The median is one of the three main measures of central tendency, which is commonly used in statistics for finding the center of a data sample or population, e.g. for calculating a typical salary, household income, home price, real-estate tax, etc. In this tutorial, you will learn the general concept of the median, in what way it is different from arithmetic mean, and how to get median in Excel.
In simple terms, the median is the middle value in a group of numbers, separating the higher half of values from the lower half. More technically, it is the center element of the data set arranged in order of magnitude.
In a data set with an odd number of values, the median is the middle element. If there are an even number of values, the median is the average of the middle two.
For example, in the group of values {1, 2, 3, 4, 7} the median is 3. In the dataset {1, 2, 2, 3, 4, 7} the median is 2.5.
Compared to the arithmetic mean, the median is less susceptible to outliers (extremely high or low values) and therefore it is the preferred measures of central tendency for an asymmetrical distribution. A classic example is a median salary, which gives a better idea of how much people typically earn than an average salary because the latter may be skewed by a small number of abnormally high or low salaries. For more information, please see Mean vs. median: which is better?
Microsoft Excel provides a special function to find a median of numeric values. The syntax of the MEDIAN function is as follows:
MEDIAN(number1, [number2], …)
Where Number1, number2, … are numeric values for which you want to calculate the median. These can be numbers, dates, named ranges, arrays, or references to cells containing numbers. Number1 is required, subsequent numbers are optional.
In the recent versions of Excel 2016, 2013, 2010 and 2007, the MEDIAN function accepts up to 255 arguments; in Excel 2003 and earlier you can only supply up to 30 arguments.
4 facts you should know about Excel Median
- When the total number of values is odd, the Excel MEDIAN function returns the middle number in the data set. When the total number of values is even, it returns an average of the two middle numbers.
- Cells with zero values (0) are included in calculations.
- Empty cells as well as cells containing text and logical values are ignored.
- The logical values of TRUE and FALSE typed directly in the MEDIAN function's arguments are counted. For example, the formula MEDIAN(FALSE, TRUE,2,3,4) returns 2, which is the median of the numbers {0, 1, 2, 3, 4}.
MEDIAN is one of the most straightforward and easy-to-use functions in Excel. However, there are still some tricks, not obvious to beginners. Say, how do you calculate a median based on a condition? The answer is in one of the following examples.
Excel Median formula
For starters, let's see how to use the classic Median formula in Excel to find the middle value in a set of numbers. In a sample sales report (please see the screenshot below), supposing you want to find the median of numbers in cells C2:C8. The formula would be as simple as this:
=MEDIAN(C2:C8)
As shown in the screenshot above, the Excel Median formula works for numbers and dates equally well since in terms of Excel dates are also numbers.
Excel Median If formula - median based on one criterion
Regrettably, Microsoft Excel does not provide any special function to calculate a median based on a condition like it does for the arithmetic mean (AVERAGEIF and AVERAGEIFS functions). Luckily, you can easily build your own Median If formula in this way:
MEDIAN(IF(criteria_range=criteria, median_range))
In our sample table, to find a median amount for a specific item, input the item name in some cell, say E2, and use the following formula to get the median based on that condition:
=MEDIAN(IF($A$2:$A$10=$E2, $C$2:$C$10))
The formula tells Excel to include in calculation only those numbers in column C (Amount) for which a value in column A (Item) matches the value in cell E2.
Please pay attention that we use the $ symbol to create absolute cell references. It is especially important if you intend to copy your Median If formula to other cells.
Finally, since you want to check every value in the specified range, make it an array formula by pressing Ctrl + Shift + Enter. If done correctly, Excel will encapsulate the formula in curly braces like this:
Excel Median Ifs formula - median based on multiple criteria
Taking the previous example further, let's add one more column (Status) to the table, and then find a median amount for each item, but count only orders with the specified status. In other words, we will be calculating median based on two conditions - item name and order status. To express multiple criteria, use two or more nested IF functions, like this:
MEDIAN(IF(criteria_range1=criteria1, IF(criteria_range2=criteria2, median_range)))
With criteria1 (Item) in cell F2 and criteria2 (Status) in cell G2, our Median Ifs formula takes the following shape:
=MEDIAN(IF($A$2:$A$10=$F2, IF($D$2:$D$10=$G2,$C$2:$C$10)))
Since it's an array formula, remember to hit Ctrl + Shift + Enter to complete it correctly. If all done properly, you will get a result similar to this:
This is how you calculate median in Excel. To have a closer look at the formulas discussed in this short tutorial, you are welcome to download the Sample Median Excel workbook. I thank you for reading and hope to see you on our blog next week!