MEDIAN function

This article describes the formula syntax and usage of the MEDIAN function in Microsoft Excel.

Description

Returns the median of the given numbers. The median is the number in the middle of a set of numbers.

Syntax

MEDIAN(number1, [number2], ...)

The MEDIAN function syntax has the following arguments:

• Number1, number2, ...    Number1 is required, subsequent numbers are optional. 1 to 255 numbers for which you want the median.

Remarks

• If there is an even number of numbers in the set, then MEDIAN calculates the average of the two numbers in the middle. See the second formula in the example.

• Arguments can either be numbers or names, arrays, or references that contain numbers.

• Logical values and text representations of numbers that you type directly into the list of arguments are counted.

• If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.

• Arguments that are error values or text that cannot be translated into numbers cause errors.

Note: The MEDIAN function measures central tendency, which is the location of the center of a group of numbers in a statistical distribution. The three most common measures of central tendency are:

• Average     which is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.

• Median     which is the middle number of a group of numbers; that is, half the numbers have values that are greater than the median, and half the numbers have values that are less than the median. For example, the median of 2, 3, 3, 5, 7, and 10 is 4.

• Mode     which is the most frequently occurring number in a group of numbers. For example, the mode of 2, 3, 3, 5, 7, and 10 is 3.

For a symmetrical distribution of a group of numbers, these three measures of central tendency are all the same. For a skewed distribution of a group of numbers, they can be different.

Example

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

Data
1
2
3
4
5
6
Formula	Description	Result
=MEDIAN(A2:A6)	Median of the 5 numbers in the range A2:A6. Because there are 5 values, the third is the median.	3
=MEDIAN(A2:A7)	Median of the 6 numbers in the range A2:A7. Because there are six numbers, the median is the midway point between the third and fourth numbers.	3.5