5 is in-between 5 and 6. So we need to take the 5^th value and 6^th value from the data set.

From the above data set, the 5^th and 6^th values are 33, 40 respectively. Add both numbers and divide by 2 to get the median. (33+40)/ 2 = 73/2 = 36.5. So here the median value of this data set is 36.5.

Example #2.2:

Consider the large set of data D = 101, 102 … 198.

The total numbers in this data set are 98.

Here the total numbers are 98. So n= 98.

Now divide the total numbers by 2. Add then subtract 1 from the result value. Here 98/2= 49. Since this is even numbers, there should be two middle values. The median value we got is 49. So it should have 48 numbers above the median and 48 numbers below the median.so 49th and 50th values are median values.

Explanation

Step 1: First arrange the given data set in the ascending order. Say the data set you have is, 4, 2, 8, and 1. So arranging this in ascending order gives you 1, 2, 4, 8.

Step 2: Here n is the number of items in the given data set. That is if you consider the above example data set, 1, 2, 4, and 8, the variable n’s value is 4.

Step 3: Just apply the variable value n in the formula to get the median. i.e. Median = (n + 1) / 2

It may seem very easy to see this formula since it is a very small set of data. But for a large set of data, it needs more effort to get the value correctly since the steps vary a little for EVEN amount of numbers and an ODD amount of numbers. So one should be very careful while finding the median.

Steps for sorting the data set in ascending order in Excel

One can sort the data set in excel sheet by the following method.

• Select the range of cells, you want to sort. Say you have 1000 values totally and it is being put from cell A1 to A1000.
• Go to Data tab -> Sort & Filter group-> click on Sort. This will give you sorted data set from smallest number to highest or Simple you can right click over the selected data-range and select sort -> Click on sort from “smallest to largest number”.

Steps for counting the data set in Excel sheet to find n value for a large set of data

• Select the range of cells (which was sorted in ascending order), you want to count. As per the above example, it is from A1 to A1000.
• Go to Formulas tab -> click on More functions-> Point on statistical and select COUNTA function to count the cells that are not empty. You will get the value for variable n. In this case, you will get n=1000.

Relevance and Uses of Median Formula

The Median value is a statistical measure used in many real-life scenarios like real estate median price, bankruptcy value, etc. This is very useful when the data set include very high and low values of grouped and ungrouped data sets. Median is simply the point where 50% of the numbers above & 50% of the numbers below. It is an instinctive centrality that denotes the middle value. This value is very useful in case of a historical data set or data set that comes over time.

Median Formula Calculator

You can use the following Median Calculator

Median Formula in Excel (With Excel Template)

Here we will do another example of the Median formula in Excel. It is very easy and simple.

Let’s take an example to calculate the median.

Arrange the data set in ascending order.

Median is calculated using the formula given below

Median = (n + 1) / 2

For Set AB

• Median = (22 + 1) / 2
• Median = 23 / 2
• Median = 11.5

For Set BC

• Median = (21 + 1) / 2
• Median = 22 / 2
• Median = 11

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